diff --git a/.github/CODEOWNERS b/.github/CODEOWNERS new file mode 100644 index 000000000..0aec70ce1 --- /dev/null +++ b/.github/CODEOWNERS @@ -0,0 +1,10 @@ +# This is a comment. +# Each line is a file pattern followed by one or more owners. + +# More details are here: https://help.github.com/articles/about-codeowners/ + +# The '*' pattern is global owners. + +# Order is important. The last matching pattern has the most precedence. + +* @raklaptudirm @yanglbme diff --git a/.github/ISSUE_TEMPLATE/bug_report.yml b/.github/ISSUE_TEMPLATE/bug_report.yml new file mode 100644 index 000000000..047b3e299 --- /dev/null +++ b/.github/ISSUE_TEMPLATE/bug_report.yml @@ -0,0 +1,45 @@ +name: "Bug report" +description: "Create a report to help us improve" +title: "[BUG]" +labels: ["bug"] +body: + - type: textarea + id: description + attributes: + label: "Description" + description: "A clear and concise description of what the bug is." + validations: + required: true + - type: textarea + id: steps + attributes: + label: "Steps to reproduce" + description: "Steps to reproduce the behavior (if applicable)" + placeholder: | + 1. Go to '...' + 2. Click on '....' + 3. Scroll down to '....' + 4. See error + validations: + required: false + - type: textarea + id: exceptedbhv + attributes: + label: "Excepted behavior" + description: "A clear and concise description of what you expected to happen." + validations: + required: true + - type: textarea + id: screenshots + attributes: + label: "Screenshots" + description: "If applicable, add screenshots to help explain your problem." + validations: + required: false + - type: textarea + id: context + attributes: + label: "Additional context" + description: "Add any other context about the problem here." + validations: + required: false diff --git a/.github/ISSUE_TEMPLATE/config.yml b/.github/ISSUE_TEMPLATE/config.yml new file mode 100644 index 000000000..3ba13e0ce --- /dev/null +++ b/.github/ISSUE_TEMPLATE/config.yml @@ -0,0 +1 @@ +blank_issues_enabled: false diff --git a/.github/ISSUE_TEMPLATE/new_implementation.yml b/.github/ISSUE_TEMPLATE/new_implementation.yml new file mode 100644 index 000000000..e8da888e8 --- /dev/null +++ b/.github/ISSUE_TEMPLATE/new_implementation.yml @@ -0,0 +1,35 @@ +name: "New or optimize implementation" +description: "Propose an enhancement or a new algorithm implementation." +title: "[ENHANCEMENT]" +labels: ["enhancement"] +body: + - type: textarea + id: description + attributes: + label: What would you like to share? + description: Provide a clear and concise explanation of your issue. + validations: + required: true + - type: markdown + attributes: + value: | + For new implementations, please specify the name and problem statement for the algorithm. + For algorithm enhancements, specify what needs to be changed and why. For example: + + - Adding tests. + - Optimizing logic. + - Refactoring the file and folders for better structure. + - type: textarea + id: issuedetails + attributes: + label: "Extra issue details" + description: "Write down all the issue/algorithm details mentioned above." + validations: + required: true + - type: textarea + id: extrainfo + attributes: + label: Additional information + description: Is there anything else we should know about this issue? + validations: + required: false diff --git a/.github/ISSUE_TEMPLATE/other.yml b/.github/ISSUE_TEMPLATE/other.yml new file mode 100644 index 000000000..14824ba9f --- /dev/null +++ b/.github/ISSUE_TEMPLATE/other.yml @@ -0,0 +1,22 @@ +name: Other +description: Use this for any other issues. Do NOT create blank issues +title: "[OTHER]" +labels: ["awaiting triage"] +body: + - type: markdown + attributes: + value: "# Other issue" + - type: textarea + id: issuedescription + attributes: + label: What would you like to share? + description: Provide a clear and concise explanation of your issue. + validations: + required: true + - type: textarea + id: extrainfo + attributes: + label: Additional information + description: Is there anything else we should know about this issue? + validations: + required: false diff --git a/.github/PULL_REQUEST_TEMPLATE/pull_request.md b/.github/PULL_REQUEST_TEMPLATE/pull_request.md new file mode 100644 index 000000000..69a8f4f8d --- /dev/null +++ b/.github/PULL_REQUEST_TEMPLATE/pull_request.md @@ -0,0 +1,21 @@ +#### Description of Change + + +#### Checklist + + +- [ ] Added description of change +- [ ] Added file name matches [File name guidelines](https://github.com/TheAlgorithms/Go/blob/master/CONTRIBUTING.md#New-File-Name-guidelines) +- [ ] Added tests and example, test must pass +- [ ] Added documentation so that the program is self-explanatory and educational - [GoDoc guidelines](https://blog.golang.org/godoc) +- [ ] Relevant documentation/comments is changed or added +- [ ] PR title follows semantic [commit guidelines](https://github.com/TheAlgorithms/Go/blob/master/CONTRIBUTING.md#Commit-Guidelines) +- [ ] Search previous suggestions before making a new one, as yours may be a duplicate. +- [ ] I acknowledge that all my contributions will be made under the project's license. + +Notes: \ No newline at end of file diff --git a/.github/dependabot.yml b/.github/dependabot.yml new file mode 100644 index 000000000..be006de9a --- /dev/null +++ b/.github/dependabot.yml @@ -0,0 +1,13 @@ +# Keep GitHub Actions up to date with GitHub's Dependabot... +# https://docs.github.com/en/code-security/dependabot/working-with-dependabot/keeping-your-actions-up-to-date-with-dependabot +# https://docs.github.com/en/code-security/dependabot/dependabot-version-updates/configuration-options-for-the-dependabot.yml-file#package-ecosystem +version: 2 +updates: + - package-ecosystem: github-actions + directory: / + groups: + github-actions: + patterns: + - "*" # Group all Actions updates into a single larger pull request + schedule: + interval: weekly diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml new file mode 100644 index 000000000..7a5ce1939 --- /dev/null +++ b/.github/workflows/ci.yml @@ -0,0 +1,38 @@ +# https://github.com/golangci/golangci-lint +name: Continuous Integration +on: + push: + # prevent duplication of tests with + # `pull_request` event + branches: + - master + pull_request: + +jobs: + golang_lint_and_test: + name: Code style and tests + runs-on: ubuntu-latest + strategy: + fail-fast: false + steps: + - uses: actions/checkout@v4 + - name: Setup Go + uses: actions/setup-go@v5 + with: + go-version: '^1.18' + - name: Run Golang CI Lint + uses: golangci/golangci-lint-action@v6 + with: + version: latest + args: -E gofmt + - name: Run tests + run: go test ./... + codespell: + name: Check for spelling errors + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v4 + - uses: codespell-project/actions-codespell@master + with: + ignore_words_list: "actualy,nwe" + skip: "go.mod,go.sum" diff --git a/.github/workflows/citk.yml b/.github/workflows/citk.yml new file mode 100644 index 000000000..4b675f239 --- /dev/null +++ b/.github/workflows/citk.yml @@ -0,0 +1,28 @@ +# https://github.com/golangci/golangci-lint +name: CI tool kit +on: + pull_request: + +jobs: + CITK: + name: Code style and tests + runs-on: ubuntu-latest + strategy: + fail-fast: false + steps: + - uses: actions/checkout@v4 + with: + fetch-depth: 0 + - name: Setup Go + uses: actions/setup-go@v5 + with: + go-version: "^1.18" + - name: Checkout branch + run: | + git fetch origin master:master + - name: Install citk tool + run: | + go install github.com/tjgurwara99/citk@latest + - name: Run citk tool + run: | + citk check -l go -b master diff --git a/.github/workflows/godocmd.yml b/.github/workflows/godocmd.yml new file mode 100644 index 000000000..7e7b306e3 --- /dev/null +++ b/.github/workflows/godocmd.yml @@ -0,0 +1,35 @@ +name: Generate Documentation +on: + push: + branches: + - master + +jobs: + generate_readme: + name: Markdown Generation + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v4 + with: + fetch-depth: 0 + - uses: actions/setup-go@v5 + with: + go-version: '^1.18' + - name: Install GoDocMD + run: | + go install github.com/tjgurwara99/godocmd@v0.1.3 + - name: Configure Github Action + run: | + git config --global user.name "$GITHUB_ACTOR" + git config --global user.email "$GITHUB_ACTOR@users.noreply.github.com" + - name: Update README.md file + run: | + godocmd -r -module ./ -w + - name: Commit changes if README.md is different + run: | + if [[ `git status --porcelain` ]]; then + git commit -am "Updated Documentation in README.md" + git push + else + echo "NO CHANGES DETECTED" + fi diff --git a/.github/workflows/golangci-lint.yml b/.github/workflows/golangci-lint.yml deleted file mode 100644 index 851c8d40e..000000000 --- a/.github/workflows/golangci-lint.yml +++ /dev/null @@ -1,21 +0,0 @@ -# https://github.com/golangci/golangci-lint -name: golangci-lint -on: [push, pull_request] -jobs: - golangci-lint: - runs-on: ubuntu-latest - steps: - - uses: actions/setup-go@v1 - with: - go-version: 1.13 - - uses: actions/checkout@v1 - - run: curl -sfL https://raw.githubusercontent.com/golangci/golangci-lint/master/install.sh | sh -s v1.21.0 - - run: | - go version ; ./bin/golangci-lint --version - ./bin/golangci-lint run --no-config || true - - run: ./bin/golangci-lint run --no-config ciphers strings - - run: ./bin/golangci-lint run --no-config data-structures || true - - run: ./bin/golangci-lint run --no-config dynamic-programming || true - - run: ./bin/golangci-lint run --no-config other || true - - run: ./bin/golangci-lint run --no-config searches || true - - run: ./bin/golangci-lint run --no-config sorts diff --git a/.github/workflows/stale.yml b/.github/workflows/stale.yml new file mode 100644 index 000000000..8118ebf78 --- /dev/null +++ b/.github/workflows/stale.yml @@ -0,0 +1,18 @@ +name: 'Close stale issues and PRs' +on: + schedule: + - cron: '0 0 * * *' +jobs: + stale: + runs-on: ubuntu-latest + steps: + - uses: actions/stale@v9 + with: + stale-issue-message: 'This issue is stale because it has been open 30 days with no activity. Remove stale label or comment or this will be closed in 5 days.' + close-issue-message: 'This issue was closed because it has been stalled for 7 days with no activity.' + stale-pr-message: 'This PR is stale because it has been open 30 days with no activity. Remove stale label or comment or this will be closed in 5 days.' + close-pr-message: 'This PR was closed because it has been stalled for 7 days with no activity.' + exempt-issue-labels: 'dont-close' + exempt-pr-labels: 'dont-close' + days-before-stale: 30 + days-before-close: 7 diff --git a/.github/workflows/update_directory_md.yml b/.github/workflows/update_directory_md.yml deleted file mode 100644 index 019b478b3..000000000 --- a/.github/workflows/update_directory_md.yml +++ /dev/null @@ -1,67 +0,0 @@ -# This GitHub Action updates the DIRECTORY.md file (if needed) when doing a git push -name: update_directory_md -on: [push] -jobs: - update_directory_md: - runs-on: ubuntu-latest - steps: - - uses: actions/checkout@master - - uses: actions/setup-python@master - - name: update_directory_md - shell: python - run: | - import os - from typing import Iterator - - URL_BASE = "https://github.com/TheAlgorithms/Go/blob/master" - g_output = [] - - - def good_filepaths(top_dir: str = ".") -> Iterator[str]: - for dirpath, dirnames, filenames in os.walk(top_dir): - dirnames[:] = [d for d in dirnames if d[0] not in "._"] - for filename in filenames: - if os.path.splitext(filename)[1].lower() == ".go": - yield os.path.join(dirpath, filename).lstrip("./") - - - def md_prefix(i): - return f"{i * ' '}*" if i else "\n##" - - - def print_path(old_path: str, new_path: str) -> str: - global g_output - old_parts = old_path.split(os.sep) - for i, new_part in enumerate(new_path.split(os.sep)): - if i + 1 > len(old_parts) or old_parts[i] != new_part: - if new_part: - g_output.append(f"{md_prefix(i)} {new_part.replace('_', ' ').title()}") - return new_path - - - def build_directory_md(top_dir: str = ".") -> str: - global g_output - old_path = "" - for filepath in sorted(good_filepaths(), key=str.lower): - filepath, filename = os.path.split(filepath) - if filepath != old_path: - old_path = print_path(old_path, filepath) - indent = (filepath.count(os.sep) + 1) if filepath else 0 - url = "/".join((URL_BASE, filepath, filename)).replace(" ", "%20") - filename = os.path.splitext(filename.replace("_", " ").title())[0] - g_output.append(f"{md_prefix(indent)} [{filename}]({url})") - return "\n".join(g_output) - - - with open("DIRECTORY.md", "w") as out_file: - out_file.write(build_directory_md(".") + "\n") - - - name: Update DIRECTORY.md - run: | - cat DIRECTORY.md - git config --global user.name github-actions - git config --global user.email '${GITHUB_ACTOR}@users.noreply.github.com' - git remote set-url origin https://x-access-token:${{ secrets.GITHUB_TOKEN }}@github.com/$GITHUB_REPOSITORY - git add DIRECTORY.md - git commit -am "updating DIRECTORY.md" || true - git push --force origin HEAD:$GITHUB_REF || true diff --git a/.github/workflows/upload_coverage_report.yml b/.github/workflows/upload_coverage_report.yml new file mode 100644 index 000000000..50ce54650 --- /dev/null +++ b/.github/workflows/upload_coverage_report.yml @@ -0,0 +1,39 @@ +--- +name: upload_coverage_report + +on: + workflow_dispatch: + push: + branches: + - master + pull_request: + +env: + REPORT_NAME: "coverage.out" + +jobs: + upload_coverage_report: + runs-on: ubuntu-latest + steps: + - uses: actions/checkout@v4 + - name: Setup Go + uses: actions/setup-go@v5 + with: + go-version: '^1.18' + - name: Generate code coverage + run: | + go test -coverprofile="${{ env.REPORT_NAME }}" ./... + - name: Upload coverage to codecov (tokenless) + if: github.event_name == 'pull_request' && github.event.pull_request.head.repo.full_name != github.repository + uses: codecov/codecov-action@v5 + with: + files: "${{ env.REPORT_NAME }}" + fail_ci_if_error: true + - name: Upload coverage to codecov (with token) + if: "! github.event.pull_request.head.repo.fork " + uses: codecov/codecov-action@v5 + with: + token: ${{ secrets.CODECOV_TOKEN }} + files: "${{ env.REPORT_NAME }}" + fail_ci_if_error: true +... diff --git a/.gitignore b/.gitignore new file mode 100644 index 000000000..1af018398 --- /dev/null +++ b/.gitignore @@ -0,0 +1,3 @@ +.idea/ +.vscode/ +coverage.out diff --git a/.gitpod.dockerfile b/.gitpod.dockerfile new file mode 100644 index 000000000..84fa1774b --- /dev/null +++ b/.gitpod.dockerfile @@ -0,0 +1 @@ +FROM gitpod/workspace-go diff --git a/.gitpod.yml b/.gitpod.yml new file mode 100644 index 000000000..f9199716f --- /dev/null +++ b/.gitpod.yml @@ -0,0 +1,7 @@ +--- +image: + file: .gitpod.dockerfile + +tasks: + - init: | + echo "Welcome to TheAlgorithms/Go" diff --git a/.golangci.yml b/.golangci.yml new file mode 100644 index 000000000..586ace461 --- /dev/null +++ b/.golangci.yml @@ -0,0 +1,2 @@ +run: + go: 1.19 diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md new file mode 100644 index 000000000..bc45ed171 --- /dev/null +++ b/CONTRIBUTING.md @@ -0,0 +1,223 @@ +# CONTRIBUTION GUIDELINES + +## Before contributing + +Welcome to [TheAlgorithms/Go](https://github.com/TheAlgorithms/Go)! Before submitting pull requests, please make sure that you have **read the whole guidelines**. If you have any doubts about this contribution guide, please open [an issue](https://github.com/TheAlgorithms/Go/issues/new/choose) or ask in our [Discord server](https://the-algorithms.com/discord/) / [Gitter](https://gitter.im/TheAlgorithms), and clearly state your concerns. + +## Contributing + +### Maintainers +--- + +Please check the [`CODEOWNERS`](https://github.com/TheAlgorithms/Go/blob/master/.github/CODEOWNERS) file for a list of repository maintainers. + +### Contributor +--- + +Being a contributor at The Algorithms, we request you to follow the points mentioned below: + +- You did your own work. + - No plagiarism is allowed. Any plagiarized work will not be merged. +- Your work will be distributed under the [MIT License](https://github.com/TheAlgorithms/Go/blob/master/LICENSE) once your pull request has been merged. +- Please follow the repository guidelines and standards mentioned below. + +#### New implementation + +- New implementations are welcome! + +- You can add new algorithms or data structures that are **not present in the repository** or that can **improve** the old implementations (**documentation**, **improving test cases**, **removing bugs**, or in any other reasonable sense) + +#### Issues + +- Please avoid opening issues asking to be "assigned” to a particular algorithm. This merely creates unnecessary noise for maintainers. Instead, please submit your implementation in a pull request, and it will be evaluated by project maintainers. + +### Making Changes +--- + +#### Code + +- Please use the directory structure of the repository. +- Make sure the file extensions should be `*.go`. +- Use meaningful variable names. +- Use standard library inside your code and avoid to import packages from other repositories +- If an implementation of the algorithm already exists, please refer to the [filename section below](#new-file-name-guidelines). +- You can suggest reasonable changes to existing algorithms. +- Strictly use snake_case (underscore_separated) in filenames. +- If you have added or modified code, please make sure the code compiles before submitting. +- Our automated testing runs [LGTM](https://lgtm.com/projects/g/TheAlgorithms/Go/) on all the pull requests, so please be sure that your code passes before submitting. +- Please conform to [GoDoc](https://blog.golang.org/godoc) standard and document the code as much as possible. This not only facilitates the readers but also generates the correct info on the website. +- **Be consistent in the use of these guidelines.** + +#### Documentation + +- Make sure you put useful comments in your code. Do not comment on obvious things. +- Please avoid creating new directories if at all possible. Try to fit your work into the existing directory structure. If you want to create a new directory, then please check if a similar category has been recently suggested or created by other pull requests. +- If you have modified/added documentation, please ensure that your language is concise and must not contain grammatical errors. +- Do not update [`README.md`](https://github.com/TheAlgorithms/Go/blob/master/README.md) along with other changes. First, create an issue and then link to that issue in your pull request to suggest specific changes required to [`README.md`](https://github.com/TheAlgorithms/Go/blob/master/README.md). +- The repository follows [GoDoc](https://blog.golang.org/godoc) standards and auto-generates the [repository website](https://thealgorithms.github.io/). Please ensure the code is documented in this structure. A sample implementation is given below. + +#### Test + +- Make sure to add examples and test cases in your `filename_test.go` file. +- If you find an algorithm or document without tests, please feel free to create a pull request or issue describing suggested changes. +- Please try to add one or more `Test` functions that will invoke the algorithm implementation on random test data with the expected output. + +### Benchmark +--- + +- Make sure to add examples and benchmark cases in your `filename_test.go` or `filename_bench.go` if you want separated test and benchmark files. +- If you find an algorithm or document without benchmarks, please feel free to create a pull request or issue describing suggested changes. +- Please try to add one or more `Benchmark` functions that will invoke the algorithm implementation. +- For running the benchmark, you could use this command `go test -bench=.` for more details, read this article [Using Subtests and Sub-benchmarks](https://go.dev/blog/subtests) + +#### Typical structure of a program + +```go + +// filename +// description: Add one line description here +// details: +// This is a multi-line +// description containing links, references, +// math equations, etc. +// author(s) [Name](https://github.com/handle), [Name](https://github.com/handle) +// see relatedfile.go, anotherfile.go, file_test.go + +// ** Is just an example of how to write description for package and function and other stuff ... ** + +// Package sort provides primitives for sorting slices and user-defined +// collections. +package sort + +// Reasons why you used those packages +// name package : Add one line description here +// name2 package : Add one line description here +// ... +import ( + ... +) + + +// Fprint formats using the default formats for its operands and writes to w. +// Spaces are added between operands when neither is a string. +// It returns the number of bytes written, and any write error encountered. +func Fprint(w io.Writer, a ...any) (n int, err error) { + ... +} + + +``` + +#### New File Name guidelines + +- Use lowercase words without ``"_"`` for the file name +- Use ``"_"`` as a separator only for `_test.go` or `_bench.go` +- For instance + +```markdown +MyNewGoFile.GO is incorrect +my_new_go_file.go is incorrect +mynewgofile.go is the correct format +mynewgofile_test.go is the correct format +``` + +- It will be used to dynamically create a directory of files and implementation. +- File name validation will run on Docker to ensure validity. +- If an implementation of the algorithm already exists and your version is different from that implemented, please use incremental numeric digit as a suffix. For example: if `binarysearch.go` already exists in the `search` folder, and you are contributing a new implementation, the filename should be `binarysearch2.go` and for a third implementation, `binarysearch3.go`. +- Check out `Go` [Package names](https://go.dev/blog/package-names) roles + +#### New Directory guidelines + +- We recommend adding files to existing directories as much as possible. +- Use lowercase words with ``"_"`` as separator ( no spaces or ```"-"``` allowed ) +- For instance + +```markdown +SomeNew Fancy-Category is incorrect +some_new_fancy_category is correct +``` + +- Filepaths will be used to dynamically create a directory of our algorithms. +- Filepath validation will run on GitHub Actions to ensure compliance. + +#### Commit Guidelines + +- It is recommended to keep your changes grouped logically within individual commits. Maintainers find it easier to understand changes that are logically spilled across multiple commits. Try to modify just one or two files in the same directory. Pull requests that span multiple directories are often rejected. + +```bash +git add filexyz.go +git commit -m "your message" +``` + +Examples of commit messages with semantic prefixes: + +```markdown +fix: XYZ algorithm bug +feat: add XYZ algorithm +test: add test for XYZ algorithm +docs: add comments and explanation to XYZ algorithm +``` + +Common prefixes: + +- fix: A bug fix +- feat: A new feature +- docs: Documentation changes +- test: Correct existing tests or add new ones + +### For New Gophers +--- + +#### Installing Go + +- Installation (only needs to be installed once.) + - Mac (using home-brew): `brew install go` + - Windows (MSYS2 64-bit): `choco install golang` [Chocolatey Package Manager](https://chocolatey.org/) + - Linux (Debian): `sudo apt-get install golang` + - Manual Installation: [Downloads - The Go Programming Language](https://golang.org/dl/) +- Running (all platforms): `go run filexyz.go` + +> Note: New packages should not be `main`, and never implement `main` functions for any package. + +#### Code formatter +To format your code, you can use the gofmt tool directly: + +```bash +gofmt -w filexyz.go +``` + +Or you can use the "go fmt" command: + +```bash +go fmt path/to/your/package +``` + +#### Building + +To build you code locally, simply run: + +```bash +go build . +``` + +### Pull Requests +--- + +- Check out our [pull request template](https://github.com/TheAlgorithms/Go/blob/master/.github/PULL_REQUEST_TEMPLATE/pull_request.md + ) + +#### Building Locally + +Before submitting a pull request, [build the code locally](#building) or using the convenient [![Gitpod Ready-to-Code](https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod)](https://gitpod.io/#https://github.com/TheAlgorithms/Go) service. + +#### GitHub Actions + +- Enable GitHub Actions on your fork of the repository. + After enabling, it will execute `golang_lint_and_test` after every push (not a commit). +- The result can create another commit if the actions made any changes on your behalf. +- Hence, it is better to wait and check the results of GitHub Actions after every push. +- Run `git pull` in your local clone if these actions made many changes to avoid merge conflicts. + +Most importantly, + +- Happy coding! diff --git a/DIRECTORY.md b/DIRECTORY.md deleted file mode 100644 index 9572f98a4..000000000 --- a/DIRECTORY.md +++ /dev/null @@ -1,49 +0,0 @@ - -## Ciphers - * [Caesarcipher](https://github.com/TheAlgorithms/Go/blob/master/ciphers/CaesarCipher.go) - -## Data-Structures - * Binary-Tree - * [Binary-Search-Tree](https://github.com/TheAlgorithms/Go/blob/master/data-structures/binary-tree/binary-search-tree.go) - * [Binary-Tree](https://github.com/TheAlgorithms/Go/blob/master/data-structures/binary-tree/binary-tree.go) - * Dynamic-Array - * [Dynamic Array](https://github.com/TheAlgorithms/Go/blob/master/data-structures/dynamic-array/dynamic_array.go) - * Linked-List - * [Double-Linkedlist](https://github.com/TheAlgorithms/Go/blob/master/data-structures/linked-list/double-linkedlist.go) - * [Linkedlist](https://github.com/TheAlgorithms/Go/blob/master/data-structures/linked-list/Linkedlist.go) - * [Single-Linkedlist](https://github.com/TheAlgorithms/Go/blob/master/data-structures/linked-list/single-linkedlist.go) - * Trie - * [Trie](https://github.com/TheAlgorithms/Go/blob/master/data-structures/trie/trie.go) - * [Trie Test](https://github.com/TheAlgorithms/Go/blob/master/data-structures/trie/trie_test.go) - -## Dynamic-Programming - * [Longest-Palindromic-Subsequence](https://github.com/TheAlgorithms/Go/blob/master/dynamic-programming/longest-palindromic-subsequence.go) - * [Matrix-Multiplication](https://github.com/TheAlgorithms/Go/blob/master/dynamic-programming/matrix-multiplication.go) - * [Rod-Cutting](https://github.com/TheAlgorithms/Go/blob/master/dynamic-programming/rod-cutting.go) - -## Other - * [Maxsubarraysum](https://github.com/TheAlgorithms/Go/blob/master/other/maxSubarraySum.go) - * [Nestedbrackets](https://github.com/TheAlgorithms/Go/blob/master/other/NestedBrackets.go) - * [Passwordgenerator](https://github.com/TheAlgorithms/Go/blob/master/other/PasswordGenerator.go) - * [Prime Numbers](https://github.com/TheAlgorithms/Go/blob/master/other/prime_numbers.go) - * [Primenumbers](https://github.com/TheAlgorithms/Go/blob/master/other/PrimeNumbers.go) - * [String Combinations](https://github.com/TheAlgorithms/Go/blob/master/other/string_combinations.go) - -## Searches - * [Binary Search](https://github.com/TheAlgorithms/Go/blob/master/searches/binary_search.go) - * [Linear Search](https://github.com/TheAlgorithms/Go/blob/master/searches/linear_search.go) - -## Sorts - * [Bubble Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/bubble_sort.go) - * [Heap Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/heap_sort.go) - * [Insertion Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/insertion_sort.go) - * [Merge Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/merge_sort.go) - * [Quick Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/quick_sort.go) - * [Selection Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/selection_sort.go) - * [Shell Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/shell_sort.go) - * [Sorts Case Test](https://github.com/TheAlgorithms/Go/blob/master/sorts/sorts_case_test.go) - * [Sorts Test](https://github.com/TheAlgorithms/Go/blob/master/sorts/sorts_test.go) - * [Topological Sort](https://github.com/TheAlgorithms/Go/blob/master/sorts/topological_sort.go) - -## Strings - * [Naivestringsearch](https://github.com/TheAlgorithms/Go/blob/master/strings/naiveStringSearch.go) diff --git a/LICENSE b/LICENSE index 3b7951527..71b9656b7 100644 --- a/LICENSE +++ b/LICENSE @@ -1,6 +1,6 @@ MIT License -Copyright (c) 2020 The Algorithms +Copyright (c) 2021 The Algorithms and contributors Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal diff --git a/README.md b/README.md index 653ced575..51f244249 100644 --- a/README.md +++ b/README.md @@ -1,169 +1,1218 @@ # The Algorithms - Go +[![Gitpod Ready-to-Code](https://img.shields.io/badge/Gitpod-Ready--to--Code-blue?logo=gitpod&style=flat-square)](https://gitpod.io/#https://github.com/TheAlgorithms/Go)  +[![Continuous Integration](https://github.com/TheAlgorithms/Go/actions/workflows/ci.yml/badge.svg)](https://github.com/TheAlgorithms/Go/actions/workflows/ci.yml) +[![codecov](https://codecov.io/gh/TheAlgorithms/Go/graph/badge.svg?token=aSWh7N8tNx)](https://codecov.io/gh/TheAlgorithms/Go) +![godocmd](https://github.com/tjgurwara99/Go/workflows/godocmd/badge.svg) +![](https://img.shields.io/github/repo-size/TheAlgorithms/Go.svg?label=Repo%20size&style=flat-square)  +![update_directory_md](https://github.com/TheAlgorithms/Go/workflows/update_directory_md/badge.svg) +[![Discord chat](https://img.shields.io/discord/808045925556682782.svg?logo=discord&colorB=7289DA&style=flat-square)](https://the-algorithms.com/discord/)  ### Algorithms implemented in Go (for education) -These algorithms are for demonstration purposes only. There are many sort implementations in the Go standard library that may have better performance. +The repository is a collection of open-source implementation of a variety of algorithms implemented in Go and licensed under [MIT License](LICENSE). -For a full list of all algorithms, please see: [DIRECTORY.md](https://github.com/TheAlgorithms/Go/blob/master/DIRECTORY.md) +Read our [Contribution Guidelines](CONTRIBUTING.md) before you contribute. -## Sort Algorithms +## List of Algorithms + + +# Packages: +
+ ahocorasick -### Bubble -![alt text][bubble-image] +--- -From [Wikipedia][bubble-wiki]: Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the list to be sorted, compares each pair of adjacent items and swaps them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which indicates that the list is sorted. +##### Functions: -__Properties__ -* Worst case performance O(n^2) -* Best case performance O(n) -* Average case performance O(n^2) +1. [`Advanced`](./strings/ahocorasick/advancedahocorasick.go#L10): Advanced Function performing the Advanced Aho-Corasick algorithm. Finds and prints occurrences of each pattern. +2. [`AhoCorasick`](./strings/ahocorasick/ahocorasick.go#L15): AhoCorasick Function performing the Basic Aho-Corasick algorithm. Finds and prints occurrences of each pattern. +3. [`ArrayUnion`](./strings/ahocorasick/shared.go#L86): ArrayUnion Concats two arrays of int's into one. +4. [`BoolArrayCapUp`](./strings/ahocorasick/shared.go#L78): BoolArrayCapUp Dynamically increases an array size of bool's by 1. +5. [`BuildAc`](./strings/ahocorasick/ahocorasick.go#L54): Functions that builds Aho Corasick automaton. +6. [`BuildExtendedAc`](./strings/ahocorasick/advancedahocorasick.go#L46): BuildExtendedAc Functions that builds extended Aho Corasick automaton. +7. [`ComputeAlphabet`](./strings/ahocorasick/shared.go#L61): ComputeAlphabet Function that returns string of all the possible characters in given patterns. +8. [`ConstructTrie`](./strings/ahocorasick/shared.go#L4): ConstructTrie Function that constructs Trie as an automaton for a set of reversed & trimmed strings. +9. [`Contains`](./strings/ahocorasick/shared.go#L39): Contains Returns 'true' if array of int's 's' contains int 'e', 'false' otherwise. +10. [`CreateNewState`](./strings/ahocorasick/shared.go#L111): CreateNewState Automaton function for creating a new state 'state'. +11. [`CreateTransition`](./strings/ahocorasick/shared.go#L116): CreateTransition Creates a transition for function σ(state,letter) = end. +12. [`GetParent`](./strings/ahocorasick/shared.go#L99): GetParent Function that finds the first previous state of a state and returns it. Used for trie where there is only one parent. +13. [`GetTransition`](./strings/ahocorasick/shared.go#L121): GetTransition Returns ending state for transition σ(fromState,overChar), '-1' if there is none. +14. [`GetWord`](./strings/ahocorasick/shared.go#L49): GetWord Function that returns word found in text 't' at position range 'begin' to 'end'. +15. [`IntArrayCapUp`](./strings/ahocorasick/shared.go#L70): IntArrayCapUp Dynamically increases an array size of int's by 1. +16. [`StateExists`](./strings/ahocorasick/shared.go#L133): StateExists Checks if state 'state' exists. Returns 'true' if it does, 'false' otherwise. -###### View the algorithm in [action][bubble-toptal] +--- +##### Types +1. [`Result`](./strings/ahocorasick/ahocorasick.go#L9): No description provided. -### Insertion -![alt text][insertion-image] +--- +
+ armstrong -From [Wikipedia][insertion-wiki]: Insertion sort is a simple sorting algorithm that builds the final sorted array (or list) one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort. +--- -__Properties__ -* Worst case performance O(n^2) -* Best case performance O(n) -* Average case performance O(n^2) +##### Functions: -###### View the algorithm in [action][insertion-toptal] +1. [`IsArmstrong`](./math/armstrong/isarmstrong.go#L14): No description provided. +--- +
+ binary -### Merge -![alt text][merge-image] +--- -From [Wikipedia][merge-wiki]: In computer science, merge sort (also commonly spelled mergesort) is an efficient, general-purpose, comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Mergesort is a divide and conquer algorithm that was invented by John von Neumann in 1945. +##### Package binary describes algorithms that use binary operations for different calculations. -__Properties__ -* Worst case performance O(n log n) -* Best case performance O(n) -* Average case performance O(n) +--- +##### Functions: +1. [`Abs`](./math/binary/abs.go#L10): Abs returns absolute value using binary operation Principle of operation: 1) Get the mask by right shift by the base 2) Base is the size of an integer variable in bits, for example, for int32 it will be 32, for int64 it will be 64 3) For negative numbers, above step sets mask as 1 1 1 1 1 1 1 1 and 0 0 0 0 0 0 0 0 for positive numbers. 4) Add the mask to the given number. 5) XOR of mask + n and mask gives the absolute value. +2. [`BitCounter`](./math/binary/bitcounter.go#L11): BitCounter - The function returns the number of set bits for an unsigned integer number +3. [`FastInverseSqrt`](./math/binary/fast_inverse_sqrt.go#L15): FastInverseSqrt assumes that argument is always positive, and it does not deal with negative numbers. The "magic" number 0x5f3759df is hex for 1597463007 in decimals. The math.Float32bits is alias to *(*uint32)(unsafe.Pointer(&f)) and math.Float32frombits is to *(*float32)(unsafe.Pointer(&b)). +4. [`IsPowerOfTwo`](./math/binary/checkisnumberpoweroftwo.go#L21): IsPowerOfTwo This function uses the fact that powers of 2 are represented like 10...0 in binary, and numbers one less than the power of 2 are represented like 11...1. Therefore, using the and function: 10...0 & 01...1 00...0 -> 0 This is also true for 0, which is not a power of 2, for which we have to add and extra condition. +5. [`IsPowerOfTwoLeftShift`](./math/binary/checkisnumberpoweroftwo.go#L28): IsPowerOfTwoLeftShift This function takes advantage of the fact that left shifting a number by 1 is equivalent to multiplying by 2. For example, binary 00000001 when shifted by 3 becomes 00001000, which in decimal system is 8 or = 2 * 2 * 2 +6. [`LogBase2`](./math/binary/logarithm.go#L7): LogBase2 Finding the exponent of n = 2**x using bitwise operations (logarithm in base 2 of n) [See more](https://en.wikipedia.org/wiki/Logarithm) +7. [`MeanUsingAndXor`](./math/binary/arithmeticmean.go#L12): MeanUsingAndXor This function finds arithmetic mean using "AND" and "XOR" operations +8. [`MeanUsingRightShift`](./math/binary/arithmeticmean.go#L17): MeanUsingRightShift This function finds arithmetic mean using right shift +9. [`ReverseBits`](./math/binary/reversebits.go#L14): ReverseBits This function initialized the result by 0 (all bits 0) and process the given number starting from its least significant bit. If the current bit is 1, set the corresponding most significant bit in the result and finally move on to the next bit in the input number. Repeat this till all its bits are processed. +10. [`SequenceGrayCode`](./math/binary/rbc.go#L11): SequenceGrayCode The function generates an "Gray code" sequence of length n +11. [`Sqrt`](./math/binary/sqrt.go#L10): No description provided. +12. [`XorSearchMissingNumber`](./math/binary/xorsearch.go#L11): XorSearchMissingNumber This function finds a missing number in a sequence -###### View the algorithm in [action][merge-toptal] +--- +
+ cache -### Quick -![alt text][quick-image] +--- -From [Wikipedia][quick-wiki]: Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. +##### Functions: -__Properties__ -* Worst case performance O(n^2) -* Best case performance O(n log n) or O(n) with three-way partition -* Average case performance O(n^2) +1. [`NewLRU`](./cache/lru.go#L22): NewLRU represent initiate lru cache with capacity +2. [`NewLFU`](./cache/lfu.go#L33): NewLFU represent initiate lfu cache with capacity +3. [`Get`](./cache/lfu.go#L52): Get the value by key from LFU cache +4. [`Put`](./cache/lfu.go#L66): Put the key and value in LFU cache -###### View the algorithm in [action][quick-toptal] +--- +##### Types -### Selection -![alt text][selection-image] +1. [`LRU`](./cache/lru.go#L15): Default the struct of lru cache algorithm. +2. [`LFU`](./cache/lfu.go#L19): Default the struct of lfu cache algorithm. -From [Wikipedia][selection-wiki]: The algorithm divides the input list into two parts: the sublist of items already sorted, which is built up from left to right at the front (left) of the list, and the sublist of items remaining to be sorted that occupy the rest of the list. Initially, the sorted sublist is empty and the unsorted sublist is the entire input list. The algorithm proceeds by finding the smallest (or largest, depending on sorting order) element in the unsorted sublist, exchanging (swapping) it with the leftmost unsorted element (putting it in sorted order), and moving the sublist boundaries one element to the right. -__Properties__ -* Worst case performance O(n^2) -* Best case performance O(n^2) -* Average case performance O(n^2) +--- +
+ caesar -###### View the algorithm in [action][selection-toptal] +--- -### Shell -![alt text][shell-image] +##### Package caesar is the shift cipher ref: https://en.wikipedia.org/wiki/Caesar_cipher -From [Wikipedia][shell-wiki]: Shellsort is a generalization of insertion sort that allows the exchange of items that are far apart. The idea is to arrange the list of elements so that, starting anywhere, considering every nth element gives a sorted list. Such a list is said to be h-sorted. Equivalently, it can be thought of as h interleaved lists, each individually sorted. +--- +##### Functions: -__Properties__ -* Worst case performance O(nlog2 2n) -* Best case performance O(n log n) -* Average case performance depends on gap sequence +1. [`Decrypt`](./cipher/caesar/caesar.go#L27): Decrypt decrypts by left shift of "key" each character of "input" +2. [`Encrypt`](./cipher/caesar/caesar.go#L6): Encrypt encrypts by right shift of "key" each character of "input" +3. [`FuzzCaesar`](./cipher/caesar/caesar_test.go#L158): No description provided. -###### View the algorithm in [action][shell-toptal] +--- +
+ catalan -### Time-Compexity Graphs +--- -Comparing the complexity of sorting algorithms (Bubble Sort, Insertion Sort, Selection Sort) +##### Functions: -[Complexity Graphs](https://github.com/prateekiiest/Python/blob/master/sorts/sortinggraphs.png) +1. [`CatalanNumber`](./math/catalan/catalannumber.go#L16): CatalanNumber This function returns the `nth` Catalan number ----------------------------------------------------------------------------------- +--- +
+ checksum -## Search Algorithms +--- -### Linear -![alt text][linear-image] +##### Package checksum describes algorithms for finding various checksums -From [Wikipedia][linear-wiki]: linear search or sequential search is a method for finding a target value within a list. It sequentially checks each element of the list for the target value until a match is found or until all the elements have been searched. - Linear search runs in at worst linear time and makes at most n comparisons, where n is the length of the list. +--- +##### Functions: -__Properties__ -* Worst case performance O(n) -* Best case performance O(1) -* Average case performance O(n) -* Worst case space complexity O(1) iterative +1. [`CRC8`](./checksum/crc8.go#L25): CRC8 calculates CRC8 checksum of the given data. +2. [`Luhn`](./checksum/luhn.go#L11): Luhn validates the provided data using the Luhn algorithm. -### Binary -![alt text][binary-image] +--- +##### Types -From [Wikipedia][binary-wiki]: Binary search, also known as half-interval search or logarithmic search, is a search algorithm that finds the position of a target value within a sorted array. It compares the target value to the middle element of the array; if they are unequal, the half in which the target cannot lie is eliminated and the search continues on the remaining half until it is successful. +1. [`CRCModel`](./checksum/crc8.go#L15): No description provided. -__Properties__ -* Worst case performance O(log n) -* Best case performance O(1) -* Average case performance O(log n) -* Worst case space complexity O(1) ----------------------------------------------------------------------------------------------------------------------- +--- +
+ coloring -## Ciphers +--- -### Caesar -![alt text][caesar]
-In cryptography, a **Caesar cipher**, also known as Caesar's cipher, the shift cipher, Caesar's code or Caesar shift, is one of the simplest and most widely known encryption techniques.
-It is **a type of substitution cipher** in which each letter in the plaintext is replaced by a letter some fixed number of positions down the alphabet. For example, with a left shift of 3, D would be replaced by A, E would become B, and so on.
-The method is named after **Julius Caesar**, who used it in his private correspondence.
-The encryption step performed by a Caesar cipher is often incorporated as part of more complex schemes, such as the Vigenère cipher, and still has modern application in the ROT13 system. As with all single-alphabet substitution ciphers, the Caesar cipher is easily broken and in modern practice offers essentially no communication security. -###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Caesar_cipher) +##### Package coloring provides implementation of different graph coloring algorithms, e.g. coloring using BFS, using Backtracking, using greedy approach. Author(s): [Shivam](https://github.com/Shivam010) -### Transposition -In cryptography, a **transposition cipher** is a method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext. That is, the order of the units is changed (the plaintext is reordered).
-Mathematically a bijective function is used on the characters' positions to encrypt and an inverse function to decrypt. -###### Source: [Wikipedia](https://en.wikipedia.org/wiki/Transposition_cipher) +--- +##### Functions: -[bubble-toptal]: https://www.toptal.com/developers/sorting-algorithms/bubble-sort -[bubble-wiki]: https://en.wikipedia.org/wiki/Bubble_sort -[bubble-image]: https://upload.wikimedia.org/wikipedia/commons/thumb/8/83/Bubblesort-edited-color.svg/220px-Bubblesort-edited-color.svg.png "Bubble Sort" +1. [`BipartiteCheck`](./graph/coloring/bipartite.go#L40): basically tries to color the graph in two colors if each edge connects 2 differently colored nodes the graph can be considered bipartite -[insertion-toptal]: https://www.toptal.com/developers/sorting-algorithms/insertion-sort -[insertion-wiki]: https://en.wikipedia.org/wiki/Insertion_sort -[insertion-image]: https://upload.wikimedia.org/wikipedia/commons/7/7e/Insertionsort-edited.png "Insertion Sort" +--- +##### Types -[quick-toptal]: https://www.toptal.com/developers/sorting-algorithms/quick-sort -[quick-wiki]: https://en.wikipedia.org/wiki/Quicksort -[quick-image]: https://upload.wikimedia.org/wikipedia/commons/6/6a/Sorting_quicksort_anim.gif "Quick Sort" +1. [`Graph`](./graph/coloring/graph.go#L14): No description provided. -[merge-toptal]: https://www.toptal.com/developers/sorting-algorithms/merge-sort -[merge-wiki]: https://en.wikipedia.org/wiki/Merge_sort -[merge-image]: https://upload.wikimedia.org/wikipedia/commons/c/cc/Merge-sort-example-300px.gif "Merge Sort" -[selection-toptal]: https://www.toptal.com/developers/sorting-algorithms/selection-sort -[selection-wiki]: https://en.wikipedia.org/wiki/Selection_sort -[selection-image]: https://upload.wikimedia.org/wikipedia/commons/thumb/b/b0/Selection_sort_animation.gif/250px-Selection_sort_animation.gif "Selection Sort Sort" +--- +
+ combination -[shell-toptal]: https://www.toptal.com/developers/sorting-algorithms/shell-sort -[shell-wiki]: https://en.wikipedia.org/wiki/Shellsort -[shell-image]: https://upload.wikimedia.org/wikipedia/commons/d/d8/Sorting_shellsort_anim.gif "Shell Sort" +--- -[linear-wiki]: https://en.wikipedia.org/wiki/Linear_search -[linear-image]: http://www.tutorialspoint.com/data_structures_algorithms/images/linear_search.gif +##### Package combination ... -[binary-wiki]: https://en.wikipedia.org/wiki/Binary_search_algorithm -[binary-image]: https://upload.wikimedia.org/wikipedia/commons/f/f7/Binary_search_into_array.png +--- +##### Functions: +1. [`Start`](./strings/combination/combination.go#L13): Start ... -[caesar]: https://upload.wikimedia.org/wikipedia/commons/4/4a/Caesar_cipher_left_shift_of_3.svg +--- +##### Types + +1. [`Combinations`](./strings/combination/combination.go#L7): No description provided. + + +--- +
+ compression + +--- + +##### Functions: + +1. [`HuffDecode`](./compression/huffmancoding.go#L104): HuffDecode recursively decodes the binary code in, by traversing the Huffman compression tree pointed by root. current stores the current node of the traversing algorithm. out stores the current decoded string. +2. [`HuffEncode`](./compression/huffmancoding.go#L93): HuffEncode encodes the string in by applying the mapping defined by codes. +3. [`HuffEncoding`](./compression/huffmancoding.go#L76): HuffEncoding recursively traverses the Huffman tree pointed by node to obtain the map codes, that associates a rune with a slice of booleans. Each code is prefixed by prefix and left and right children are labelled with the booleans false and true, respectively. +4. [`HuffTree`](./compression/huffmancoding.go#L33): HuffTree returns the root Node of the Huffman tree by compressing listfreq. The compression produces the most optimal code lengths, provided listfreq is ordered, i.e.: listfreq[i] <= listfreq[j], whenever i < j. + +--- +##### Types + +1. [`Node`](./compression/huffmancoding.go#L17): No description provided. + +2. [`SymbolFreq`](./compression/huffmancoding.go#L25): No description provided. + + +--- +
+ compression_test + +--- + +##### Functions: + +1. [`SymbolCountOrd`](./compression/huffmancoding_test.go#L16): SymbolCountOrd computes sorted symbol-frequency list of input message + +--- +
+ conversion + +--- + +##### Package conversion is a package of implementations which converts one data structure to another. + +--- +##### Functions: + +1. [`Base64Decode`](./conversion/base64.go#L57): Base64Decode decodes the received input base64 string into a byte slice. The implementation follows the RFC4648 standard, which is documented at https://datatracker.ietf.org/doc/html/rfc4648#section-4 +2. [`Base64Encode`](./conversion/base64.go#L19): Base64Encode encodes the received input bytes slice into a base64 string. The implementation follows the RFC4648 standard, which is documented at https://datatracker.ietf.org/doc/html/rfc4648#section-4 +3. [`BinaryToDecimal`](./conversion/binarytodecimal.go#L25): BinaryToDecimal() function that will take Binary number as string, and return its Decimal equivalent as integer. +4. [`DecimalToBinary`](./conversion/decimaltobinary.go#L32): DecimalToBinary() function that will take Decimal number as int, and return its Binary equivalent as string. +5. [`FuzzBase64Encode`](./conversion/base64_test.go#L113): No description provided. +6. [`HEXToRGB`](./conversion/rgbhex.go#L10): HEXToRGB splits an RGB input (e.g. a color in hex format; 0x) into the individual components: red, green and blue +7. [`IntToRoman`](./conversion/inttoroman.go#L17): IntToRoman converts an integer value to a roman numeral string. An error is returned if the integer is not between 1 and 3999. +8. [`RGBToHEX`](./conversion/rgbhex.go#L41): RGBToHEX does exactly the opposite of HEXToRGB: it combines the three components red, green and blue to an RGB value, which can be converted to e.g. Hex +9. [`Reverse`](./conversion/decimaltobinary.go#L22): Reverse() function that will take string, and returns the reverse of that string. +10. [`RomanToInt`](./conversion/romantoint.go#L40): RomanToInt converts a roman numeral string to an integer. Roman numerals for numbers outside the range 1 to 3,999 will return an error. Nil or empty string return 0 with no error thrown. + +--- +
+ deque + +--- + +##### Package deque implements a Double Ended Queue data structure. + +--- +##### Functions: + +1. [`New`](./structure/deque/deque.go#L22): New returns a new DoublyEndedQueue. + +--- +##### Types + +1. [`DoublyEndedQueue`](./structure/deque/deque.go#L17): No description provided. + + +--- +
+ deque_test + +--- + +##### Types + +1. [`QueryStructure`](./structure/deque/deque_test.go#L20): No description provided. + +2. [`TestCaseData`](./structure/deque/deque_test.go#L27): No description provided. + + +--- +
+ diffiehellman + +--- + +##### Package diffiehellman implements Diffie-Hellman Key Exchange Algorithm for more information watch : https://www.youtube.com/watch?v=NmM9HA2MQGI + +--- +##### Functions: + +1. [`GenerateMutualKey`](./cipher/diffiehellman/diffiehellmankeyexchange.go#L19): GenerateMutualKey : generates a mutual key that can be used by only alice and bob mutualKey = (shareKey^prvKey)%primeNumber +2. [`GenerateShareKey`](./cipher/diffiehellman/diffiehellmankeyexchange.go#L13): GenerateShareKey : generates a key using client private key , generator and primeNumber this key can be made public shareKey = (g^key)%primeNumber + +--- +
+ dynamic + +--- + +##### Package dynamic is a package of certain implementations of dynamically run algorithms. + +--- +##### Functions: + +1. [`Abbreviation`](./dynamic/abbreviation.go#L24): Returns true if it is possible to make a equals b (if b is an abbreviation of a), returns false otherwise +2. [`Bin2`](./dynamic/binomialcoefficient.go#L21): Bin2 function +3. [`CoinChange`](./dynamic/coinchange.go#L5): CoinChange finds the number of possible combinations of coins of different values which can get to the target amount. +4. [`CutRodDp`](./dynamic/rodcutting.go#L21): CutRodDp solve the same problem using dynamic programming +5. [`CutRodRec`](./dynamic/rodcutting.go#L8): CutRodRec solve the problem recursively: initial approach +6. [`EditDistanceDP`](./dynamic/editdistance.go#L35): EditDistanceDP is an optimised implementation which builds on the ideas of the recursive implementation. We use dynamic programming to compute the DP table where dp[i][j] denotes the edit distance value of first[0..i-1] and second[0..j-1]. Time complexity is O(m * n) where m and n are lengths of the strings, first and second respectively. +7. [`EditDistanceRecursive`](./dynamic/editdistance.go#L10): EditDistanceRecursive is a naive implementation with exponential time complexity. +8. [`IsSubsetSum`](./dynamic/subsetsum.go#L14): No description provided. +9. [`Knapsack`](./dynamic/knapsack.go#L17): Knapsack solves knapsack problem return maxProfit +10. [`LongestCommonSubsequence`](./dynamic/longestcommonsubsequence.go#L13): LongestCommonSubsequence function +11. [`LongestIncreasingSubsequence`](./dynamic/longestincreasingsubsequence.go#L9): LongestIncreasingSubsequence returns the longest increasing subsequence where all elements of the subsequence are sorted in increasing order +12. [`LongestIncreasingSubsequenceGreedy`](./dynamic/longestincreasingsubsequencegreedy.go#L9): LongestIncreasingSubsequenceGreedy is a function to find the longest increasing subsequence in a given array using a greedy approach. The dynamic programming approach is implemented alongside this one. Worst Case Time Complexity: O(nlogn) Auxiliary Space: O(n), where n is the length of the array(slice). Reference: https://www.geeksforgeeks.org/construction-of-longest-monotonically-increasing-subsequence-n-log-n/ +13. [`LpsDp`](./dynamic/longestpalindromicsubsequence.go#L25): LpsDp function +14. [`LpsRec`](./dynamic/longestpalindromicsubsequence.go#L20): LpsRec function +15. [`MatrixChainDp`](./dynamic/matrixmultiplication.go#L24): MatrixChainDp function +16. [`MatrixChainRec`](./dynamic/matrixmultiplication.go#L10): MatrixChainRec function +17. [`Max`](./dynamic/knapsack.go#L11): Max function - possible duplicate +18. [`NthCatalanNumber`](./dynamic/catalan.go#L13): NthCatalan returns the n-th Catalan Number Complexity: O(n²) +19. [`NthFibonacci`](./dynamic/fibonacci.go#L6): NthFibonacci returns the nth Fibonacci Number +20. [`TrapRainWater`](./dynamic/traprainwater.go#L17): Calculate the amount of trapped rainwater between bars represented by an elevation map using dynamic programming. +--- +
+ dynamicarray + +--- + +##### Package dynamicarray A dynamic array is quite similar to a regular array, but its Size is modifiable during program runtime, very similar to how a slice in Go works. The implementation is for educational purposes and explains how one might go about implementing their own version of slices. For more details check out those links below here: GeeksForGeeks article : https://www.geeksforgeeks.org/how-do-dynamic-arrays-work/ Go blog: https://blog.golang.org/slices-intro Go blog: https://blog.golang.org/slices authors [Wesllhey Holanda](https://github.com/wesllhey), [Milad](https://github.com/miraddo) see dynamicarray.go, dynamicarray_test.go + +--- +##### Types + +1. [`DynamicArray`](./structure/dynamicarray/dynamicarray.go#L21): No description provided. + + +--- +
+ factorial + +--- + +##### Package factorial describes algorithms Factorials calculations. + +--- +##### Functions: + +1. [`Iterative`](./math/factorial/factorial.go#L12): Iterative returns the iteratively brute forced factorial of n +2. [`Recursive`](./math/factorial/factorial.go#L21): Recursive This function recursively computes the factorial of a number +3. [`UsingTree`](./math/factorial/factorial.go#L30): UsingTree This function finds the factorial of a number using a binary tree + +--- +
+ fibonacci + +--- + +##### Functions: + +1. [`Formula`](./math/fibonacci/fibonacci.go#L42): Formula This function calculates the n-th fibonacci number using the [formula](https://en.wikipedia.org/wiki/Fibonacci_number#Relation_to_the_golden_ratio) Attention! Tests for large values fall due to rounding error of floating point numbers, works well, only on small numbers +2. [`Matrix`](./math/fibonacci/fibonacci.go#L15): Matrix This function calculates the n-th fibonacci number using the matrix method. [See](https://en.wikipedia.org/wiki/Fibonacci_number#Matrix_form) +3. [`Recursive`](./math/fibonacci/fibonacci.go#L51): Recursive calculates the n-th fibonacci number recursively by adding the previous two Fibonacci numbers. This algorithm is extremely slow for bigger numbers, but provides a simpler implementation. + +--- +
+ gcd + +--- + +##### Functions: + +1. [`Extended`](./math/gcd/extended.go#L12): Extended simple extended gcd +2. [`ExtendedIterative`](./math/gcd/extendedgcditerative.go#L4): ExtendedIterative finds and returns gcd(a, b), x, y satisfying a*x + b*y = gcd(a, b). +3. [`ExtendedRecursive`](./math/gcd/extendedgcd.go#L4): ExtendedRecursive finds and returns gcd(a, b), x, y satisfying a*x + b*y = gcd(a, b). +4. [`Iterative`](./math/gcd/gcditerative.go#L4): Iterative Faster iterative version of GcdRecursive without holding up too much of the stack +5. [`Recursive`](./math/gcd/gcd.go#L4): Recursive finds and returns the greatest common divisor of a given integer. +6. [`TemplateBenchmarkExtendedGCD`](./math/gcd/extendedgcd_test.go#L44): No description provided. +7. [`TemplateBenchmarkGCD`](./math/gcd/gcd_test.go#L37): No description provided. +8. [`TemplateTestExtendedGCD`](./math/gcd/extendedgcd_test.go#L7): No description provided. +9. [`TemplateTestGCD`](./math/gcd/gcd_test.go#L18): No description provided. + +--- +
+ generateparentheses + +--- + +##### Functions: + +1. [`GenerateParenthesis`](./strings/generateparentheses/generateparentheses.go#L12): No description provided. + +--- +
+ genetic + +--- + +##### Package genetic provides functions to work with strings using genetic algorithm. https://en.wikipedia.org/wiki/Genetic_algorithm Author: D4rkia + +--- +##### Functions: + +1. [`GeneticString`](./strings/genetic/genetic.go#L71): GeneticString generates PopulationItem based on the imputed target string, and a set of possible runes to build a string with. In order to optimise string generation additional configurations can be provided with Conf instance. Empty instance of Conf (&Conf{}) can be provided, then default values would be set. Link to the same algorithm implemented in python: https://github.com/TheAlgorithms/Python/blob/master/genetic_algorithm/basic_string.py + +--- +##### Types + +1. [`Conf`](./strings/genetic/genetic.go#L32): No description provided. + +2. [`PopulationItem`](./strings/genetic/genetic.go#L26): No description provided. + +3. [`Result`](./strings/genetic/genetic.go#L52): No description provided. + + +--- +
+ geometry + +--- + +##### Package geometry contains geometric algorithms Package geometry contains geometric algorithms + +--- +##### Functions: + +1. [`Distance`](./math/geometry/straightlines.go#L18): Distance calculates the shortest distance between two points. +2. [`EuclideanDistance`](./math/geometry/distance.go#L20): EuclideanDistance returns the Euclidean distance between points in any `n` dimensional Euclidean space. +3. [`IsParallel`](./math/geometry/straightlines.go#L42): IsParallel checks if two lines are parallel or not. +4. [`IsPerpendicular`](./math/geometry/straightlines.go#L47): IsPerpendicular checks if two lines are perpendicular or not. +5. [`PointDistance`](./math/geometry/straightlines.go#L53): PointDistance calculates the distance of a given Point from a given line. The slice should contain the coefficiet of x, the coefficient of y and the constant in the respective order. +6. [`Section`](./math/geometry/straightlines.go#L24): Section calculates the Point that divides a line in specific ratio. DO NOT specify the ratio in the form m:n, specify it as r, where r = m / n. +7. [`Slope`](./math/geometry/straightlines.go#L32): Slope calculates the slope (gradient) of a line. +8. [`YIntercept`](./math/geometry/straightlines.go#L37): YIntercept calculates the Y-Intercept of a line from a specific Point. + +--- +##### Types + +1. [`EuclideanPoint`](./math/geometry/distance.go#L14): No description provided. + +2. [`Line`](./math/geometry/straightlines.go#L13): No description provided. + +3. [`Point`](./math/geometry/straightlines.go#L9): No description provided. + + +--- +
+ graph + +--- + +##### Package graph demonstrates Graph search algorithms reference: https://en.wikipedia.org/wiki/Tree_traversal + +--- +##### Functions: + +1. [`ArticulationPoint`](./graph/articulationpoints.go#L19): ArticulationPoint is a function to identify articulation points in a graph. The function takes the graph as an argument and returns a boolean slice which indicates whether a vertex is an articulation point or not. Worst Case Time Complexity: O(|V| + |E|) Auxiliary Space: O(|V|) reference: https://en.wikipedia.org/wiki/Biconnected_component and https://cptalks.quora.com/Cut-Vertex-Articulation-point +2. [`BreadthFirstSearch`](./graph/breadthfirstsearch.go#L9): BreadthFirstSearch is an algorithm for traversing and searching graph data structures. It starts at an arbitrary node of a graph, and explores all of the neighbor nodes at the present depth prior to moving on to the nodes at the next depth level. Worst-case performance O(|V|+|E|)=O(b^{d})}O(|V|+|E|)=O(b^{d}) Worst-case space complexity O(|V|)=O(b^{d})}O(|V|)=O(b^{d}) reference: https://en.wikipedia.org/wiki/Breadth-first_search +3. [`DepthFirstSearch`](./graph/depthfirstsearch.go#L53): No description provided. +4. [`DepthFirstSearchHelper`](./graph/depthfirstsearch.go#L21): No description provided. +5. [`FloydWarshall`](./graph/floydwarshall.go#L15): FloydWarshall Returns all pair's shortest path using Floyd Warshall algorithm +6. [`GetIdx`](./graph/depthfirstsearch.go#L3): No description provided. +7. [`KruskalMST`](./graph/kruskal.go#L23): No description provided. +8. [`PrimMST`](./graph/prim.go#30): Computes the minimum spanning tree of a weighted undirected graph +9. [`LowestCommonAncestor`](./graph/lowestcommonancestor.go#L111): For each node, we will precompute its ancestor above him, its ancestor two nodes above, its ancestor four nodes above, etc. Let's call `jump[j][u]` is the `2^j`-th ancestor above the node `u` with `u` in range `[0, numbersVertex)`, `j` in range `[0,MAXLOG)`. These information allow us to jump from any node to any ancestor above it in `O(MAXLOG)` time. +10. [`New`](./graph/graph.go#L16): Constructor functions for graphs (undirected by default) +11. [`NewTree`](./graph/lowestcommonancestor.go#L84): No description provided. +12. [`NewUnionFind`](./graph/unionfind.go#L24): Initialise a new union find data structure with s nodes +13. [`NotExist`](./graph/depthfirstsearch.go#L12): No description provided. +14. [`Topological`](./graph/topological.go#L7): Topological assumes that graph given is valid and that its possible to get a topological ordering. constraints are array of []int{a, b}, representing an edge going from a to b +15. [`Edmond-Karp`](./graph/edmondkarp.go#L43): Computes the maximum possible flow between a pair of s-t vertices in a weighted graph + +--- +##### Types + +1. [`Edge`](./graph/kruskal.go#L17): No description provided. + +2. [`Graph`](./graph/graph.go#L9): No description provided. + +3. [`Item`](./graph/dijkstra.go#L5): No description provided. + +4. [`Query`](./graph/lowestcommonancestor_test.go#L9): No description provided. + +5. [`Tree`](./graph/lowestcommonancestor.go#L25): No description provided. + +6. [`TreeEdge`](./graph/lowestcommonancestor.go#L12): No description provided. + +7. [`UnionFind`](./graph/unionfind.go#L18): No description provided. + +8. [`WeightedGraph`](./graph/floydwarshall.go#L9): No description provided. + + +--- +
+ guid + +--- + +##### Package guid provides facilities for generating random globally unique identifiers. + +--- +##### Functions: + +1. [`New`](./strings/guid/guid.go#L28): New returns a randomly generated global unique identifier. + +--- +
+ hashmap + +--- + +##### Functions: + +1. [`Make`](./structure/hashmap/hashmap.go#L32): Make creates a new HashMap instance with input size and capacity +2. [`New`](./structure/hashmap/hashmap.go#L24): New return new HashMap instance + +--- +##### Types + +1. [`HashMap`](./structure/hashmap/hashmap.go#L17): No description provided. + + +--- +
+ heap + +--- + +##### Functions: + +1. [`New`](./structure/heap/heap.go#L15): New gives a new heap object. +2. [`NewAny`](./structure/heap/heap.go#L24): NewAny gives a new heap object. element can be anything, but must provide less function. + +--- +##### Types + +1. [`Heap`](./structure/heap/heap.go#L9): No description provided. + + +--- +
+ heap_test + +--- + +##### Types + +1. [`testInt`](#L0): + + Methods: + 1. [`Less`](./structure/heap/heap_test.go#L11): No description provided. +2. [`testStudent`](#L0): + + Methods: + 1. [`Less`](./structure/heap/heap_test.go#L20): No description provided. + +--- +
+ horspool + +--- + +##### Functions: + +1. [`Horspool`](./strings/horspool/horspool.go#L10): No description provided. + +--- +
+ kmp + +--- + +##### Functions: + +1. [`Kmp`](./strings/kmp/kmp.go#L4): Kmp Function kmp performing the Knuth-Morris-Pratt algorithm. + +--- +##### Types + +1. [`args`](./strings/kmp/kmp_test.go#L39): No description provided. + + +--- +
+ lcm + +--- + +##### Functions: + +1. [`Lcm`](./math/lcm/lcm.go#L10): Lcm returns the lcm of two numbers using the fact that lcm(a,b) * gcd(a,b) = | a * b | + +--- +
+ levenshtein + +--- + +##### Functions: + +1. [`Distance`](./strings/levenshtein/levenshteindistance.go#L10): Distance Function that gives Levenshtein Distance + +--- +
+ linkedlist + +--- + +##### Package linkedlist demonstrates different implementations on linkedlists. + +--- +##### Functions: + +1. [`JosephusProblem`](./structure/linkedlist/cyclic.go#L120): https://en.wikipedia.org/wiki/Josephus_problem This is a struct-based solution for Josephus problem. +2. [`NewCyclic`](./structure/linkedlist/cyclic.go#L12): Create new list. +3. [`NewDoubly`](./structure/linkedlist/doubly.go#L31): No description provided. +4. [`NewNode`](./structure/linkedlist/shared.go#L12): Create new node. +5. [`NewSingly`](./structure/linkedlist/singlylinkedlist.go#L19): NewSingly returns a new instance of a linked list + +--- +##### Types + +1. [`Cyclic`](./structure/linkedlist/cyclic.go#L6): No description provided. + +2. [`Doubly`](./structure/linkedlist/doubly.go#L18): No description provided. + +3. [`Node`](./structure/linkedlist/shared.go#L5): No description provided. + +4. [`Singly`](./structure/linkedlist/singlylinkedlist.go#L10): No description provided. + +5. [`testCase`](./structure/linkedlist/cyclic_test.go#L105): No description provided. + + +--- +
+ manacher + +--- + +##### Functions: + +1. [`LongestPalindrome`](./strings/manacher/longestpalindrome.go#L37): No description provided. + +--- +
+ math + +--- + +##### Package math is a package that contains mathematical algorithms and its different implementations. filename : krishnamurthy.go description: A program which contains the function that returns true if a given number is Krishnamurthy number or not. details: A number is a Krishnamurthy number if the sum of all the factorials of the digits is equal to the number. Ex: 1! = 1, 145 = 1! + 4! + 5! author(s): [GooMonk](https://github.com/GooMonk) see krishnamurthy_test.go + +--- +##### Functions: + +1. [`Abs`](./math/abs.go#L11): Abs returns absolute value +2. [`AliquotSum`](./math/aliquotsum.go#L14): This function returns s(n) for given number +3. [`Combinations`](./math/binomialcoefficient.go#L20): C is Binomial Coefficient function This function returns C(n, k) for given n and k +4. [`Cos`](./math/cos.go#L10): Cos returns the cosine of the radian argument x. [See more](https://en.wikipedia.org/wiki/Sine_and_cosine) [Based on the idea of Bhaskara approximation of cos(x)](https://math.stackexchange.com/questions/3886552/bhaskara-approximation-of-cosx) +5. [`DefaultPolynomial`](./math/pollard.go#L16): DefaultPolynomial is the commonly used polynomial g(x) = (x^2 + 1) mod n +6. [`FindKthMax`](./math/kthnumber.go#L11): FindKthMax returns the kth large element given an integer slice with nil `error` if found and returns -1 with `error` `search.ErrNotFound` if not found. NOTE: The `nums` slice gets mutated in the process. +7. [`FindKthMin`](./math/kthnumber.go#L19): FindKthMin returns kth small element given an integer slice with nil `error` if found and returns -1 with `error` `search.ErrNotFound` if not found. NOTE: The `nums` slice gets mutated in the process. +8. [`IsAutomorphic`](./math/isautomorphic.go#L16): No description provided. +9. [`IsKrishnamurthyNumber`](./math/krishnamurthy.go#L12): IsKrishnamurthyNumber returns if the provided number n is a Krishnamurthy number or not. +10. [`IsPerfectNumber`](./math/perfectnumber.go#L34): Checks if inNumber is a perfect number +11. [`IsPowOfTwoUseLog`](./math/checkisnumberpoweroftwo.go#L10): IsPowOfTwoUseLog This function checks if a number is a power of two using the logarithm. The limiting degree can be from 0 to 63. See alternatives in the binary package. +12. [`Lerp`](./math/lerp.go#L5): Lerp or Linear interpolation This function will return new value in 't' percentage between 'v0' and 'v1' +13. [`LiouvilleLambda`](./math/liouville.go#L24): Lambda is the liouville function This function returns λ(n) for given number +14. [`Mean`](./math/mean.go#L7): No description provided. +15. [`Median`](./math/median.go#L12): No description provided. +16. [`Mode`](./math/mode.go#L19): No description provided. +17. [`Mu`](./math/mobius.go#L21): Mu is the Mobius function This function returns μ(n) for given number +18. [`Phi`](./math/eulertotient.go#L5): Phi is the Euler totient function. This function computes the number of numbers less then n that are coprime with n. +19. [`PollardsRhoFactorization`](./math/pollard.go#L29): PollardsRhoFactorization is an implementation of Pollard's rho factorization algorithm using the default parameters x = y = 2 +20. [`PronicNumber`](./math/pronicnumber.go#L15): PronicNumber returns true if argument passed to the function is pronic and false otherwise. +21. [`Sin`](./math/sin.go#L9): Sin returns the sine of the radian argument x. [See more](https://en.wikipedia.org/wiki/Sine_and_cosine) +22. [`SumOfProperDivisors`](./math/perfectnumber.go#L17): Returns the sum of proper divisors of inNumber. + +--- +
+ matrix + +--- + +##### filename: strassenmatrixmultiply.go description: Implements matrix multiplication using the Strassen algorithm. details: This program takes two matrices as input and performs matrix multiplication using the Strassen algorithm, which is an optimized divide-and-conquer approach. It allows for efficient multiplication of large matrices. author(s): Mohit Raghav(https://github.com/mohit07raghav19) See strassenmatrixmultiply_test.go for test cases + +--- +##### Functions: + +1. [`IsValid`](./math/matrix/isvalid.go#L6): IsValid checks if the input matrix has consistent row lengths. +2. [`New`](./math/matrix/matrix.go#L17): NewMatrix creates a new Matrix based on the provided arguments. +3. [`NewFromElements`](./math/matrix/matrix.go#L43): NewFromElements creates a new Matrix from the given elements. + +--- +##### Types + +1. [`Matrix`](./math/matrix/matrix.go#L10): No description provided. + + +--- +
+ matrix_test + +--- + +##### Functions: + +1. [`MakeRandomMatrix`](./math/matrix/strassenmatrixmultiply_test.go#L105): No description provided. + +--- +
+ max + +--- + +##### Functions: + +1. [`Bitwise`](./math/max/bitwisemax.go#L11): Bitwise computes using bitwise operator the maximum of all the integer input and returns it +2. [`Int`](./math/max/max.go#L6): Int is a function which returns the maximum of all the integers provided as arguments. + +--- +
+ maxsubarraysum + +--- + +##### Package maxsubarraysum is a package containing a solution to a common problem of finding max contiguous sum within a array of ints. + +--- +##### Functions: + +1. [`MaxSubarraySum`](./other/maxsubarraysum/maxsubarraysum.go#L13): MaxSubarraySum returns the maximum subarray sum + +--- +
+ min + +--- + +##### Functions: + +1. [`Bitwise`](./math/min/bitwisemin.go#L11): Bitwise This function returns the minimum integer using bit operations +2. [`Int`](./math/min/min.go#L6): Int is a function which returns the minimum of all the integers provided as arguments. + +--- +
+ modular + +--- + +##### Functions: + +1. [`Exponentiation`](./math/modular/exponentiation.go#L22): Exponentiation returns base^exponent % mod +2. [`Inverse`](./math/modular/inverse.go#L19): Inverse Modular function +3. [`Multiply64BitInt`](./math/modular/exponentiation.go#L51): Multiply64BitInt Checking if the integer multiplication overflows + +--- +
+ moserdebruijnsequence + +--- + +##### Functions: + +1. [`MoserDeBruijnSequence`](./math/moserdebruijnsequence/sequence.go#L7): No description provided. + +--- +
+ nested + +--- + +##### Package nested provides functions for testing strings proper brackets nesting. + +--- +##### Functions: + +1. [`IsBalanced`](./other/nested/nestedbrackets.go#L20): IsBalanced returns true if provided input string is properly nested. Input is a sequence of brackets: '(', ')', '[', ']', '{', '}'. A sequence of brackets `s` is considered properly nested if any of the following conditions are true: - `s` is empty; - `s` has the form (U) or [U] or {U} where U is a properly nested string; - `s` has the form VW where V and W are properly nested strings. For example, the string "()()[()]" is properly nested but "[(()]" is not. **Note** Providing characters other then brackets would return false, despite brackets sequence in the string. Make sure to filter input before usage. + +--- +
+ palindrome + +--- + +##### Functions: + +1. [`IsPalindrome`](./strings/palindrome/ispalindrome.go#L26): No description provided. +2. [`IsPalindromeRecursive`](./strings/palindrome/ispalindrome.go#L39): No description provided. + +--- +
+ pangram + +--- + +##### Functions: + +1. [`IsPangram`](./strings/pangram/ispangram.go#L21): No description provided. + +--- +
+ parenthesis + +--- + +##### Functions: + +1. [`Parenthesis`](./strings/parenthesis/parenthesis.go#L8): Parenthesis algorithm checks if every opened parenthesis is closed correctly. When parcounter is less than 0 when a closing parenthesis is detected without an opening parenthesis that surrounds it and parcounter will be 0 if all open parenthesis are closed correctly. + +--- +
+ pascal + +--- + +##### Functions: + +1. [`GenerateTriangle`](./math/pascal/pascaltriangle.go#L24): GenerateTriangle This function generates a Pascal's triangle of n lines + +--- +
+ password + +--- + +##### Package password contains functions to help generate random passwords + +--- +##### Functions: + +1. [`Generate`](./other/password/generator.go#L15): Generate returns a newly generated password + +--- +
+ permutation + +--- + +##### Functions: + +1. [`GenerateElementSet`](./math/permutation/heaps.go#L37): No description provided. +2. [`Heaps`](./math/permutation/heaps.go#L8): Heap's Algorithm for generating all permutations of n objects +3. [`NextPermutation`](./math/permutation/next_permutation.go#8): A solution to find next permutation of an integer array in constant memory + +--- +
+ pi + +--- + +##### spigotpi_test.go description: Test for Spigot Algorithm for the Digits of Pi author(s) [red_byte](https://github.com/i-redbyte) see spigotpi.go + +--- +##### Functions: + +1. [`MonteCarloPi`](./math/pi/montecarlopi.go#L17): No description provided. +2. [`MonteCarloPiConcurrent`](./math/pi/montecarlopi.go#L36): MonteCarloPiConcurrent approximates the value of pi using the Monte Carlo method. Unlike the MonteCarloPi function (first version), this implementation uses goroutines and channels to parallelize the computation. More details on the Monte Carlo method available at https://en.wikipedia.org/wiki/Monte_Carlo_method. More details on goroutines parallelization available at https://go.dev/doc/effective_go#parallel. +3. [`Spigot`](./math/pi/spigotpi.go#L12): No description provided. + +--- +
+ polybius + +--- + +##### Package polybius is encrypting method with polybius square ref: https://en.wikipedia.org/wiki/Polybius_square#Hybrid_Polybius_Playfair_Cipher + +--- +##### Functions: + +1. [`FuzzPolybius`](./cipher/polybius/polybius_test.go#L154): No description provided. +2. [`NewPolybius`](./cipher/polybius/polybius.go#L21): NewPolybius returns a pointer to object of Polybius. If the size of "chars" is longer than "size", "chars" are truncated to "size". + +--- +##### Types + +1. [`Polybius`](./cipher/polybius/polybius.go#L12): No description provided. + + +--- +
+ power + +--- + +##### Functions: + +1. [`IterativePower`](./math/power/fastexponent.go#L4): IterativePower is iterative O(logn) function for pow(x, y) +2. [`RecursivePower`](./math/power/fastexponent.go#L18): RecursivePower is recursive O(logn) function for pow(x, y) +3. [`RecursivePower1`](./math/power/fastexponent.go#L30): RecursivePower1 is recursive O(n) function for pow(x, y) +4. [`UsingLog`](./math/power/powvialogarithm.go#L14): No description provided. + +--- +
+ prime + +--- + +##### Functions: + +1. [`Factorize`](./math/prime/primefactorization.go#L5): Factorize is a function that computes the exponents of each prime in the prime factorization of n +2. [`Generate`](./math/prime/sieve.go#L26): Generate returns a int slice of prime numbers up to the limit +3. [`GenerateChannel`](./math/prime/sieve.go#L9): Generate generates the sequence of integers starting at 2 and sends it to the channel `ch` +4. [`MillerRabinDeterministic`](./math/prime/millerrabintest.go#L121): MillerRabinDeterministic is a Deterministic version of the Miller-Rabin test, which returns correct results for all valid int64 numbers. +5. [`MillerRabinProbabilistic`](./math/prime/millerrabintest.go#L101): MillerRabinProbabilistic is a probabilistic test for primality of an integer based of the algorithm devised by Miller and Rabin. +6. [`MillerRandomTest`](./math/prime/millerrabintest.go#L77): MillerRandomTest This is the intermediate step that repeats within the miller rabin primality test for better probabilitic chances of receiving the correct result with random witnesses. +7. [`MillerTest`](./math/prime/millerrabintest.go#L49): MillerTest tests whether num is a strong probable prime to a witness. Formally: a^d ≡ 1 (mod n) or a^(2^r * d) ≡ -1 (mod n), 0 <= r <= s +8. [`MillerTestMultiple`](./math/prime/millerrabintest.go#L84): MillerTestMultiple is like MillerTest but runs the test for multiple witnesses. +9. [`OptimizedTrialDivision`](./math/prime/primecheck.go#L26): OptimizedTrialDivision checks primality of an integer using an optimized trial division method. The optimizations include not checking divisibility by the even numbers and only checking up to the square root of the given number. +10. [`Sieve`](./math/prime/sieve.go#L16): Sieve Sieving the numbers that are not prime from the channel - basically removing them from the channels +11. [`TrialDivision`](./math/prime/primecheck.go#L9): TrialDivision tests whether a number is prime by trying to divide it by the numbers less than it. +12. [`Twin`](./math/prime/twin.go#L15): This function returns twin prime for given number returns (n + 2) if both n and (n + 2) are prime -1 otherwise + +--- +
+ pythagoras + +--- + +##### Functions: + +1. [`Distance`](./math/pythagoras/pythagoras.go#L15): Distance calculates the distance between to vectors with the Pythagoras theorem + +--- +##### Types + +1. [`Vector`](./math/pythagoras/pythagoras.go#L8): No description provided. + + +--- +
+ queue + +--- + +##### Functions: + +1. [`BackQueue`](./structure/queue/queuearray.go#L32): BackQueue return the Back value +2. [`DeQueue`](./structure/queue/queuearray.go#L20): DeQueue it will be removed the first value that added into the list +3. [`EnQueue`](./structure/queue/queuearray.go#L15): EnQueue it will be added new value into our list +4. [`FrontQueue`](./structure/queue/queuearray.go#L27): FrontQueue return the Front value +5. [`IsEmptyQueue`](./structure/queue/queuearray.go#L42): IsEmptyQueue check our list is empty or not +6. [`LenQueue`](./structure/queue/queuearray.go#L37): LenQueue will return the length of the queue list + +--- +##### Types + +1. [`LQueue`](./structure/queue/queuelinklistwithlist.go#L20): No description provided. + +2. [`Node`](./structure/queue/queuelinkedlist.go#L13): No description provided. + +3. [`Queue`](./structure/queue/queuelinkedlist.go#L19): No description provided. + + +--- +
+ rot13 + +--- + +##### Package rot13 is a simple letter substitution cipher that replaces a letter with the 13th letter after it in the alphabet. ref: https://en.wikipedia.org/wiki/ROT13 + +--- +##### Functions: + +1. [`FuzzRot13`](./cipher/rot13/rot13_test.go#L72): No description provided. + +--- +
+ rsa + +--- + +##### Package rsa shows a simple implementation of RSA algorithm + +--- +##### Functions: + +1. [`Decrypt`](./cipher/rsa/rsa.go#L43): Decrypt decrypts encrypted rune slice based on the RSA algorithm +2. [`Encrypt`](./cipher/rsa/rsa.go#L28): Encrypt encrypts based on the RSA algorithm - uses modular exponentitation in math directory +3. [`FuzzRsa`](./cipher/rsa/rsa_test.go#L79): No description provided. + +--- +
+ search + +--- + +##### Functions: + +1. [`BoyerMoore`](./strings/search/boyermoore.go#L5): Implementation of boyer moore string search O(l) where l=len(text) +2. [`Naive`](./strings/search/naive.go#L5): Implementation of naive string search O(n*m) where n=len(txt) and m=len(pattern) + +--- +
+ segmenttree + +--- + +##### Functions: + +1. [`NewSegmentTree`](./structure/segmenttree/segmenttree.go#L116): No description provided. + +--- +##### Types + +1. [`SegmentTree`](./structure/segmenttree/segmenttree.go#L17): No description provided. + + +--- +
+ set + +--- + +##### package set implements a Set using a golang map. This implies that only the types that are accepted as valid map keys can be used as set elements. For instance, do not try to Add a slice, or the program will panic. + +--- +##### Functions: + +1. [`New`](./structure/set/set.go#L7): New gives new set. + +--- +
+ sha256 + +--- + +##### Functions: + +1. [`Hash`](./hashing/sha256/sha256.go#L50): Hash hashes the input message using the sha256 hashing function, and return a 32 byte array. The implementation follows the RGC6234 standard, which is documented at https://datatracker.ietf.org/doc/html/rfc6234 + +--- +
+ sort + +--- + +##### Package sort a package for demonstrating sorting algorithms in Go + +--- +##### Functions: + +1. [`BinaryInsertion`](./sort/binaryinsertionsort.go#L13): No description provided. +2. [`Bogo`](./sort/bogosort.go#L32): No description provided. +3. [`Bubble`](./sort/bubblesort.go#L9): Bubble is a simple generic definition of Bubble sort algorithm. +4. [`Bucket`](./sort/bucketsort.go#L7): Bucket sorts a slice. It is mainly useful when input is uniformly distributed over a range. +5. [`Cocktail`](./sort/cocktailsort.go#L9): Cocktail sort is a variation of bubble sort, operating in two directions (beginning to end, end to beginning) +6. [`Comb`](./sort/combSort.go#L17): Comb is a simple sorting algorithm which is an improvement of the bubble sorting algorithm. +7. [`Count`](./sort/countingsort.go#L11): No description provided. +8. [`Cycle`](./sort/cyclesort.go#L10): Cycle sort is an in-place, unstable sorting algorithm that is particularly useful when sorting arrays containing elements with a small range of values. It is theoretically optimal in terms of the total number of writes to the original array. +9. [`Exchange`](./sort/exchangesort.go#L8): No description provided. +10. [`HeapSort`](./sort/heapsort.go#L116): No description provided. +11. [`ImprovedSimple`](./sort/simplesort.go#L27): ImprovedSimple is a improve SimpleSort by skipping an unnecessary comparison of the first and last. This improved version is more similar to implementation of insertion sort +12. [`Insertion`](./sort/insertionsort.go#L5): No description provided. +13. [`Merge`](./sort/mergesort.go#L41): Merge Perform merge sort on a slice +14. [`MergeIter`](./sort/mergesort.go#L55): No description provided. +15. [`Pancake`](./sort/pancakesort.go#L8): Pancake sorts a slice using flip operations, where flip refers to the idea of reversing the slice from index `0` to `i`. +16. [`ParallelMerge`](./sort/mergesort.go#L66): ParallelMerge Perform merge sort on a slice using goroutines +17. [`Partition`](./sort/quicksort.go#L12): No description provided. +18. [`Patience`](./sort/patiencesort.go#L13): No description provided. +19. [`Pigeonhole`](./sort/pigeonholesort.go#L15): Pigeonhole sorts a slice using pigeonhole sorting algorithm. NOTE: To maintain time complexity O(n + N), this is the reason for having only Integer constraint instead of Ordered. +20. [`Quicksort`](./sort/quicksort.go#L39): Quicksort Sorts the entire array +21. [`QuicksortRange`](./sort/quicksort.go#L26): QuicksortRange Sorts the specified range within the array +22. [`RadixSort`](./sort/radixsort.go#L43): No description provided. +23. [`Selection`](./sort/selectionsort.go#L5): No description provided. +24. [`Shell`](./sort/shellsort.go#L5): No description provided. +25. [`Simple`](./sort/simplesort.go#L13): No description provided. + +--- +##### Types + +1. [`MaxHeap`](./sort/heapsort.go#L5): No description provided. + + +--- +
+ sqrt + +--- + +##### Package sqrt contains algorithms and data structures that contains a √n in their complexity + +--- +##### Functions: + +1. [`NewSqrtDecomposition`](./sqrt/sqrtdecomposition.go#L34): Create a new SqrtDecomposition instance with the parameters as specified by SqrtDecomposition comment Assumptions: - len(elements) > 0 + +--- +##### Types + +1. [`SqrtDecomposition`](./sqrt/sqrtdecomposition.go#L21): No description provided. + + +--- +
+ stack + +--- + +##### Functions: + +1. [`NewStack`](./structure/stack/stackarray.go#L17): NewStack creates and returns a new stack. + +--- +##### Types + +1. [`Array`](./structure/stack/stackarray.go#L12): No description provided. + +2. [`Node`](./structure/stack/stacklinkedlist.go#L13): No description provided. + +3. [`SList`](./structure/stack/stacklinkedlistwithlist.go#L18): No description provided. + +4. [`Stack`](./structure/stack/stacklinkedlist.go#L19): No description provided. + + +--- +
+ strings + +--- + +##### Package strings is a package that contains all algorithms that are used to analyse and manipulate strings. + +--- +##### Functions: + +1. [`CountChars`](./strings/charoccurrence.go#L12): CountChars counts the number of a times a character has occurred in the provided string argument and returns a map with `rune` as keys and the count as value. +2. [`IsIsogram`](./strings/isisogram.go#L34): No description provided. +3. [`IsSubsequence`](./strings/issubsequence.go#L10): Returns true if s is subsequence of t, otherwise return false. + +--- +
+ transposition + +--- + +##### Functions: + +1. [`Decrypt`](./cipher/transposition/transposition.go#L81): No description provided. +2. [`Encrypt`](./cipher/transposition/transposition.go#L51): No description provided. +3. [`FuzzTransposition`](./cipher/transposition/transposition_test.go#L103): No description provided. + +--- +
+ tree + +--- + +##### For more details check out those links below here: Wikipedia article: https://en.wikipedia.org/wiki/Binary_search_tree authors [guuzaa](https://github.com/guuzaa) + +--- +##### Functions: + +1. [`NewAVL`](./structure/tree/avl.go#L54): NewAVL creates a novel AVL tree +2. [`NewBinarySearch`](./structure/tree/bstree.go#L46): NewBinarySearch creates a novel Binary-Search tree +3. [`NewRB`](./structure/tree/rbtree.go#L57): NewRB creates a new Red-Black Tree + +--- +##### Types + +1. [`AVL`](./structure/tree/avl.go#L48): No description provided. + +2. [`AVLNode`](./structure/tree/avl.go#L18): No description provided. + +3. [`BSNode`](./structure/tree/bstree.go#L15): No description provided. + +4. [`BinarySearch`](./structure/tree/bstree.go#L40): No description provided. + +5. [`RB`](./structure/tree/rbtree.go#L51): No description provided. + +6. [`RBNode`](./structure/tree/rbtree.go#L25): No description provided. + + +--- +
+ trie + +--- + +##### Package trie provides Trie data structures in golang. Wikipedia: https://en.wikipedia.org/wiki/Trie + +--- +##### Functions: + +1. [`NewNode`](./structure/trie/trie.go#L14): NewNode creates a new Trie node with initialized children map. + +--- +##### Types + +1. [`Node`](./structure/trie/trie.go#L7): No description provided. + + +--- +
+ xor + +--- + +##### Package xor is an encryption algorithm that operates the exclusive disjunction(XOR) ref: https://en.wikipedia.org/wiki/XOR_cipher + +--- +##### Functions: + +1. [`Decrypt`](./cipher/xor/xor.go#L19): Decrypt decrypts with Xor encryption +2. [`Encrypt`](./cipher/xor/xor.go#L10): Encrypt encrypts with Xor encryption after converting each character to byte The returned value might not be readable because there is no guarantee which is within the ASCII range If using other type such as string, []int, or some other types, add the statements for converting the type to []byte. +3. [`FuzzXOR`](./cipher/xor/xor_test.go#L108): No description provided. + +--- +
+ +##### Package rail fence is a classical type of transposition cipher ref : https://en.wikipedia.org/wiki/Rail_fence_cipher + +--- +##### Functions: + +1. [`Encrypt`](.cipher/railfence/railfence.go#L7): Encrypt encrypts a message using rail fence cipher +2. [`Decrypt`](.cipher/railfence/railfence.go#L44): decrypt decrypts a message using rail fence cipher +3. [`TestEncrypt`](.cipher/railfence/railfence_test.go#L7) Test function for Encrypt +4. [`TestDecrypt`](.cipher/railfence/railfence_test.go#L50) Test function for Decrypt + +--- + + diff --git a/STYLE.md b/STYLE.md new file mode 100644 index 000000000..e72214bc8 --- /dev/null +++ b/STYLE.md @@ -0,0 +1,188 @@ +# The Algorithms Go Repository Style Guide + +This guide contains a set of go idioms and best practices which should be followed while writing +code whenever they are applicable. The instructions in this document should be given precedence +if there is a conflict between this document and [contribution guidelines](./CONTRIBUTING.md). If you find any issue or ambiguity in +this document, the maintainers of this repository should be consulted. + +## Table of Contents + +- [Formatting](#formatting) +- [Commenting](#commenting) + - [Package Comments](#package-comments) + - [Documentation Comments](#documentation-comments) + - [Author Comments](#author-comments) +- [Naming](#naming) + - [Package Naming](#package-naming) + - [Symbol Naming](#symbol-naming) + - [Function Naming](#function-naming) + - [Constructor Naming](#constructor-naming) + - [Getter Naming](#getter-naming) + - [Setter Naming](#setter-naming) + - [Interface Naming](#interface-naming) + +## Formatting + +All go code should be formatted with the official formatting tool `gofmt`. This requirement is +verified by the repository workflows. + +## Commenting + +All exported symbols should be commented with documentation, so that their motivation and use is +clear. All documentation should record any nuances of the symbol so that users are well aware of +them. + +C++ style line comments should be preferred over C-style block comments. + + + + + +
BadGood
+ +```go +/* + Unmarshal converts a JSON string into a go interface + ... +*/ +``` + + + +```go +// Unmarshal converts a JSON string into a go interface +// ... +``` + +
+ +### Package Comments + +Package comments should start with the word "Package" followed by the package name. For packages +spanning multiple files or with a need for a large documentation, use a separate `doc.go` file for package level documentation comment. + + + + + +
BadGood
+ +```go +// sort is a package which implements sorting functions. +``` + + + +```go +// Package sort implements sorting functions. +``` + +
+ +### Documentation Comments + +All doc comments for symbols should start with the symbol name. + + + + + +
BadGood
+ +```go +// Function Quick is an implementation +// of the Quicksort algorithm. +``` + + + +```go +// Quick is an implementation +// of the Quicksort algorithm. +``` + +
+ +### Author Comments + +A comment recording the author of a particular file may also be added. This comment should be +written at the top of the file and it should not be a part of the package documentation. + + + + + +
BadGood
+ +```go +// author: Rak Laptudirm (@raklaptudirm) +package sort +``` +Comment is a part of the package documentation. + + + +```go +// author: Rak Laptudirm (@raklaptudirm) + +package sort +``` +Comment is not a part of the package documentation. + +
+ +## Naming + +### Package Naming + +Package names should be short and to the point. Keep in mind that this identifier will be used to +refer to your package, so make it easy to remember. It should be only composed of lower case +letters. Prefer `json` to `JSON` or `Json`. If your package name has two words, merge them +together. Prefer `jsonencoding` to `jsonEncoding` or `json_encoding`. Although, there is almost always a word to succinctly describe the package with an appropriate name. So if you have a name that describes the package nicely, please use that. + +Add the `_test` suffix to your package name to implement black-box testing for your package in the test files. + +### Symbol Naming + +Go symbols should be named in the `camelCase` or `PascalCase`, depending of whether the symbol +is exported or not. The case when using acronyms in names should be consistent. Use `json` or +`JSON` instead of `Json`. + +For exported symbols, use the package name to your advantage to write concise symbol names. For +example, if you have a package `png`, instead of defining a `png.PNGFile`, define a `png.File`. +It is much clearer and avoids repetition. + +### Function Naming + +#### Constructor Naming + +Constructors should use the naming format `New()` for constructors which return pointers and +`Make()` for constructors which return values in accordance with the Go Programming Language's +`new` and `make` functions. If the package only exports a single constructor, use the name `New()`. +Some valid names are `reader.New()`, `metainfo.NewFile()`. + +#### Getter Naming + +Usage of Getters and Setters are discouraged. Use exported variables instead. + +Getters should use the name of the field that is being fetched. For example, prefer a getter +name like `user.Name()` to `user.GetName()`. + +#### Setter Naming + +Setters should use names in the format `Set`. For example, `user.SetName()`. + +### Interface Naming + +Interfaces should use names in the format of `er` or ``. For example, some +valid interface names are: + +```go +type Node interface { + Node() +} + +type Writer interface { + Write() +} +``` diff --git a/cache/lfu.go b/cache/lfu.go new file mode 100644 index 000000000..e22670c68 --- /dev/null +++ b/cache/lfu.go @@ -0,0 +1,127 @@ +// lfu.go +// description: a type of cache algorithm used to manage memory within a computer. +// details: +// The standard characteristics of this method involve the system keeping track of the number of times a block is referenced in memory. +// When the cache is full and requires more room the system will purge the item with the lowest reference frequency. +// ref: (https://en.wikipedia.org/wiki/Least_frequently_used) +// time complexity: O(N) +// space complexity: O(1) +// author: [CocaineCong](https://github.com/CocaineCong) + +package cache + +import ( + "container/list" + "math" +) + +// LFU the Least Frequently Used (LFU) page-replacement algorithm +type LFU struct { + len int // length + cap int // capacity + minFreq int // The element that operates least frequently in LFU + + // key: key of element, value: value of element + itemMap map[string]*list.Element + + // key: frequency of possible occurrences of all elements in the itemMap + // value: elements with the same frequency + freqMap map[int]*list.List +} + +// NewLFU init the LFU cache with capacity +func NewLFU(capacity int) LFU { + return LFU{ + len: 0, + cap: capacity, + minFreq: math.MaxInt, + itemMap: make(map[string]*list.Element), + freqMap: make(map[int]*list.List), + } +} + +// initItem to init item for LFU +func initItem(k string, v any, f int) item { + return item{ + key: k, + value: v, + freq: f, + } +} + +// Get the key in cache by LFU +func (c *LFU) Get(key string) any { + // if existed, will return value + if e, ok := c.itemMap[key]; ok { + // the frequency of e +1 and change freqMap + c.increaseFreq(e) + obj := e.Value.(item) + return obj.value + } + + // if not existed, return nil + return nil +} + +// Put the key in LFU cache +func (c *LFU) Put(key string, value any) { + if e, ok := c.itemMap[key]; ok { + // if key existed, update the value + obj := e.Value.(item) + obj.value = value + c.increaseFreq(e) + } else { + // if key not existed + obj := initItem(key, value, 1) + // if the length of item gets to the top line + // remove the least frequently operated element + if c.len == c.cap { + c.eliminate() + c.len-- + } + // insert in freqMap and itemMap + c.insertMap(obj) + // change minFreq to 1 because insert the newest one + c.minFreq = 1 + // length++ + c.len++ + } +} + +// increaseFreq increase the frequency if element +func (c *LFU) increaseFreq(e *list.Element) { + obj := e.Value.(item) + // remove from low frequency first + oldLost := c.freqMap[obj.freq] + oldLost.Remove(e) + // change the value of minFreq + if c.minFreq == obj.freq && oldLost.Len() == 0 { + // if it is the last node of the minimum frequency that is removed + c.minFreq++ + } + // add to high frequency list + c.insertMap(obj) +} + +// insertMap insert item in map +func (c *LFU) insertMap(obj item) { + // add in freqMap + l, ok := c.freqMap[obj.freq] + if !ok { + l = list.New() + c.freqMap[obj.freq] = l + } + e := l.PushFront(obj) + // update or add the value of itemMap key to e + c.itemMap[obj.key] = e +} + +// eliminate clear the least frequently operated element +func (c *LFU) eliminate() { + l := c.freqMap[c.minFreq] + e := l.Back() + obj := e.Value.(item) + l.Remove(e) + + delete(c.itemMap, obj.key) +} diff --git a/cache/lfu_test.go b/cache/lfu_test.go new file mode 100644 index 000000000..7e891412f --- /dev/null +++ b/cache/lfu_test.go @@ -0,0 +1,58 @@ +package cache_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/cache" +) + +func TestLFU(t *testing.T) { + lfuCache := cache.NewLFU(3) + t.Run("Test 1: Put number and Get is correct", func(t *testing.T) { + key, value := "1", 1 + lfuCache.Put(key, value) + got := lfuCache.Get(key) + + if got != value { + t.Errorf("expected: %v, got: %v", value, got) + } + }) + + t.Run("Test 2: Get data not stored in cache should return nil", func(t *testing.T) { + got := lfuCache.Get("2") + if got != nil { + t.Errorf("expected: nil, got: %v", got) + } + }) + + t.Run("Test 3: Put data over capacity and Get should return nil", func(t *testing.T) { + lfuCache.Put("2", 2) + lfuCache.Put("3", 3) + lfuCache.Put("4", 4) + + got := lfuCache.Get("1") + if got != nil { + t.Errorf("expected: nil, got: %v", got) + } + }) + + t.Run("test 4: Put key over capacity but recent key exists", func(t *testing.T) { + lfuCache.Put("4", 4) + lfuCache.Put("3", 3) + lfuCache.Put("2", 2) + lfuCache.Put("1", 1) + + got := lfuCache.Get("4") + if got != nil { + t.Errorf("expected: nil, got: %v", got) + } + + expected := 3 + got = lfuCache.Get("3") + + if got != expected { + t.Errorf("expected: %v, got: %v", expected, got) + } + + }) +} diff --git a/cache/lru.go b/cache/lru.go new file mode 100644 index 000000000..b9578a9fe --- /dev/null +++ b/cache/lru.go @@ -0,0 +1,75 @@ +// lru.go +// description : Least Recently Used (LRU) cache +// details : A Least Recently Used (LRU) cache is a type of cache algorithm used to manage memory within a computer. The LRU algorithm is designed to remove the least recently used items first when the cache reaches its limit. +// time complexity : O(1) +// space complexity : O(n) +// ref : https://en.wikipedia.org/wiki/Cache_replacement_policies#Least_recently_used_(LRU) + +package cache + +import ( + "github.com/TheAlgorithms/Go/structure/linkedlist" +) + +type item struct { + key string + value any + + // the frequency of key + freq int +} + +type LRU struct { + dl *linkedlist.Doubly[any] + size int + capacity int + storage map[string]*linkedlist.Node[any] +} + +// NewLRU represent initiate lru cache with capacity +func NewLRU(capacity int) LRU { + return LRU{ + dl: linkedlist.NewDoubly[any](), + storage: make(map[string]*linkedlist.Node[any], capacity), + size: 0, + capacity: capacity, + } +} + +// Get value from lru +// if not found, return nil +func (c *LRU) Get(key string) any { + v, ok := c.storage[key] + if ok { + c.dl.MoveToBack(v) + return v.Val.(item).value + } + + return nil +} + +// Put cache with key and value to lru +func (c *LRU) Put(key string, value any) { + e, ok := c.storage[key] + if ok { + n := e.Val.(item) + n.value = value + e.Val = n + c.dl.MoveToBack(e) + return + } + + if c.size >= c.capacity { + e := c.dl.Front() + dk := e.Val.(item).key + c.dl.Remove(e) + delete(c.storage, dk) + c.size-- + } + + n := item{key: key, value: value} + c.dl.AddAtEnd(n) + ne := c.dl.Back() + c.storage[key] = ne + c.size++ +} diff --git a/cache/lru_test.go b/cache/lru_test.go new file mode 100644 index 000000000..34ab3752b --- /dev/null +++ b/cache/lru_test.go @@ -0,0 +1,59 @@ +package cache_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/cache" +) + +func TestLRU(t *testing.T) { + cache := cache.NewLRU(3) + + t.Run("Test 1: Put number and Get is correct", func(t *testing.T) { + key, value := "1", 1 + cache.Put(key, value) + got := cache.Get(key) + + if got != value { + t.Errorf("expected: %v, got: %v", value, got) + } + }) + + t.Run("Test 2: Get data not stored in cache should return nil", func(t *testing.T) { + got := cache.Get("2") + if got != nil { + t.Errorf("expected: nil, got: %v", got) + } + }) + + t.Run("Test 3: Put data over capacity and Get should return nil", func(t *testing.T) { + cache.Put("2", 2) + cache.Put("3", 3) + cache.Put("4", 4) + + got := cache.Get("1") + if got != nil { + t.Errorf("expected: nil, got: %v", got) + } + }) + + t.Run("test 4: Put key over capacity but recent key exists", func(t *testing.T) { + cache.Put("4", 4) + cache.Put("3", 3) + cache.Put("2", 2) + cache.Put("1", 1) + + got := cache.Get("4") + if got != nil { + t.Errorf("expected: nil, got: %v", got) + } + + expected := 3 + got = cache.Get("3") + + if got != expected { + t.Errorf("expected: %v, got: %v", expected, got) + } + + }) +} diff --git a/checksum/crc8.go b/checksum/crc8.go new file mode 100644 index 000000000..29c6214b5 --- /dev/null +++ b/checksum/crc8.go @@ -0,0 +1,67 @@ +// crc8.go +// description: Calculate CRC8 +// details: +// A cyclic redundancy check (CRC) is an error-detecting code commonly used in digital networks +// and storage devices to detect accidental changes to raw data. +// time complexity: O(n) +// space complexity: O(1) +// See more [CRC](https://en.wikipedia.org/wiki/Cyclic_redundancy_check) +// author(s) [red_byte](https://github.com/i-redbyte) +// see crc8_test.go + +package checksum + +import "math/bits" + +// CRCModel contains the necessary parameters for calculating the DRC algorithm +type CRCModel struct { + Poly uint8 + Init uint8 + RefIn bool + RefOut bool + XorOut uint8 + Name string +} + +// CRC8 calculates CRC8 checksum of the given data. +func CRC8(data []byte, model CRCModel) uint8 { + table := getTable(model) + crcResult := model.Init + crcResult = addBytes(data, model, crcResult, table) + if model.RefOut { + crcResult = bits.Reverse8(crcResult) + } + return crcResult ^ model.XorOut +} + +// This function get the result of adding the bytes in data to the crc +func addBytes(data []byte, model CRCModel, crcResult uint8, table []uint8) uint8 { + if model.RefIn { + for _, d := range data { + d = bits.Reverse8(d) + crcResult = table[crcResult^d] + } + return crcResult + } + for _, d := range data { + crcResult = table[crcResult^d] + } + return crcResult +} + +// This function get 256-byte (256x8) table for efficient processing. +func getTable(model CRCModel) []uint8 { + table := make([]uint8, 256) + for i := 0; i < 256; i++ { + crc := uint8(i) + for j := 0; j < 8; j++ { + isSetBit := (crc & 0x80) != 0 + crc <<= 1 + if isSetBit { + crc ^= model.Poly + } + } + table[i] = crc + } + return table +} diff --git a/checksum/crc8_test.go b/checksum/crc8_test.go new file mode 100644 index 000000000..15e93e453 --- /dev/null +++ b/checksum/crc8_test.go @@ -0,0 +1,61 @@ +// crc8_test.go +// description: Test for calculate crc8 +// author(s) [red_byte](https://github.com/i-redbyte) +// see crc8.go + +package checksum_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/checksum" +) + +var ( + CRC8 = checksum.CRCModel{0x07, 0x00, false, false, 0x00, "CRC-8"} + CRC8CDMA2000 = checksum.CRCModel{0x9B, 0xFF, false, false, 0x00, "CRC-8/CDMA2000"} + CRC8DARC = checksum.CRCModel{0x39, 0x00, true, true, 0x00, "CRC-8/DARC"} + CRC8DVBS2 = checksum.CRCModel{0xD5, 0x00, false, false, 0x00, "CRC-8/DVB-S2"} + CRC8EBU = checksum.CRCModel{0x1D, 0xFF, true, true, 0x00, "CRC-8/EBU"} + CRC8ICODE = checksum.CRCModel{0x1D, 0xFD, false, false, 0x00, "CRC-8/I-CODE"} + CRC8ITU = checksum.CRCModel{0x07, 0x00, false, false, 0x55, "CRC-8/ITU"} + CRC8MAXIM = checksum.CRCModel{0x31, 0x00, true, true, 0x00, "CRC-8/MAXIM"} + CRC8ROHC = checksum.CRCModel{0x07, 0xFF, true, true, 0x00, "CRC-8/ROHC"} + CRC8WCDMA = checksum.CRCModel{0x9B, 0x00, true, true, 0x00, "CRC-8/WCDMA"} +) + +func TestCalculateCRC8(t *testing.T) { + data := []byte("123456789") + tests := []struct { + name string + data []byte + model checksum.CRCModel + want uint8 + }{ + {CRC8.Name, data, CRC8, 0xF4}, + {CRC8CDMA2000.Name, data, CRC8CDMA2000, 0xDA}, + {CRC8DARC.Name, data, CRC8DARC, 0x15}, + {CRC8DVBS2.Name, data, CRC8DVBS2, 0xBC}, + {CRC8EBU.Name, data, CRC8EBU, 0x97}, + {CRC8ICODE.Name, data, CRC8ICODE, 0x7E}, + {CRC8ITU.Name, data, CRC8ITU, 0xA1}, + {CRC8MAXIM.Name, data, CRC8MAXIM, 0xA1}, + {CRC8ROHC.Name, data, CRC8ROHC, 0xD0}, + {CRC8WCDMA.Name, data, CRC8WCDMA, 0x25}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + fmt.Println(checksum.CRC8(test.data, test.model)) + if got := checksum.CRC8(test.data, test.model); got != test.want { + t.Errorf("CalculateCRC8() = %v, want %v", got, test.want) + } + }) + } +} + +func BenchmarkCalculateCRC8(b *testing.B) { + for i := 0; i < b.N; i++ { + checksum.CRC8([]byte("123456789"), CRC8) + } +} diff --git a/checksum/luhn.go b/checksum/luhn.go new file mode 100644 index 000000000..b28236d95 --- /dev/null +++ b/checksum/luhn.go @@ -0,0 +1,30 @@ +// lunh.go +// description: Luhn algorithm +// details: is a simple checksum formula used to validate a variety of identification numbers, such as credit card numbers, IMEI numbers, etc [Lunh](https://en.wikipedia.org/wiki/Luhn_algorithm) +// time complexity: O(n) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see lunh_test.go + +// Package checksum describes algorithms for finding various checksums +package checksum + +// Luhn validates the provided data using the Luhn algorithm. +func Luhn(s []byte) bool { + n := len(s) + number := 0 + result := 0 + for i := 0; i < n; i++ { + number = int(s[i]) - '0' + if i%2 != 0 { + result += number + continue + } + number *= 2 + if number > 9 { + number -= 9 + } + result += number + } + return result%10 == 0 +} diff --git a/checksum/luhn_test.go b/checksum/luhn_test.go new file mode 100644 index 000000000..e81560a64 --- /dev/null +++ b/checksum/luhn_test.go @@ -0,0 +1,41 @@ +// luhn_test.go +// description: Test for Luhn algorithm +// author(s) [red_byte](https://github.com/i-redbyte) +// see luhn.go + +package checksum_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/checksum" +) + +func TestLuhn(t *testing.T) { + tests := []struct { + name string + s []byte + want bool + }{ + {"check 4242424242424242", []byte("4242424242424242"), true}, + {"check 6200000000000005", []byte("6200000000000005"), true}, + {"check 5534200028533164", []byte("5534200028533164"), true}, + {"check 36227206271667", []byte("36227206271667"), true}, + {"check 471629309440", []byte("471629309440"), false}, + {"check 1111", []byte("1111"), false}, + {"check 12345674", []byte("12345674"), true}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := checksum.Luhn(test.s); got != test.want { + t.Errorf("LuhnAlgorithm() = %v, want %v", got, test.want) + } + }) + } +} + +func BenchmarkBruteForceFactorial(b *testing.B) { + for i := 0; i < b.N; i++ { + checksum.Luhn([]byte("4242424242424242")) + } +} diff --git a/cipher/caesar/caesar.go b/cipher/caesar/caesar.go new file mode 100644 index 000000000..f2f945e71 --- /dev/null +++ b/cipher/caesar/caesar.go @@ -0,0 +1,34 @@ +// Package caesar is the shift cipher +// description: Caesar cipher +// details : Caesar cipher is a type of substitution cipher in which each letter in the plaintext is shifted a certain number of places down the alphabet. +// time complexity: O(n) +// space complexity: O(n) +// ref: https://en.wikipedia.org/wiki/Caesar_cipher +package caesar + +// Encrypt encrypts by right shift of "key" each character of "input" +func Encrypt(input string, key int) string { + // if key is negative value, + // updates "key" the number which congruents to "key" modulo 26 + key8 := byte(key%26+26) % 26 + + var outputBuffer []byte + // b is a byte, which is the equivalent of uint8. + for _, b := range []byte(input) { + newByte := b + if 'A' <= b && b <= 'Z' { + outputBuffer = append(outputBuffer, 'A'+(newByte-'A'+key8)%26) + } else if 'a' <= b && b <= 'z' { + outputBuffer = append(outputBuffer, 'a'+(newByte-'a'+key8)%26) + } else { + outputBuffer = append(outputBuffer, newByte) + } + } + return string(outputBuffer) +} + +// Decrypt decrypts by left shift of "key" each character of "input" +func Decrypt(input string, key int) string { + // left shift of "key" is same as right shift of 26-"key" + return Encrypt(input, 26-key) +} diff --git a/cipher/caesar/caesar_test.go b/cipher/caesar/caesar_test.go new file mode 100644 index 000000000..1e22a8c34 --- /dev/null +++ b/cipher/caesar/caesar_test.go @@ -0,0 +1,167 @@ +package caesar + +import ( + "fmt" + "math/rand" + "testing" + "time" +) + +func TestEncrypt(t *testing.T) { + var caesarTestData = []struct { + description string + input string + key int + expected string + }{ + { + "Basic caesar encryption with letter 'a'", + "a", + 3, + "d", + }, + { + "Basic caesar encryption wrap around alphabet on letter 'z'", + "z", + 3, + "c", + }, + { + "Encrypt a simple string with caesar encryiption", + "hello", + 3, + "khoor", + }, + { + "Encrypt a simple string with key 13", + "hello", + 13, + "uryyb", + }, + { + "Encrypt a simple string with key -13", + "hello", + -13, + "uryyb", + }, + { + "With key of 26 output should be the same as the input", + "no change", + 26, + "no change", + }, + { + "Encrypt sentence with key 10", + "the quick brown fox jumps over the lazy dog.", + 10, + "dro aesmu lbygx pyh tewzc yfob dro vkji nyq.", + }, + { + "Encrypt sentence with key 10", + "The Quick Brown Fox Jumps over the Lazy Dog.", + 10, + "Dro Aesmu Lbygx Pyh Tewzc yfob dro Vkji Nyq.", + }, + } + for _, test := range caesarTestData { + t.Run(test.description, func(t *testing.T) { + actual := Encrypt(test.input, test.key) + if actual != test.expected { + t.Logf("FAIL: %s", test.description) + t.Fatalf("With input string '%s' and key '%d' was expecting '%s' but actual was '%s'", + test.input, test.key, test.expected, actual) + } + }) + } +} + +func TestDecrypt(t *testing.T) { + var caesarTestData = []struct { + description string + input string + key int + expected string + }{ + { + "Basic caesar decryption with letter 'a'", + "a", + 3, + "x", + }, + { + "Basic caesar decryption wrap around alphabet on letter 'z'", + "z", + 3, + "w", + }, + { + "Decrypt a simple string with caesar encryiption", + "hello", + 3, + "ebiil", + }, + { + "Decrypt a simple string with key 13", + "hello", + 13, + "uryyb", + }, + { + "Decrypt a simple string with key -13", + "hello", + -13, + "uryyb", + }, + { + "With key of 26 output should be the same as the input", + "no change", + 26, + "no change", + }, + { + "Decrypt sentence with key 10", + "Dro Aesmu Lbygx Pyh Tewzc yfob dro Vkji Nyq.", + 10, + "The Quick Brown Fox Jumps over the Lazy Dog.", + }, + } + + for _, test := range caesarTestData { + t.Run(test.description, func(t *testing.T) { + actual := Decrypt(test.input, test.key) + if actual != test.expected { + t.Logf("FAIL: %s", test.description) + t.Fatalf("With input string '%s' and key '%d' was expecting '%s' but actual was '%s'", + test.input, test.key, test.expected, actual) + } + }) + } +} + +func Example() { + const ( + key = 10 + input = "The Quick Brown Fox Jumps over the Lazy Dog." + ) + + encryptedText := Encrypt(input, key) + fmt.Printf("Encrypt=> key: %d, input: %s, encryptedText: %s\n", key, input, encryptedText) + + decryptedText := Decrypt(encryptedText, key) + fmt.Printf("Decrypt=> key: %d, input: %s, decryptedText: %s\n", key, encryptedText, decryptedText) + + // Output: + // Encrypt=> key: 10, input: The Quick Brown Fox Jumps over the Lazy Dog., encryptedText: Dro Aesmu Lbygx Pyh Tewzc yfob dro Vkji Nyq. + // Decrypt=> key: 10, input: Dro Aesmu Lbygx Pyh Tewzc yfob dro Vkji Nyq., decryptedText: The Quick Brown Fox Jumps over the Lazy Dog. +} + +func FuzzCaesar(f *testing.F) { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + f.Add("The Quick Brown Fox Jumps over the Lazy Dog.") + f.Fuzz(func(t *testing.T, input string) { + key := rnd.Intn(26) + if result := Decrypt(Encrypt(input, key), key); result != input { + t.Fatalf("With input: '%s' and key: %d\n\tExpected: '%s'\n\tGot: '%s'", input, key, input, result) + } + }) +} diff --git a/cipher/cipher_test.go b/cipher/cipher_test.go new file mode 100644 index 000000000..5a56f3ae3 --- /dev/null +++ b/cipher/cipher_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package cipher diff --git a/cipher/diffiehellman/diffiehellmankeyexchange.go b/cipher/diffiehellman/diffiehellmankeyexchange.go new file mode 100644 index 000000000..8a779efd4 --- /dev/null +++ b/cipher/diffiehellman/diffiehellmankeyexchange.go @@ -0,0 +1,45 @@ +// Package diffiehellman implements Diffie-Hellman Key Exchange Algorithm +// description: Diffie-Hellman key exchange +// details : Diffie-Hellman key exchange is a method of securely exchanging cryptographic keys over a public channel by combining private keys of two parties to generate a shared secret key. +// time complexity: O(log(n)) +// space complexity: O(1) +// for more information watch : https://www.youtube.com/watch?v=NmM9HA2MQGI +package diffiehellman + +const ( + generator = 3 + primeNumber int64 = 6700417 // prime number discovered by Leonhard Euler +) + +// GenerateShareKey : generates a key using client private key , generator and primeNumber +// this key can be made public +// shareKey = (g^key)%primeNumber +func GenerateShareKey(prvKey int64) int64 { + return modularExponentiation(generator, prvKey, primeNumber) +} + +// GenerateMutualKey : generates a mutual key that can be used by only alice and bob +// mutualKey = (shareKey^prvKey)%primeNumber +func GenerateMutualKey(prvKey, shareKey int64) int64 { + return modularExponentiation(shareKey, prvKey, primeNumber) +} + +// r = (b^e)%mod +func modularExponentiation(b, e, mod int64) int64 { + + //runs in O(log(n)) where n = e + //uses exponentiation by squaring to speed up the process + if mod == 1 { + return 0 + } + var r int64 = 1 + b = b % mod + for e > 0 { + if e&1 == 1 { + r = (r * b) % mod + } + e = e >> 1 + b = (b * b) % mod + } + return r +} diff --git a/cipher/diffiehellman/diffiehellmankeyexchange_test.go b/cipher/diffiehellman/diffiehellmankeyexchange_test.go new file mode 100644 index 000000000..7fe5ca7b9 --- /dev/null +++ b/cipher/diffiehellman/diffiehellmankeyexchange_test.go @@ -0,0 +1,41 @@ +package diffiehellman + +import ( + "crypto/rand" + "crypto/rsa" + "testing" +) + +func TestDiffieHellmanKeyExchange(t *testing.T) { + t.Run("Test 1: modularExponentiation", func(t *testing.T) { + var want int64 = 9 // (3^5)mod13 = 243mod13 = 9 + var prvKey int64 = 5 + var generator int64 = 3 + var primeNumber int64 = 13 + got := modularExponentiation(generator, prvKey, primeNumber) + if got != want { + t.Errorf(`with privateKey=%d, generator=%d and primeNumber=%d + modularExponentiation should result=%d, but resulted=%d`, prvKey, generator, primeNumber, want, got) + } + }) + + t.Run("Test 2: Key Exchange", func(t *testing.T) { + // generating a small sized rsa_cipher key for testing + alicePrvKey, _ := rsa.GenerateKey(rand.Reader, 31) + bobPrvKey, _ := rsa.GenerateKey(rand.Reader, 31) + + // alice and bob generates their respective share key with their privateKey + shareKeyByAlice := GenerateShareKey(alicePrvKey.D.Int64()) + shareKeyByBob := GenerateShareKey(bobPrvKey.D.Int64()) + + // generated share key now can be exchanged even via insecure channel + + // mutualKey can be computed using shared key + mutualKeyComputedByAlice := GenerateMutualKey(alicePrvKey.D.Int64(), shareKeyByBob) + mutualKeyComputedByBob := GenerateMutualKey(bobPrvKey.D.Int64(), shareKeyByAlice) + + if mutualKeyComputedByAlice != mutualKeyComputedByBob { + t.Errorf("mutual key computed by alice and bob should be same, but got un-equal") + } + }) +} diff --git a/cipher/doc.go b/cipher/doc.go new file mode 100644 index 000000000..0b1ebfb19 --- /dev/null +++ b/cipher/doc.go @@ -0,0 +1,2 @@ +// Package cipher is a package containing different implementations of certain ciphers +package cipher diff --git a/cipher/dsa/dsa.go b/cipher/dsa/dsa.go new file mode 100644 index 000000000..7d4eb574a --- /dev/null +++ b/cipher/dsa/dsa.go @@ -0,0 +1,196 @@ +/* +dsa.go +description: DSA encryption and decryption including key generation +details: [DSA wiki](https://en.wikipedia.org/wiki/Digital_Signature_Algorithm) +author(s): [ddaniel27](https://github.com/ddaniel27) +*/ +package dsa + +import ( + "crypto/rand" + "io" + "math/big" +) + +const ( + numMRTests = 64 // Number of Miller-Rabin tests + L = 1024 // Number of bits in p + N = 160 // Number of bits in q +) + +type ( + // parameters represents the DSA parameters + parameters struct { + P, Q, G *big.Int + } + + // dsa represents the DSA + dsa struct { + parameters + pubKey *big.Int // public key (y) + privKey *big.Int // private key (x) + } +) + +// New creates a new DSA instance +func New() *dsa { + d := new(dsa) + d.dsaParameterGeneration() + d.keyGen() + return d +} + +// Parameter generation for DSA +// 1. FIPS 186-4 specifies that the L and N values must be (1024, 160), (2048, 224), or (3072, 256) +// 2. Choose a N-bit prime q +// 3. Choose a L-bit prime p such that p-1 is a multiple of q +// 4. Choose an integer h randomly from the range [2, p-2] +// 5. Compute g = h^((p-1)/q) mod p +// 6. Return (p, q, g) +func (dsa *dsa) dsaParameterGeneration() { + var err error + p, q, bigInt := new(big.Int), new(big.Int), new(big.Int) + one, g, h := big.NewInt(1), big.NewInt(1), big.NewInt(2) + pBytes := make([]byte, L/8) + + // GPLoop is a label for the loop + // We use this loop to change the prime q if we don't find a prime p +GPLoop: + for { + // 2. Choose a N-bit prime q + q, err = rand.Prime(rand.Reader, N) + if err != nil { + panic(err) + } + + for i := 0; i < 4*L; i++ { + // 3. Choose a L-bit prime p such that p-1 is a multiple of q + // In this case we generate a random number of L bits + if _, err := io.ReadFull(rand.Reader, pBytes); err != nil { + panic(err) + } + + // This are the minimum conditions for p being a possible prime + pBytes[len(pBytes)-1] |= 1 // p is odd + pBytes[0] |= 0x80 // p has the highest bit set + p.SetBytes(pBytes) + + // Instead of using (p-1)%q == 0 + // We ensure that p-1 is a multiple of q and validates if p is prime + bigInt.Mod(p, q) + bigInt.Sub(bigInt, one) + p.Sub(p, bigInt) + if p.BitLen() < L || !p.ProbablyPrime(numMRTests) { // Check if p is prime and has L bits + continue + } + + dsa.P = p + dsa.Q = q + break GPLoop + } + } + + // 4. Choose an integer h randomly from the range [2, p-2]. Commonly, h = 2 + // 5. Compute g = h^((p-1)/q) mod p. In case g == 1, increment h until g != 1 + pm1 := new(big.Int).Sub(p, one) + + for g.Cmp(one) == 0 { + g.Exp(h, new(big.Int).Div(pm1, q), p) + h.Add(h, one) + } + + dsa.G = g +} + +// keyGen is key generation for DSA +// 1. Choose a random integer x from the range [1, q-1] +// 2. Compute y = g^x mod p +func (dsa *dsa) keyGen() { + // 1. Choose a random integer x from the range [1, q-1] + x, err := rand.Int(rand.Reader, new(big.Int).Sub(dsa.Q, big.NewInt(1))) + if err != nil { + panic(err) + } + + dsa.privKey = x + + // 2. Compute y = g^x mod p + dsa.pubKey = new(big.Int).Exp(dsa.G, x, dsa.P) +} + +// Sign is signature generation for DSA +// 1. Choose a random integer k from the range [1, q-1] +// 2. Compute r = (g^k mod p) mod q +// 3. Compute s = (k^-1 * (H(m) + x*r)) mod q +func Sign(m []byte, p, q, g, x *big.Int) (r, s *big.Int) { + // 1. Choose a random integer k from the range [1, q-1] + k, err := rand.Int(rand.Reader, new(big.Int).Sub(q, big.NewInt(1))) + if err != nil { + panic(err) + } + + // 2. Compute r = (g^k mod p) mod q + r = new(big.Int).Exp(g, k, p) + r.Mod(r, q) + + // 3. Compute s = (k^-1 * (H(m) + x*r)) mod q + h := new(big.Int).SetBytes(m) // This should be the hash of the message + s = new(big.Int).ModInverse(k, q) // k^-1 mod q + s.Mul( + s, + new(big.Int).Add( // (H(m) + x*r) + h, + new(big.Int).Mul(x, r), + ), + ) + s.Mod(s, q) // mod q + + return r, s +} + +// Verify is signature verification for DSA +// 1. Compute w = s^-1 mod q +// 2. Compute u1 = (H(m) * w) mod q +// 3. Compute u2 = (r * w) mod q +// 4. Compute v = ((g^u1 * y^u2) mod p) mod q +// 5. If v == r, the signature is valid +func Verify(m []byte, r, s, p, q, g, y *big.Int) bool { + // 1. Compute w = s^-1 mod q + w := new(big.Int).ModInverse(s, q) + + // 2. Compute u1 = (H(m) * w) mod q + h := new(big.Int).SetBytes(m) // This should be the hash of the message + u1 := new(big.Int).Mul(h, w) + u1.Mod(u1, q) + + // 3. Compute u2 = (r * w) mod q + u2 := new(big.Int).Mul(r, w) + u2.Mod(u2, q) + + // 4. Compute v = ((g^u1 * y^u2) mod p) mod q + v := new(big.Int).Exp(g, u1, p) + v.Mul( + v, + new(big.Int).Exp(y, u2, p), + ) + v.Mod(v, p) + v.Mod(v, q) + + // 5. If v == r, the signature is valid + return v.Cmp(r) == 0 +} + +// GetPublicKey returns the public key (y) +func (dsa *dsa) GetPublicKey() *big.Int { + return dsa.pubKey +} + +// GetParameters returns the DSA parameters (p, q, g) +func (dsa *dsa) GetParameters() parameters { + return dsa.parameters +} + +// GetPrivateKey returns the private Key (x) +func (dsa *dsa) GetPrivateKey() *big.Int { + return dsa.privKey +} diff --git a/cipher/dsa/dsa_test.go b/cipher/dsa/dsa_test.go new file mode 100644 index 000000000..3ef1930e4 --- /dev/null +++ b/cipher/dsa/dsa_test.go @@ -0,0 +1,114 @@ +package dsa_test + +import ( + "math/big" + "testing" + + "github.com/TheAlgorithms/Go/cipher/dsa" +) + +func TestDSA(t *testing.T) { + tests := []struct { + name string + message string + alter bool + want bool + }{ + { + name: "valid signature", + message: "Hello, world!", + alter: false, + want: true, + }, + { + name: "invalid signature", + message: "Hello, world!", + alter: true, + want: false, + }, + } + // Generate a DSA key pair + dsaInstance := dsa.New() + pubKey := dsaInstance.GetPublicKey() + params := dsaInstance.GetParameters() + privKey := dsaInstance.GetPrivateKey() + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + + // Sign the message + r, s := dsa.Sign( + []byte(tt.message), + params.P, + params.Q, + params.G, + privKey, + ) + + if tt.alter { + // Alter the signature + r.Add(r, big.NewInt(1)) + } + + // Verify the signature + if got := dsa.Verify( + []byte(tt.message), + r, + s, + params.P, + params.Q, + params.G, + pubKey, + ); got != tt.want { + t.Errorf("got %v, want %v", got, tt.want) + } + }) + } +} + +/* ------------------- BENCHMARKS ------------------- */ +func BenchmarkDSANew(b *testing.B) { + for i := 0; i < b.N; i++ { + dsa.New() + } +} + +func BenchmarkDSASign(b *testing.B) { + dsaInstance := dsa.New() + params := dsaInstance.GetParameters() + privKey := dsaInstance.GetPrivateKey() + for i := 0; i < b.N; i++ { + dsa.Sign( + []byte("Hello, World!"), + params.P, + params.Q, + params.G, + privKey, + ) + } +} + +func BenchmarkDSAVerify(b *testing.B) { + dsaInstance := dsa.New() + pubKey := dsaInstance.GetPublicKey() + params := dsaInstance.GetParameters() + privKey := dsaInstance.GetPrivateKey() + r, s := dsa.Sign( + []byte("Hello, World!"), + params.P, + params.Q, + params.G, + privKey, + ) + for i := 0; i < b.N; i++ { + dsa.Verify( + []byte("Hello, World!"), + r, + s, + params.P, + params.Q, + params.G, + pubKey, + ) + } +} diff --git a/cipher/polybius/polybius.go b/cipher/polybius/polybius.go new file mode 100644 index 000000000..e022dabae --- /dev/null +++ b/cipher/polybius/polybius.go @@ -0,0 +1,102 @@ +// Package polybius is encrypting method with polybius square +// description: Polybius square +// details : The Polybius algorithm is a simple algorithm that is used to encode a message by converting each letter to a pair of numbers. +// time complexity: O(n) +// space complexity: O(n) +// ref: https://en.wikipedia.org/wiki/Polybius_square#Hybrid_Polybius_Playfair_Cipher +package polybius + +import ( + "fmt" + "math" + "strings" +) + +// Polybius is struct having size, characters, and key +type Polybius struct { + size int + characters string + key string +} + +// NewPolybius returns a pointer to object of Polybius. +// If the size of "chars" is longer than "size", +// "chars" are truncated to "size". +func NewPolybius(key string, size int, chars string) (*Polybius, error) { + if size < 0 { + return nil, fmt.Errorf("provided size %d cannot be negative", size) + } + key = strings.ToUpper(key) + if size > len(chars) { + return nil, fmt.Errorf("provided size %d is too small to use to slice string %q of len %d", size, chars, len(chars)) + } + for _, r := range chars { + if (r < 'a' || r > 'z') && (r < 'A' || r > 'Z') { + return nil, fmt.Errorf("provided string %q should only contain latin characters", chars) + } + } + chars = strings.ToUpper(chars)[:size] + for i, r := range chars { + if strings.ContainsRune(chars[i+1:], r) { + return nil, fmt.Errorf("%q contains same character %q", chars[i+1:], r) + } + } + + if len(key) != size*size { + return nil, fmt.Errorf("len(key): %d must be as long as size squared: %d", len(key), size*size) + } + return &Polybius{size, chars, key}, nil +} + +// Encrypt encrypts with polybius encryption +func (p *Polybius) Encrypt(text string) (string, error) { + encryptedText := "" + for _, char := range strings.ToUpper(text) { + encryptedChar, err := p.encipher(char) + if err != nil { + return "", fmt.Errorf("failed encipher: %w", err) + } + encryptedText += encryptedChar + } + return encryptedText, nil +} + +// Decrypt decrypts with polybius encryption +func (p *Polybius) Decrypt(text string) (string, error) { + chars := []rune(strings.ToUpper(text)) + decryptedText := "" + for i := 0; i < len(chars); i += 2 { + decryptedChar, err := p.decipher(chars[i:int(math.Min(float64(i+2), float64(len(chars))))]) + if err != nil { + return "", fmt.Errorf("failed decipher: %w", err) + } + decryptedText += decryptedChar + } + return decryptedText, nil +} + +func (p *Polybius) encipher(char rune) (string, error) { + index := strings.IndexRune(p.key, char) + if index < 0 { + return "", fmt.Errorf("%q does not exist in keys", char) + } + row := index / p.size + col := index % p.size + chars := []rune(p.characters) + return string([]rune{chars[row], chars[col]}), nil +} + +func (p *Polybius) decipher(chars []rune) (string, error) { + if len(chars) != 2 { + return "", fmt.Errorf("the size of \"chars\" must be even") + } + row := strings.IndexRune(p.characters, chars[0]) + if row < 0 { + return "", fmt.Errorf("%c does not exist in characters", chars[0]) + } + col := strings.IndexRune(p.characters, chars[1]) + if col < 0 { + return "", fmt.Errorf("%c does not exist in characters", chars[1]) + } + return string(p.key[row*p.size+col]), nil +} diff --git a/cipher/polybius/polybius_test.go b/cipher/polybius/polybius_test.go new file mode 100644 index 000000000..03fb4ca00 --- /dev/null +++ b/cipher/polybius/polybius_test.go @@ -0,0 +1,190 @@ +package polybius + +import ( + "fmt" + "log" + "strings" + "testing" +) + +func ExampleNewPolybius() { + // initialize + const ( + plainText = "HogeFugaPiyoSpam" + size = 5 + characters = "HogeF" + key = "abcdefghijklmnopqrstuvwxy" + ) + p, err := NewPolybius(key, size, characters) + if err != nil { + log.Fatalf("failed NewPolybius: %v", err) + } + encryptedText, err := p.Encrypt(plainText) + if err != nil { + log.Fatalf("failed Encrypt: %v", err) + } + fmt.Printf("Encrypt=> plainText: %s, encryptedText: %s\n", plainText, encryptedText) + + decryptedText, err := p.Decrypt(encryptedText) + if err != nil { + log.Fatalf("failed Decrypt: %v", err) + } + fmt.Printf("Decrypt=> encryptedText: %s, decryptedText: %s\n", encryptedText, decryptedText) + + // Output: + // Encrypt=> plainText: HogeFugaPiyoSpam, encryptedText: OGGFOOHFOHFHOOHHEHOEFFGFEEEHHHGG + // Decrypt=> encryptedText: OGGFOOHFOHFHOOHHEHOEFFGFEEEHHHGG, decryptedText: HOGEFUGAPIYOSPAM +} + +func TestNewPolybius(t *testing.T) { + t.Parallel() + cases := []struct { + name string + size int + characters string + key string + wantErr string + }{ + { + name: "correct initialization", size: 5, characters: "HogeF", key: "abcdefghijklmnopqrstuvwxy", wantErr: "", + }, + { + name: "truncate characters", size: 5, characters: "HogeFuga", key: "abcdefghijklmnopqrstuvwxy", wantErr: "", + }, + { + name: "invalid key", size: 5, characters: "HogeFuga", key: "abcdefghi", wantErr: "len(key): 9 must be as long as size squared: 25", + }, + { + name: "invalid characters", size: 5, characters: "HogeH", key: "abcdefghijklmnopqrstuvwxy", wantErr: "\"OGEH\" contains same character 'H'", + }, + } + + for _, tc := range cases { + t.Run(tc.name, func(t *testing.T) { + _, err := NewPolybius(tc.key, tc.size, tc.characters) + if err != nil && err.Error() != tc.wantErr { + t.Errorf("failed NewPolybius: %v", err) + } + }) + } +} + +func TestPolybiusEncrypt(t *testing.T) { + t.Parallel() + cases := []struct { + name string + text string + want string + }{ + { + name: "correct encryption", text: "HogeFugaPiyoSpam", want: "OGGFOOHFOHFHOOHHEHOEFFGFEEEHHHGG", + }, + { + name: "invalid encryption", text: "hogz", want: "failed encipher: 'Z' does not exist in keys", + }, + } + // initialize + const ( + size = 5 + characters = "HogeF" + key = "abcdefghijklmnopqrstuvwxy" + ) + p, err := NewPolybius(key, size, characters) + if err != nil { + t.Fatalf("failed NewPolybius: %v", err) + } + for _, tc := range cases { + t.Run(tc.name, func(t *testing.T) { + encrypted, err := p.Encrypt(tc.text) + if err != nil { + if err.Error() != tc.want { + t.Errorf("failed Encrypt: %v", err) + } + } else if encrypted != tc.want { + t.Errorf("Encrypt: %v, want: %v", encrypted, tc.want) + } + }) + } +} + +func TestPolybiusDecrypt(t *testing.T) { + t.Parallel() + cases := []struct { + name string + text string + want string + }{ + { + name: "correct decryption", text: "OGGFOOHFOHFHOOHHEHOEFFGFEEEHHHGG", want: "HOGEFUGAPIYOSPAM", + }, + { + name: "invalid decryption(position of even number)", text: "hogz", want: "failed decipher: Z does not exist in characters", + }, + { + name: "invalid decryption(position of odd number)", text: "hode", want: "failed decipher: D does not exist in characters", + }, + { + name: "invalid text size which is odd", text: "hog", want: "failed decipher: the size of \"chars\" must be even", + }, + } + // initialize + const ( + size = 5 + characters = "HogeF" + key = "abcdefghijklmnopqrstuvwxy" + ) + p, err := NewPolybius(key, size, characters) + if err != nil { + t.Fatalf("failed NewPolybius: %v", err) + } + for _, tc := range cases { + t.Run(tc.name, func(t *testing.T) { + encrypted, err := p.Decrypt(tc.text) + if err != nil { + if err.Error() != tc.want { + t.Errorf("failed Encrypt: %v", err) + } + } else if encrypted != tc.want { + t.Errorf("Encrypt: %v, want: %v", encrypted, tc.want) + } + }) + } +} + +func FuzzPolybius(f *testing.F) { + const ( + size = 5 + characters = "HogeF" + key = "abcdefghijklmnopqrstuvwxy" + ) + f.Add(size, characters, key) + f.Fuzz(func(t *testing.T, size int, characters, key string) { + p, err := NewPolybius(key, size, characters) + switch { + case err == nil: + case strings.Contains(err.Error(), "cannot be negative"), + strings.Contains(err.Error(), "is too small"), + strings.Contains(err.Error(), "should only contain latin characters"), + strings.Contains(err.Error(), "contains same character"), + strings.Contains(err.Error(), "must be as long as size squared"): + return + default: + t.Fatalf("unexpected error when creating a new polybius variable: %v", err) + } + encrypted, err := p.Encrypt(characters) + switch { + case err == nil: + case strings.Contains(err.Error(), "does not exist in keys"): + return + default: + t.Fatalf("unexpected error during encryption: %v", err) + } + decrypted, err := p.Decrypt(encrypted) + if err != nil { + t.Fatalf("unexpected error during decryption: %v", err) + } + if decrypted != strings.ToUpper(characters) { + t.Errorf("Expecting output to match with %q but was %q", characters, decrypted) + } + }) +} diff --git a/cipher/railfence/railfence.go b/cipher/railfence/railfence.go new file mode 100644 index 000000000..aeeaed3fa --- /dev/null +++ b/cipher/railfence/railfence.go @@ -0,0 +1,81 @@ +// railfence.go +// description: Rail Fence Cipher +// details: The rail fence cipher is a an encryption algorithm that uses a rail fence pattern to encode a message. it is a type of transposition cipher that rearranges the characters of the plaintext to form the ciphertext. +// time complexity: O(n) +// space complexity: O(n) +// ref: https://en.wikipedia.org/wiki/Rail_fence_cipher +package railfence + +import ( + "strings" +) + +func Encrypt(text string, rails int) string { + if rails == 1 { + return text + } + + // Create a matrix for the rail fence pattern + matrix := make([][]rune, rails) + for i := range matrix { + matrix[i] = make([]rune, len(text)) + } + + // Fill the matrix + dirDown := false + row, col := 0, 0 + for _, char := range text { + if row == 0 || row == rails-1 { + dirDown = !dirDown + } + matrix[row][col] = char + col++ + if dirDown { + row++ + } else { + row-- + } + } + var result strings.Builder + for _, line := range matrix { + for _, char := range line { + if char != 0 { + result.WriteRune(char) + } + } + } + + return result.String() +} +func Decrypt(cipherText string, rails int) string { + if rails == 1 || rails >= len(cipherText) { + return cipherText + } + + // Placeholder for the decrypted message + decrypted := make([]rune, len(cipherText)) + + // Calculate the zigzag pattern and place characters accordingly + index := 0 + for rail := 0; rail < rails; rail++ { + position := rail + down := true // Direction flag + for position < len(cipherText) { + decrypted[position] = rune(cipherText[index]) + index++ + + // Determine the next position based on the current rail and direction + if rail == 0 || rail == rails-1 { + position += 2 * (rails - 1) + } else if down { + position += 2 * (rails - 1 - rail) + down = false + } else { + position += 2 * rail + down = true + } + } + } + + return string(decrypted) +} diff --git a/cipher/railfence/railfence_test.go b/cipher/railfence/railfence_test.go new file mode 100644 index 000000000..7f7bfa53a --- /dev/null +++ b/cipher/railfence/railfence_test.go @@ -0,0 +1,91 @@ +package railfence + +import ( + "testing" +) + +func TestEncrypt(t *testing.T) { + var railFenceTestData = []struct { + description string + input string + rails int + expected string + }{ + { + "Encrypt with 2 rails", + "hello", + 2, + "hloel", + }, + { + "Encrypt with 3 rails", + "hello world", + 3, + "horel ollwd", + }, + { + "Encrypt with edge case: 1 rail", + "hello", + 1, + "hello", + }, + { + "Encrypt with more rails than letters", + "hi", + 100, + "hi", + }, + } + + for _, test := range railFenceTestData { + t.Run(test.description, func(t *testing.T) { + actual := Encrypt(test.input, test.rails) + if actual != test.expected { + t.Errorf("FAIL: %s - Encrypt(%s, %d) = %s, want %s", test.description, test.input, test.rails, actual, test.expected) + } + }) + } +} + +func TestDecrypt(t *testing.T) { + var railFenceTestData = []struct { + description string + input string + rails int + expected string + }{ + { + "Decrypt with 2 rails", + "hloel", + 2, + "hello", + }, + { + "Decrypt with 3 rails", + "ho l lewrdlo", + 3, + "hld olle wor", + }, + { + "Decrypt with edge case: 1 rail", + "hello", + 1, + "hello", + }, + { + "Decrypt with more rails than letters", + "hi", + 100, + "hi", + }, + } + + for _, test := range railFenceTestData { + t.Run(test.description, func(t *testing.T) { + actual := Decrypt(test.input, test.rails) + if actual != test.expected { + t.Errorf("FAIL: %s - Decrypt(%s, %d) = %s, want %s", test.description, test.input, test.rails, actual, test.expected) + } + }) + } +} diff --git a/cipher/rot13/rot13.go b/cipher/rot13/rot13.go new file mode 100644 index 000000000..d50d97c53 --- /dev/null +++ b/cipher/rot13/rot13.go @@ -0,0 +1,16 @@ +// Package rot13 is a simple letter substitution cipher that replaces a letter with the 13th letter after it in the alphabet. +// description: ROT13 +// details: ROT13 is a simple letter substitution cipher that replaces a letter with the 13th letter after it in the alphabet. it is a special case of the Caesar cipher +// time complexity: O(n) +// space complexity: O(n) +// ref: https://en.wikipedia.org/wiki/ROT13 +package rot13 + +import ( + "github.com/TheAlgorithms/Go/cipher/caesar" +) + +// rot13 is a special case, which is fixed the shift of 13, of the Caesar cipher +func rot13(input string) string { + return caesar.Encrypt(input, 13) +} diff --git a/cipher/rot13/rot13_test.go b/cipher/rot13/rot13_test.go new file mode 100644 index 000000000..235039bbb --- /dev/null +++ b/cipher/rot13/rot13_test.go @@ -0,0 +1,82 @@ +package rot13 + +import ( + "testing" +) + +var rot13TestData = []struct { + description string + input string + expected string +}{ + { + "Basic rotation with letter 'a' gives 'n", + "a", + "n", + }, + { + "Rotation with wrapping around alphabet on letter 'z' gives 'm'", + "z", + "m", + }, + { + "Rotation on 'hello world'", + "hello world", + "uryyb jbeyq", + }, + { + "Rotation on the rotation of 'hello world' gives 'hello world' back", + "uryyb jbeyq", + "hello world", + }, + { + "Full sentence rotation", + "the quick brown fox jumps over the lazy dog.", + "gur dhvpx oebja sbk whzcf bire gur ynml qbt.", + }, + { + "Sentence from Rot13.go main function", + "we'll just make him an offer he can't refuse... tell me you get the pop culture reference", + "jr'yy whfg znxr uvz na bssre ur pna'g ershfr... gryy zr lbh trg gur cbc phygher ersrerapr", + }, +} + +func TestRot13Encrypt(t *testing.T) { + for _, test := range rot13TestData { + t.Run(test.description, func(t *testing.T) { + input := test.input + expected := test.expected + assertRot13Output(t, input, expected) + }) + } +} + +func TestRot13Decrypt(t *testing.T) { + for _, test := range rot13TestData { + t.Run(test.description, func(t *testing.T) { + input := test.expected + expected := test.input + assertRot13Output(t, input, expected) + }) + } +} + +func assertRot13Output(t *testing.T, input, expected string) { + actual := rot13(input) + if actual != expected { + t.Fatalf("With input string %q was expecting %q but actual was %q", + input, expected, actual) + } +} + +func FuzzRot13(f *testing.F) { + for _, rot13TestInput := range rot13TestData { + f.Add(rot13TestInput.input) + } + f.Fuzz(func(t *testing.T, input string) { + if result := rot13(rot13(input)); result != input { + t.Fatalf("With input string %q was expecting %q but actual was %q", + input, input, result) + } + }) +} diff --git a/cipher/rsa/rsa.go b/cipher/rsa/rsa.go new file mode 100644 index 000000000..1eb506e2c --- /dev/null +++ b/cipher/rsa/rsa.go @@ -0,0 +1,56 @@ +// rsa.go +// description: Simple RSA algorithm implementation +// details: +// A simple RSA Encryption and Decryption algorithm. +// It uses prime numbers that fit in int64 datatypes and +// thus both the Encrypt and Decrypt are not a production +// ready implementation. The OpenSSL implementation of RSA +// also adds a padding which is not present in this algorithm. +// time complexity: O(n) +// space complexity: O(n) +// author(s) [Taj](https://github.com/tjgurwara99) +// see rsa_test.go + +// Package rsa shows a simple implementation of RSA algorithm +package rsa + +import ( + "errors" + + modular "github.com/TheAlgorithms/Go/math/modular" +) + +// ErrorFailedToEncrypt Raised when Encrypt function fails to encrypt the message +var ErrorFailedToEncrypt = errors.New("failed to Encrypt") + +// ErrorFailedToDecrypt Raised when Decrypt function fails to decrypt the encrypted message +var ErrorFailedToDecrypt = errors.New("failed to Decrypt") + +// Encrypt encrypts based on the RSA algorithm - uses modular exponentitation in math directory +func Encrypt(message []rune, publicExponent, modulus int64) ([]rune, error) { + var encrypted []rune + + for _, letter := range message { + encryptedLetter, err := modular.Exponentiation(int64(letter), publicExponent, modulus) + if err != nil { + return nil, ErrorFailedToEncrypt + } + encrypted = append(encrypted, rune(encryptedLetter)) + } + + return encrypted, nil +} + +// Decrypt decrypts encrypted rune slice based on the RSA algorithm +func Decrypt(encrypted []rune, privateExponent, modulus int64) (string, error) { + var decrypted []rune + + for _, letter := range encrypted { + decryptedLetter, err := modular.Exponentiation(int64(letter), privateExponent, modulus) + if err != nil { + return "", ErrorFailedToDecrypt + } + decrypted = append(decrypted, rune(decryptedLetter)) + } + return string(decrypted), nil +} diff --git a/cipher/rsa/rsa2.go b/cipher/rsa/rsa2.go new file mode 100644 index 000000000..18b6e1391 --- /dev/null +++ b/cipher/rsa/rsa2.go @@ -0,0 +1,125 @@ +/* +rsa2.go +description: RSA encryption and decryption including key generation +details: [RSA wiki](https://en.wikipedia.org/wiki/RSA_(cryptosystem)) +time complexity: O(n) +space complexity: O(1) +author(s): [ddaniel27](https://github.com/ddaniel27) +*/ +package rsa + +import ( + "encoding/binary" + "fmt" + "math/big" + "math/rand" + + "github.com/TheAlgorithms/Go/math/gcd" + "github.com/TheAlgorithms/Go/math/lcm" + "github.com/TheAlgorithms/Go/math/modular" + "github.com/TheAlgorithms/Go/math/prime" +) + +// rsa struct contains the public key, private key and modulus +type rsa struct { + publicKey uint64 + privateKey uint64 + modulus uint64 +} + +// New initializes the RSA algorithm +// returns the RSA object +func New() *rsa { + // The following code generates keys for RSA encryption/decryption + // 1. Choose two large prime numbers, p and q and compute n = p * q + p, q := randomPrime() // p and q stands for prime numbers + modulus := p * q // n stands for common number + + // 2. Compute the totient of n, lcm(p-1, q-1) + totient := uint64(lcm.Lcm(int64(p-1), int64(q-1))) + + // 3. Choose an integer e such that 1 < e < totient(n) and gcd(e, totient(n)) = 1 + publicKey := uint64(2) // e stands for encryption key (public key) + for publicKey < totient { + if gcd.Recursive(int64(publicKey), int64(totient)) == 1 { + break + } + publicKey++ + } + + // 4. Compute d such that d * e ≡ 1 (mod totient(n)) + inv, _ := modular.Inverse(int64(publicKey), int64(totient)) + privateKey := uint64(inv) + + return &rsa{ + publicKey: publicKey, + privateKey: privateKey, + modulus: modulus, + } +} + +// EncryptString encrypts the data using RSA algorithm +// returns the encrypted string +func (rsa *rsa) EncryptString(data string) string { + var nums []byte + + for _, char := range data { + slice := make([]byte, 8) + binary.BigEndian.PutUint64( // convert uint64 to byte slice + slice, + encryptDecryptInt(rsa.publicKey, rsa.modulus, uint64(char)), // encrypt each character + ) + nums = append(nums, slice...) + } + + return string(nums) +} + +// DecryptString decrypts the data using RSA algorithm +// returns the decrypted string +func (rsa *rsa) DecryptString(data string) string { + result := "" + middle := []byte(data) + + for i := 0; i < len(middle); i += 8 { + if i+8 > len(middle) { + break + } + + slice := middle[i : i+8] + num := binary.BigEndian.Uint64(slice) // convert byte slice to uint64 + result += fmt.Sprintf("%c", encryptDecryptInt(rsa.privateKey, rsa.modulus, num)) + } + + return result +} + +// GetPublicKey returns the public key and modulus +func (rsa *rsa) GetPublicKey() (uint64, uint64) { + return rsa.publicKey, rsa.modulus +} + +// GetPrivateKey returns the private key +func (rsa *rsa) GetPrivateKey() uint64 { + return rsa.privateKey +} + +// encryptDecryptInt encrypts or decrypts the data using RSA algorithm +func encryptDecryptInt(e, n, data uint64) uint64 { + pow := new(big.Int).Exp(big.NewInt(int64(data)), big.NewInt(int64(e)), big.NewInt(int64(n))) + return pow.Uint64() +} + +// randomPrime returns two random prime numbers +func randomPrime() (uint64, uint64) { + sieve := prime.SieveEratosthenes(1000) + sieve = sieve[10:] // remove first 10 prime numbers (small numbers) + index1 := rand.Intn(len(sieve)) + index2 := rand.Intn(len(sieve)) + + for index1 == index2 { + index2 = rand.Intn(len(sieve)) + } + + return uint64(sieve[index1]), uint64(sieve[index2]) +} diff --git a/cipher/rsa/rsa2_test.go b/cipher/rsa/rsa2_test.go new file mode 100644 index 000000000..29e15c557 --- /dev/null +++ b/cipher/rsa/rsa2_test.go @@ -0,0 +1,49 @@ +package rsa_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/cipher/rsa" +) + +func TestRSA(t *testing.T) { + tests := []struct { + name string + message string + }{ + { + name: "Encrypt letter 'a' and decrypt it back", + message: "a", + }, + { + name: "Encrypt 'Hello, World!' and decrypt it back", + message: "Hello, World!", + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + rsa := rsa.New() + encrypted := rsa.EncryptString(tt.message) + decrypted := rsa.DecryptString(encrypted) + if decrypted != tt.message { + t.Errorf("expected %s, got %s", tt.message, decrypted) + } + }) + } +} + +func BenchmarkRSAEncryption(b *testing.B) { + rsa := rsa.New() + for i := 0; i < b.N; i++ { + rsa.EncryptString("Hello, World!") + } +} + +func BenchmarkRSADecryption(b *testing.B) { + rsa := rsa.New() + encrypted := rsa.EncryptString("Hello, World!") + for i := 0; i < b.N; i++ { + rsa.DecryptString(encrypted) + } +} diff --git a/cipher/rsa/rsa_test.go b/cipher/rsa/rsa_test.go new file mode 100644 index 000000000..43ce90245 --- /dev/null +++ b/cipher/rsa/rsa_test.go @@ -0,0 +1,97 @@ +// rsa_test.go +// description: Test for RSA Encrypt and Decrypt algorithms +// author(s) [Taj](https://github.com/tjgurwara99) +// see rsa.go + +package rsa + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/gcd" + "github.com/TheAlgorithms/Go/math/lcm" + "github.com/TheAlgorithms/Go/math/modular" +) + +var rsaTestData = []struct { + description string + input string +}{ + { + "Encrypt letter 'a'", + "a", + }, + { + "Encrypt 'hello world'", + "hello world", + }, + { + "Encrypt full sentence", + "the quick brown fox jumps over the lazy dog.", + }, + { + "Encrypt full sentence from rsacipher.go main function", + "I think RSA is really great", + }, +} + +func testPrecondition(t *testing.T) (int64, int64, int64) { + // Both prime numbers + t.Helper() + p := int64(61) + q := int64(53) + n := p * q + delta := lcm.Lcm(p-1, q-1) + e := int64(17) // Coprime with delta + if gcd.Recursive(e, delta) != 1 { + t.Fatal("something went wrong: prime numbers are chosen statically and it shouldn't fail at this stage") + } + d, err := modular.Inverse(e, delta) + if err != nil { + t.Fatalf("something went wrong: problem with %q: %v", "modular.Inverse", err) + } + return e, d, n +} + +func TestEncryptDecrypt(t *testing.T) { + for _, test := range rsaTestData { + t.Run(test.description, func(t *testing.T) { + e, d, n := testPrecondition(t) + message := []rune(test.input) + encrypted, err := Encrypt(message, e, n) + if err != nil { + t.Fatalf("Failed to Encrypt test string:\n\tDescription: %v\n\tErrMessage: %v", test.description, err) + } + + decrypted, err := Decrypt(encrypted, d, n) + if err != nil { + t.Fatalf("Failed to Decrypt test message:\n\tDescription: %v\n\tErrMessage: %v", test.description, err) + } + + if actual := test.input; actual != decrypted { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expecting %v, actual %v", decrypted, actual) + } + }) + } +} + +func FuzzRsa(f *testing.F) { + for _, rsaTestInput := range rsaTestData { + f.Add(rsaTestInput.input) + } + f.Fuzz(func(t *testing.T, input string) { + e, d, n := testPrecondition(t) + encrypted, err := Encrypt([]rune(input), e, n) + if err != nil { + t.Fatalf("failed to encrypt string: %v", err) + } + decrypted, err := Decrypt(encrypted, d, n) + if err != nil { + t.Fatalf("failed to decrypt string: %v", err) + } + if decrypted != input { + t.Fatalf("expected: %q, got: %q", input, decrypted) + } + }) +} diff --git a/cipher/transposition/transposition.go b/cipher/transposition/transposition.go new file mode 100644 index 000000000..7a18293ea --- /dev/null +++ b/cipher/transposition/transposition.go @@ -0,0 +1,107 @@ +// transposition.go +// description: Transposition cipher +// details: +// Implementation "Transposition cipher" is a method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext [Transposition cipher](https://en.wikipedia.org/wiki/Transposition_cipher) +// time complexity: O(n) +// space complexity: O(n) +// author(s) [red_byte](https://github.com/i-redbyte) +// see transposition_test.go + +package transposition + +import ( + "errors" + "fmt" + "sort" + "strings" +) + +var ErrNoTextToEncrypt = errors.New("no text to encrypt") +var ErrKeyMissing = errors.New("missing Key") + +const placeholder = ' ' + +func getKey(keyWord string) []int { + keyWord = strings.ToLower(keyWord) + word := []rune(keyWord) + var sortedWord = make([]rune, len(word)) + copy(sortedWord, word) + sort.Slice(sortedWord, func(i, j int) bool { return sortedWord[i] < sortedWord[j] }) + usedLettersMap := make(map[rune]int) + wordLength := len(word) + resultKey := make([]int, wordLength) + for i := 0; i < wordLength; i++ { + char := word[i] + numberOfUsage := usedLettersMap[char] + resultKey[i] = getIndex(sortedWord, char) + numberOfUsage + 1 //+1 -so that indexing does not start at 0 + numberOfUsage++ + usedLettersMap[char] = numberOfUsage + } + return resultKey +} + +func getIndex(wordSet []rune, subString rune) int { + n := len(wordSet) + for i := 0; i < n; i++ { + if wordSet[i] == subString { + return i + } + } + return 0 +} + +func Encrypt(text []rune, keyWord string) ([]rune, error) { + key := getKey(keyWord) + keyLength := len(key) + textLength := len(text) + if keyLength <= 0 { + return nil, ErrKeyMissing + } + if textLength <= 0 { + return nil, ErrNoTextToEncrypt + } + if text[len(text)-1] == placeholder { + return nil, fmt.Errorf("%w: cannot encrypt a text, %q, ending with the placeholder char %q", ErrNoTextToEncrypt, text, placeholder) + } + n := textLength % keyLength + + for i := 0; i < keyLength-n; i++ { + text = append(text, placeholder) + } + textLength = len(text) + var result []rune + for i := 0; i < textLength; i += keyLength { + transposition := make([]rune, keyLength) + for j := 0; j < keyLength; j++ { + transposition[key[j]-1] = text[i+j] + } + result = append(result, transposition...) + } + return result, nil +} + +func Decrypt(text []rune, keyWord string) ([]rune, error) { + key := getKey(keyWord) + textLength := len(text) + if textLength <= 0 { + return nil, ErrNoTextToEncrypt + } + keyLength := len(key) + if keyLength <= 0 { + return nil, ErrKeyMissing + } + n := textLength % keyLength + for i := 0; i < keyLength-n; i++ { + text = append(text, placeholder) + } + var result []rune + for i := 0; i < textLength; i += keyLength { + transposition := make([]rune, keyLength) + for j := 0; j < keyLength; j++ { + transposition[j] = text[i+key[j]-1] + } + result = append(result, transposition...) + } + result = []rune(strings.TrimRight(string(result), string(placeholder))) + return result, nil +} diff --git a/cipher/transposition/transposition_test.go b/cipher/transposition/transposition_test.go new file mode 100644 index 000000000..250f43832 --- /dev/null +++ b/cipher/transposition/transposition_test.go @@ -0,0 +1,133 @@ +// transposition_test.go +// description: Transposition cipher +// author(s) [red_byte](https://github.com/i-redbyte) +// see transposition.go + +package transposition + +import ( + "errors" + "math/rand" + "reflect" + "testing" +) + +const enAlphabet = "abcdefghijklmnopqrstuvwxyz" + +var texts = []string{ + "Ilya Sokolov", + "A slice literal is declared just like an array literal, except you leave out the element count", + "Go is an open source programming language that makes it easy to build simple, reliable, and efficient software.", + "Go’s treatment of errors as values has served us well over the last decade. Although the standard library’s support for errors has been minimal—just the errors.New and fmt.Errorf functions, which produce errors that contain only a message—the built-in error interface allows Go programmers to add whatever information they desire. All it requires is a type that implements an Error method:", + "А тут для примера русский текст", +} + +func getRandomString() string { + enRunes := []rune(enAlphabet) + b := make([]rune, rand.Intn(100)) + for i := range b { + b[i] = enRunes[rand.Intn(len(enRunes))] + } + return string(b) +} + +func TestEncrypt(t *testing.T) { + fn := func(text string, keyWord string) (bool, error) { + encrypt, err := Encrypt([]rune(text), keyWord) + if err != nil && !errors.Is(err, ErrNoTextToEncrypt) && !errors.Is(err, ErrKeyMissing) { + t.Error("Unexpected error ", err) + } + return text == string(encrypt), err + } + for _, s := range texts { + if check, err := fn(s, getRandomString()); check || err != nil { + t.Error("String ", s, " not encrypted") + } + } + if _, err := fn(getRandomString(), ""); err == nil { + t.Error("Error! empty string encryption") + } +} + +func TestDecrypt(t *testing.T) { + for _, s := range texts { + keyWord := getRandomString() + encrypt, errEncrypt := Encrypt([]rune(s), keyWord) + if errEncrypt != nil && + !errors.Is(errEncrypt, ErrNoTextToEncrypt) && + !errors.Is(errEncrypt, ErrKeyMissing) { + t.Error("Unexpected error ", errEncrypt) + } + if errEncrypt != nil { + t.Error(errEncrypt) + } + decrypt, errDecrypt := Decrypt([]rune(encrypt), keyWord) + if errDecrypt != nil && + !errors.Is(errDecrypt, ErrNoTextToEncrypt) && + !errors.Is(errDecrypt, ErrKeyMissing) { + t.Error("Unexpected error ", errDecrypt) + } + if errDecrypt != nil { + t.Error(errDecrypt) + } + if reflect.DeepEqual(encrypt, decrypt) { + t.Error("String ", s, " not encrypted") + } + if reflect.DeepEqual(encrypt, s) { + t.Error("String ", s, " not encrypted") + } + } +} + +func TestEncryptDecrypt(t *testing.T) { + text := []rune("Test text for checking the algorithm") + key1 := "testKey" + key2 := "Test Key2" + encrypt, errEncrypt := Encrypt(text, key1) + if errEncrypt != nil { + t.Error(errEncrypt) + } + decrypt, errDecrypt := Decrypt(encrypt, key1) + if errDecrypt != nil { + t.Error(errDecrypt) + } + if !reflect.DeepEqual(decrypt, text) { + t.Errorf("The string was not decrypted correctly %q %q", decrypt, text) + } + decrypt, _ = Decrypt([]rune(encrypt), key2) + if reflect.DeepEqual(decrypt, text) { + t.Errorf("The string was decrypted with a different key: %q %q", decrypt, text) + } +} + +func FuzzTransposition(f *testing.F) { + for _, transpositionTestInput := range texts { + f.Add(transpositionTestInput) + } + f.Fuzz(func(t *testing.T, input string) { + keyword := getRandomString() + message := []rune(input) + encrypted, err := Encrypt(message, keyword) + switch { + case err == nil: + case errors.Is(err, ErrKeyMissing), + errors.Is(err, ErrNoTextToEncrypt): + return + default: + t.Fatalf("unexpected error when encrypting string %q: %v", input, err) + } + decrypted, err := Decrypt([]rune(encrypted), keyword) + switch { + case err == nil: + case errors.Is(err, ErrKeyMissing), + errors.Is(err, ErrNoTextToEncrypt): + return + default: + t.Fatalf("unexpected error when decrypting string %q: %v", encrypted, err) + } + + if !reflect.DeepEqual(message, decrypted) { + t.Fatalf("expected: %+v, got: %+v", message, []rune(decrypted)) + } + }) +} diff --git a/cipher/xor/xor.go b/cipher/xor/xor.go new file mode 100644 index 000000000..61181b1aa --- /dev/null +++ b/cipher/xor/xor.go @@ -0,0 +1,29 @@ +// Package xor is an encryption algorithm that operates the exclusive disjunction(XOR) +// description: XOR encryption +// details: The XOR encryption is an algorithm that operates the exclusive disjunction(XOR) on each character of the plaintext with a given key +// time complexity: O(n) +// space complexity: O(n) +// ref: https://en.wikipedia.org/wiki/XOR_cipher +package xor + +// Encrypt encrypts with Xor encryption after converting each character to byte +// The returned value might not be readable because there is no guarantee +// which is within the ASCII range +// If using other type such as string, []int, or some other types, +// add the statements for converting the type to []byte. +func Encrypt(key byte, plaintext []byte) []byte { + cipherText := []byte{} + for _, ch := range plaintext { + cipherText = append(cipherText, key^ch) + } + return cipherText +} + +// Decrypt decrypts with Xor encryption +func Decrypt(key byte, cipherText []byte) []byte { + plainText := []byte{} + for _, ch := range cipherText { + plainText = append(plainText, key^ch) + } + return plainText +} diff --git a/cipher/xor/xor_test.go b/cipher/xor/xor_test.go new file mode 100644 index 000000000..5f98964e1 --- /dev/null +++ b/cipher/xor/xor_test.go @@ -0,0 +1,117 @@ +package xor + +import ( + "bytes" + "fmt" + "reflect" + "testing" +) + +func Example() { + const ( + seed = "Hello World" + key = 97 + ) + + encrypted := Encrypt(byte(key), []byte(seed)) + fmt.Printf("Encrypt=> key: %d, seed: %s, encryptedText: %v\n", key, seed, encrypted) + + decrypted := Decrypt(byte(key), encrypted) + fmt.Printf("Decrypt=> key: %d, encryptedText: %v, DecryptedText: %s\n", key, encrypted, string(decrypted)) + + // Output: + // Encrypt=> key: 97, seed: Hello World, encryptedText: [41 4 13 13 14 65 54 14 19 13 5] + // Decrypt=> key: 97, encryptedText: [41 4 13 13 14 65 54 14 19 13 5], DecryptedText: Hello World +} + +var xorTestData = []struct { + description string + input string + key int + encrypted string +}{ + { + "Encrypt letter 'a' with key 0 makes no changes", + "a", + 0, + "a", + }, + { + "Encrypt letter 'a' with key 1", + "a", + 1, + "`", + }, + { + "Encrypt letter 'a' with key 10", + "a", + 10, + "k", + }, + { + "Encrypt 'hello world' with key 0 makes no changes", + "hello world", + 0, + "hello world", + }, + { + "Encrypt 'hello world' with key 1", + "hello world", + 1, + "idmmn!vnsme", + }, + { + "Encrypt 'hello world' with key 10", + "hello world", + 10, + "boffe*}exfn", + }, + { + "Encrypt full sentence with key 64", + "the quick brown fox jumps over the lazy dog.", + 64, + "4(%`15)#+`\"2/7.`&/8`*5-03`/6%2`4(%`,!:9`$/'n", + }, + { + "Encrypt a word with key 32 make the case swap", + "abcdefghijklmNOPQRSTUVWXYZ", + 32, + "ABCDEFGHIJKLMnopqrstuvwxyz", + }, +} + +func TestXorCipherEncrypt(t *testing.T) { + for _, test := range xorTestData { + t.Run(test.description, func(t *testing.T) { + encrypted := Encrypt(byte(test.key), []byte(test.input)) + if !reflect.DeepEqual(string(encrypted), test.encrypted) { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expecting %s, actual %s", test.encrypted, string(encrypted)) + } + }) + } +} + +func TestXorCipherDecrypt(t *testing.T) { + for _, test := range xorTestData { + t.Run(test.description, func(t *testing.T) { + decrypted := Decrypt(byte(test.key), []byte(test.encrypted)) + + if !reflect.DeepEqual(string(decrypted), test.input) { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expecting %s, actual %s", test.input, string(decrypted)) + } + }) + } +} + +func FuzzXOR(f *testing.F) { + f.Add([]byte("The Quick Brown Fox Jumps over the Lazy Dog."), byte('X')) + f.Fuzz(func(t *testing.T, input []byte, key byte) { + cipherText := Encrypt(key, input) + result := Decrypt(key, cipherText) + if !bytes.Equal(input, result) { + t.Errorf("Before: %s, after: %s, key: %d", input, result, key) + } + }) +} diff --git a/ciphers/CaesarCipher.go b/ciphers/CaesarCipher.go deleted file mode 100644 index d0f506b65..000000000 --- a/ciphers/CaesarCipher.go +++ /dev/null @@ -1,41 +0,0 @@ -package main - -import ( - "bytes" - "flag" - "fmt" - "strings" -) - -func main() { - cipherKey := flag.Int("c", 0, "Cipher shift amount (-26 - 26)") - input := flag.String("i", "", "Input") - flag.Parse() - - if *cipherKey > 26 || *cipherKey < -26 { - flag.PrintDefaults() - } else { - fmt.Println(caesarCipher(*input, *cipherKey)) - } - -} - -func caesarCipher(input string, key int) string { - var outputBuffer bytes.Buffer - for _, r := range strings.ToLower(input) { - newByte := int(r) - - if newByte >= 'a' && newByte <= 'z' { - newByte += key - - if newByte > 'z' { - newByte -= 26 - } else if newByte < 'a' { - newByte += 26 - } - } - - outputBuffer.WriteString(string(newByte)) - } - return outputBuffer.String() -} diff --git a/compression/huffmancoding.go b/compression/huffmancoding.go new file mode 100644 index 000000000..ecdaa1fb2 --- /dev/null +++ b/compression/huffmancoding.go @@ -0,0 +1,118 @@ +// huffman.go +// description: Implements Huffman compression, encoding and decoding +// details: +// We implement the linear-time 2-queue method described here https://en.wikipedia.org/wiki/Huffman_coding. +// It assumes that the list of symbol-frequencies is sorted. +// time complexity: O(n) +// space complexity: O(n) +// author(s) [pedromsrocha](https://github.com/pedromsrocha) +// see also huffmancoding_test.go + +package compression + +import "fmt" + +// A Node of an Huffman tree, which can either be a leaf or an internal node. +// Each node has a weight. +// A leaf node has an associated symbol, but no children (i.e., left == right == nil). +// A parent node has a left and right child and no symbol (i.e., symbol == -1). +type Node struct { + left *Node + right *Node + symbol rune + weight int +} + +// A SymbolFreq is a pair of a symbol and its associated frequency. +type SymbolFreq struct { + Symbol rune + Freq int +} + +// HuffTree returns the root Node of the Huffman tree by compressing listfreq. +// The compression produces the most optimal code lengths, provided listfreq is ordered, +// i.e.: listfreq[i] <= listfreq[j], whenever i < j. +func HuffTree(listfreq []SymbolFreq) (*Node, error) { + if len(listfreq) < 1 { + return nil, fmt.Errorf("huffman coding: HuffTree : calling method with empty list of symbol-frequency pairs") + } + q1 := make([]Node, len(listfreq)) + q2 := make([]Node, 0, len(listfreq)) + for i, x := range listfreq { // after the loop, q1 is a slice of leaf nodes representing listfreq + q1[i] = Node{left: nil, right: nil, symbol: x.Symbol, weight: x.Freq} + } + //loop invariant: q1, q2 are ordered by increasing weights + for len(q1)+len(q2) > 1 { + var node1, node2 Node + node1, q1, q2 = least(q1, q2) + node2, q1, q2 = least(q1, q2) + node := Node{left: &node1, right: &node2, + symbol: -1, weight: node1.weight + node2.weight} + q2 = append(q2, node) + } + if len(q1) == 1 { // returns the remaining node in q1, q2 + return &q1[0], nil + } + return &q2[0], nil +} + +// least removes the node with lowest weight from q1, q2. +// It returns the node with lowest weight and the slices q1, q2 after the update. +func least(q1 []Node, q2 []Node) (Node, []Node, []Node) { + if len(q1) == 0 { + return q2[0], q1, q2[1:] + } + if len(q2) == 0 { + return q1[0], q1[1:], q2 + } + if q1[0].weight <= q2[0].weight { + return q1[0], q1[1:], q2 + } + return q2[0], q1, q2[1:] +} + +// HuffEncoding recursively traverses the Huffman tree pointed by node to obtain +// the map codes, that associates a rune with a slice of booleans. +// Each code is prefixed by prefix and left and right children are labelled with +// the booleans false and true, respectively. +func HuffEncoding(node *Node, prefix []bool, codes map[rune][]bool) { + if node.symbol != -1 { //base case + codes[node.symbol] = prefix + return + } + // inductive step + prefixLeft := make([]bool, len(prefix)) + copy(prefixLeft, prefix) + prefixLeft = append(prefixLeft, false) + HuffEncoding(node.left, prefixLeft, codes) + prefixRight := make([]bool, len(prefix)) + copy(prefixRight, prefix) + prefixRight = append(prefixRight, true) + HuffEncoding(node.right, prefixRight, codes) +} + +// HuffEncode encodes the string in by applying the mapping defined by codes. +func HuffEncode(codes map[rune][]bool, in string) []bool { + out := make([]bool, 0) + for _, s := range in { + out = append(out, codes[s]...) + } + return out +} + +// HuffDecode recursively decodes the binary code in, by traversing the Huffman compression tree pointed by root. +// current stores the current node of the traversing algorithm. +// out stores the current decoded string. +func HuffDecode(root, current *Node, in []bool, out string) string { + if current.symbol != -1 { + out += string(current.symbol) + return HuffDecode(root, root, in, out) + } + if len(in) == 0 { + return out + } + if in[0] { + return HuffDecode(root, current.right, in[1:], out) + } + return HuffDecode(root, current.left, in[1:], out) +} diff --git a/compression/huffmancoding_test.go b/compression/huffmancoding_test.go new file mode 100644 index 000000000..8c0434d85 --- /dev/null +++ b/compression/huffmancoding_test.go @@ -0,0 +1,55 @@ +// huffmancoding_test.go +// description: Tests the compression, encoding and decoding algorithms of huffmancoding.go. +// author(s) [pedromsrocha](https://github.com/pedromsrocha) +// see huffmancoding.go + +package compression_test + +import ( + "sort" + "testing" + + "github.com/TheAlgorithms/Go/compression" +) + +// SymbolCountOrd computes sorted symbol-frequency list of input message +func SymbolCountOrd(message string) []compression.SymbolFreq { + runeCount := make(map[rune]int) + for _, s := range message { + runeCount[s]++ + } + listfreq := make([]compression.SymbolFreq, len(runeCount)) + i := 0 + for s, n := range runeCount { + listfreq[i] = compression.SymbolFreq{Symbol: s, Freq: n} + i++ + } + sort.Slice(listfreq, func(i, j int) bool { return listfreq[i].Freq < listfreq[j].Freq }) + return listfreq +} + +func TestHuffman(t *testing.T) { + messages := []string{ + "hello world \U0001F600", + "colorless green ideas sleep furiously", + "the quick brown fox jumps over the lazy dog", + `Lorem ipsum dolor sit amet, consectetur adipiscing elit, + sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. + Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut + aliquip ex ea commodo consequat.`, + } + + for _, message := range messages { + t.Run("huffman: "+message, func(t *testing.T) { + tree, _ := compression.HuffTree(SymbolCountOrd(message)) + codes := make(map[rune][]bool) + compression.HuffEncoding(tree, nil, codes) + messageCoded := compression.HuffEncode(codes, message) + messageHuffDecoded := compression.HuffDecode(tree, tree, messageCoded, "") + if messageHuffDecoded != message { + t.Errorf("got: %q\nbut expected: %q", messageHuffDecoded, message) + + } + }) + } +} diff --git a/compression/rlecoding.go b/compression/rlecoding.go new file mode 100644 index 000000000..9aa9399bb --- /dev/null +++ b/compression/rlecoding.go @@ -0,0 +1,76 @@ +/* +rlecoding.go +description: run length encoding and decoding +details: +Run-length encoding (RLE) is a simple form of data compression in which runs of data are stored as a single data value and count, rather than as the original run. This is useful when the data contains many repeated values. For example, the data "WWWWWWWWWWWWBWWWWWWWWWWWWBBB" can be compressed to "12W1B12W3B". The algorithm is simple and can be implemented in a few lines of code. +time complexity: O(n) +space complexity: O(n) +ref: https://en.wikipedia.org/wiki/Run-length_encoding +author(s) [ddaniel27](https://github.com/ddaniel27) +*/ +package compression + +import ( + "bytes" + "fmt" + "regexp" + "strconv" + "strings" +) + +// RLEncode takes a string and returns its run-length encoding +func RLEncode(data string) string { + var result string + count := 1 + for i := 0; i < len(data); i++ { + if i+1 < len(data) && data[i] == data[i+1] { + count++ + continue + } + result += fmt.Sprintf("%d%c", count, data[i]) + count = 1 + } + return result +} + +// RLEdecode takes a run-length encoded string and returns the original string +func RLEdecode(data string) string { + var result string + regex := regexp.MustCompile(`(\d+)(\w)`) + + for _, match := range regex.FindAllStringSubmatch(data, -1) { + num, _ := strconv.Atoi(match[1]) + result += strings.Repeat(match[2], num) + } + + return result +} + +// RLEncodebytes takes a byte slice and returns its run-length encoding as a byte slice +func RLEncodebytes(data []byte) []byte { + var result []byte + var count byte = 1 + + for i := 0; i < len(data); i++ { + if i+1 < len(data) && data[i] == data[i+1] { + count++ + continue + } + result = append(result, count, data[i]) + count = 1 + } + + return result +} + +// RLEdecodebytes takes a run-length encoded byte slice and returns the original byte slice +func RLEdecodebytes(data []byte) []byte { + var result []byte + + for i := 0; i < len(data); i += 2 { + count := int(data[i]) + result = append(result, bytes.Repeat([]byte{data[i+1]}, count)...) + } + + return result +} diff --git a/compression/rlecoding_test.go b/compression/rlecoding_test.go new file mode 100644 index 000000000..bf9af6bf6 --- /dev/null +++ b/compression/rlecoding_test.go @@ -0,0 +1,161 @@ +package compression_test + +import ( + "bytes" + "testing" + + "github.com/TheAlgorithms/Go/compression" +) + +func TestCompressionRLEncode(t *testing.T) { + tests := []struct { + name string + data string + want string + }{ + { + name: "test 1", + data: "WWWWWWWWWWWWBWWWWWWWWWWWWBBB", + want: "12W1B12W3B", + }, + { + name: "test 2", + data: "AABCCCDEEEE", + want: "2A1B3C1D4E", + }, + { + name: "test 3", + data: "AAAABBBCCDA", + want: "4A3B2C1D1A", + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := compression.RLEncode(tt.data); got != tt.want { + t.Errorf("RLEncode() = %v, want %v", got, tt.want) + } + }) + } +} + +func TestCompressionRLEDecode(t *testing.T) { + tests := []struct { + name string + data string + want string + }{ + { + name: "test 1", + data: "12W1B12W3B", + want: "WWWWWWWWWWWWBWWWWWWWWWWWWBBB", + }, + { + name: "test 2", + data: "2A1B3C1D4E", + want: "AABCCCDEEEE", + }, + { + name: "test 3", + data: "4A3B2C1D1A", + want: "AAAABBBCCDA", + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := compression.RLEdecode(tt.data); got != tt.want { + t.Errorf("RLEdecode() = %v, want %v", got, tt.want) + } + }) + } +} + +func TestCompressionRLEncodeBytes(t *testing.T) { + tests := []struct { + name string + data []byte + want []byte + }{ + { + name: "test 1", + data: []byte("WWWWWWWWWWWWBWWWWWWWWWWWWBBB"), + want: []byte{12, 'W', 1, 'B', 12, 'W', 3, 'B'}, + }, + { + name: "test 2", + data: []byte("AABCCCDEEEE"), + want: []byte{2, 'A', 1, 'B', 3, 'C', 1, 'D', 4, 'E'}, + }, + { + name: "test 3", + data: []byte("AAAABBBCCDA"), + want: []byte{4, 'A', 3, 'B', 2, 'C', 1, 'D', 1, 'A'}, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := compression.RLEncodebytes(tt.data); !bytes.Equal(got, tt.want) { + t.Errorf("RLEncodebytes() = %v, want %v", got, tt.want) + } + }) + } +} + +func TestCompressionRLEDecodeBytes(t *testing.T) { + tests := []struct { + name string + data []byte + want []byte + }{ + { + name: "test 1", + data: []byte{12, 'W', 1, 'B', 12, 'W', 3, 'B'}, + want: []byte("WWWWWWWWWWWWBWWWWWWWWWWWWBBB"), + }, + { + name: "test 2", + data: []byte{2, 'A', 1, 'B', 3, 'C', 1, 'D', 4, 'E'}, + want: []byte("AABCCCDEEEE"), + }, + { + name: "test 3", + data: []byte{4, 'A', 3, 'B', 2, 'C', 1, 'D', 1, 'A'}, + want: []byte("AAAABBBCCDA"), + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := compression.RLEdecodebytes(tt.data); !bytes.Equal(got, tt.want) { + t.Errorf("RLEdecodebytes() = %v, want %v", got, tt.want) + } + }) + } +} + +/* --- BENCHMARKS --- */ +func BenchmarkRLEncode(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = compression.RLEncode("WWWWWWWWWWWWBWWWWWWWWWWWWBBB") + } +} + +func BenchmarkRLEDecode(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = compression.RLEdecode("12W1B12W3B") + } +} + +func BenchmarkRLEncodeBytes(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = compression.RLEncodebytes([]byte("WWWWWWWWWWWWBWWWWWWWWWWWWBBB")) + } +} + +func BenchmarkRLEDecodeBytes(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = compression.RLEdecodebytes([]byte{12, 'W', 1, 'B', 12, 'W', 3, 'B'}) + } +} diff --git a/constraints/constraints.go b/constraints/constraints.go new file mode 100644 index 000000000..ca902cec5 --- /dev/null +++ b/constraints/constraints.go @@ -0,0 +1,40 @@ +// Package constraints has some useful generic type constraints defined which is very similar to +// [golang.org/x/exp/constraints](https://pkg.go.dev/golang.org/x/exp/constraints) package. +// We refrained from using that until it gets placed into the standard library - currently +// there are some questions regarding this package [ref](https://github.com/golang/go/issues/50792). +package constraints + +// Signed is a generic type constraint for all signed integers. +type Signed interface { + ~int | ~int8 | ~int16 | ~int32 | ~int64 +} + +// Unsigned is a generic type constraint for all unsigned integers. +type Unsigned interface { + ~uint | ~uint8 | ~uint16 | ~uint32 | ~uint64 +} + +// Integer is a generic type constraint for all integers (signed and unsigned.) +type Integer interface { + Signed | Unsigned +} + +// Float is a generic type constraint for all floating point types. +type Float interface { + ~float32 | ~float64 +} + +// Number is a generic type constraint for all numeric types in Go except Complex types. +type Number interface { + Integer | Float +} + +// Ordered is a generic type constraint for all ordered data types in Go. +// Loosely speaking, in mathematics a field is an ordered field if there is a "total +// order" (a binary relation - in this case `<` symbol) such that we will always have +// if a < b then a + c < b + c and if 0 < a, 0 < b then 0 < a.b +// The idea in Go is quite similar, though only limited to Go standard types +// not user defined types. +type Ordered interface { + Integer | ~string | Float +} diff --git a/conversion/base64.go b/conversion/base64.go new file mode 100644 index 000000000..bf3a383c5 --- /dev/null +++ b/conversion/base64.go @@ -0,0 +1,83 @@ +// base64.go +// description: The base64 encoding algorithm as defined in the RFC4648 standard. +// author: [Paul Leydier] (https://github.com/paul-leydier) +// time complexity: O(n) +// space complexity: O(n) +// ref: https://datatracker.ietf.org/doc/html/rfc4648#section-4 +// ref: https://en.wikipedia.org/wiki/Base64 +// see base64_test.go + +package conversion + +import ( + "strings" // Used for efficient string builder (more efficient than simply appending strings) +) + +const Alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/" + +// Base64Encode encodes the received input bytes slice into a base64 string. +// The implementation follows the RFC4648 standard, which is documented +// at https://datatracker.ietf.org/doc/html/rfc4648#section-4 +func Base64Encode(input []byte) string { + var sb strings.Builder + // If not 24 bits (3 bytes) multiple, pad with 0 value bytes, and with "=" for the output + var padding string + for i := len(input) % 3; i > 0 && i < 3; i++ { + var zeroByte byte + input = append(input, zeroByte) + padding += "=" + } + + // encode 24 bits per 24 bits (3 bytes per 3 bytes) + for i := 0; i < len(input); i += 3 { + // select 3 8-bit input groups, and re-arrange them into 4 6-bit groups + // the literal 0x3F corresponds to the byte "0011 1111" + // the operation "byte & 0x3F" masks the two left-most bits + group := [4]byte{ + input[i] >> 2, + (input[i]<<4)&0x3F + input[i+1]>>4, + (input[i+1]<<2)&0x3F + input[i+2]>>6, + input[i+2] & 0x3F, + } + + // translate each group into a char using the static map + for _, b := range group { + sb.WriteString(string(Alphabet[int(b)])) + } + } + encoded := sb.String() + + // Apply the output padding + encoded = encoded[:len(encoded)-len(padding)] + padding[:] + + return encoded +} + +// Base64Decode decodes the received input base64 string into a byte slice. +// The implementation follows the RFC4648 standard, which is documented +// at https://datatracker.ietf.org/doc/html/rfc4648#section-4 +func Base64Decode(input string) []byte { + padding := strings.Count(input, "=") // Number of bytes which will be ignored + var decoded []byte + + // select 4 6-bit input groups, and re-arrange them into 3 8-bit groups + for i := 0; i < len(input); i += 4 { + // translate each group into a byte using the static map + byteInput := [4]byte{ + byte(strings.IndexByte(Alphabet, input[i])), + byte(strings.IndexByte(Alphabet, input[i+1])), + byte(strings.IndexByte(Alphabet, input[i+2])), + byte(strings.IndexByte(Alphabet, input[i+3])), + } + + group := [3]byte{ + byteInput[0]<<2 + byteInput[1]>>4, + byteInput[1]<<4 + byteInput[2]>>2, + byteInput[2]<<6 + byteInput[3], + } + + decoded = append(decoded, group[:]...) + } + + return decoded[:len(decoded)-padding] +} diff --git a/conversion/base64_test.go b/conversion/base64_test.go new file mode 100644 index 000000000..96342695a --- /dev/null +++ b/conversion/base64_test.go @@ -0,0 +1,123 @@ +package conversion + +import "testing" + +func TestBase64Encode(t *testing.T) { + testCases := []struct { + in string + expected string + }{ + {"Hello World!", "SGVsbG8gV29ybGQh"}, // multiple of 3 byte length (multiple of 24-bits) + {"Hello World!a", "SGVsbG8gV29ybGQhYQ=="}, // multiple of 3 byte length + 1 + {"Hello World!ab", "SGVsbG8gV29ybGQhYWI="}, // multiple of 3 byte length + 2 + {"", ""}, // empty byte slice + {"6", "Ng=="}, // short text + {"Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.", "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"}, // Long text + } + + for _, tc := range testCases { + result := Base64Encode([]byte(tc.in)) + if result != tc.expected { + t.Fatalf("Base64Encode(%s) = %s, want %s", tc.in, result, tc.expected) + } + } +} + +func BenchmarkBase64Encode(b *testing.B) { + benchmarks := []struct { + name string + in string + expected string + }{ + {"Hello World!", "Hello World!", "SGVsbG8gV29ybGQh"}, // multiple of 3 byte length (multiple of 24-bits) + {"Hello World!a", "Hello World!a", "SGVsbG8gV29ybGQhYQ=="}, // multiple of 3 byte length + 1 + {"Hello World!ab", "Hello World!ab", "SGVsbG8gV29ybGQhYWI="}, // multiple of 3 byte length + 2 + {"Empty", "", ""}, // empty byte slice + {"6", "6", "Ng=="}, // short text + {"Lorem ipsum", "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.", "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"}, // Long text + } + + for _, bm := range benchmarks { + b.Run(bm.name, func(b *testing.B) { + for i := 0; i < b.N; i++ { + Base64Encode([]byte(bm.in)) + } + }) + } +} + +func TestBase64Decode(t *testing.T) { + testCases := []struct { + expected string + in string + }{ + {"Hello World!", "SGVsbG8gV29ybGQh"}, // multiple of 3 byte length (multiple of 24-bits) + {"Hello World!a", "SGVsbG8gV29ybGQhYQ=="}, // multiple of 3 byte length + 1 + {"Hello World!ab", "SGVsbG8gV29ybGQhYWI="}, // multiple of 3 byte length + 2 + {"", ""}, // empty byte slice + {"6", "Ng=="}, // short text + {"Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.", "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"}, // Long text + } + + for _, tc := range testCases { + result := string(Base64Decode(tc.in)) + if result != tc.expected { + t.Fatalf("Base64Decode(%s) = %s, want %s", tc.in, result, tc.expected) + } + } +} + +func BenchmarkBase64Decode(b *testing.B) { + benchmarks := []struct { + name string + expected string + in string + }{ + {"Hello World!", "Hello World!", "SGVsbG8gV29ybGQh"}, // multiple of 3 byte length (multiple of 24-bits) + {"Hello World!a", "Hello World!a", "SGVsbG8gV29ybGQhYQ=="}, // multiple of 3 byte length + 1 + {"Hello World!ab", "Hello World!ab", "SGVsbG8gV29ybGQhYWI="}, // multiple of 3 byte length + 2 + {"Empty", "", ""}, // empty byte slice + {"6", "6", "Ng=="}, // short text + {"Lorem ipsum", "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.", "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"}, // Long text + } + + for _, bm := range benchmarks { + b.Run(bm.name, func(b *testing.B) { + for i := 0; i < b.N; i++ { + Base64Decode(bm.in) + } + }) + } +} + +func TestBase64EncodeDecodeInverse(t *testing.T) { + testCases := []struct { + in string + }{ + {"Hello World!"}, // multiple of 3 byte length (multiple of 24-bits) + {"Hello World!a"}, // multiple of 3 byte length + 1 + {"Hello World!ab"}, // multiple of 3 byte length + 2 + {""}, // empty byte slice + {"6"}, // short text + {"Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum."}, // Long text + } + + for _, tc := range testCases { + result := string(Base64Decode(Base64Encode([]byte(tc.in)))) + if result != tc.in { + t.Fatalf("Base64Decode(Base64Encode(%s)) = %s, want %s", tc.in, result, tc.in) + } + } +} + +func FuzzBase64Encode(f *testing.F) { + f.Add([]byte("hello")) + f.Fuzz(func(t *testing.T, input []byte) { + result := Base64Decode(Base64Encode(input)) + for i := 0; i < len(input); i++ { + if result[i] != input[i] { + t.Fatalf("with input '%s' - expected '%s', got '%s' (mismatch at position %d)", input, input, result, i) + } + } + }) +} diff --git a/conversion/binarytodecimal.go b/conversion/binarytodecimal.go new file mode 100644 index 000000000..aa308e6a8 --- /dev/null +++ b/conversion/binarytodecimal.go @@ -0,0 +1,42 @@ +/* +Author: Motasim +GitHub: https://github.com/motasimmakki +Date: 19-Oct-2021 +*/ + +// This algorithm will convert any Binary number(0 or 1) to Decimal number(+ve number). +// https://en.wikipedia.org/wiki/Binary_number +// https://en.wikipedia.org/wiki/Decimal +// Function receives a Binary Number as string and returns the Decimal number as integer. +// Supported Binary number range is 0 to 2^(31-1). +// time complexity: O(n) +// space complexity: O(1) + +package conversion + +// Importing necessary package. +import ( + "errors" + "regexp" +) + +var isValid = regexp.MustCompile("^[0-1]{1,}$").MatchString + +// BinaryToDecimal() function that will take Binary number as string, +// and return its Decimal equivalent as an integer. +func BinaryToDecimal(binary string) (int, error) { + if !isValid(binary) { + return -1, errors.New("not a valid binary string") + } + if len(binary) > 32 { + return -1, errors.New("binary number must be in range 0 to 2^(31-1)") + } + var result, base int = 0, 1 + for i := len(binary) - 1; i >= 0; i-- { + if binary[i] == '1' { + result += base + } + base *= 2 + } + return result, nil +} diff --git a/conversion/binarytodecimal_test.go b/conversion/binarytodecimal_test.go new file mode 100644 index 000000000..3cbec8099 --- /dev/null +++ b/conversion/binarytodecimal_test.go @@ -0,0 +1,46 @@ +package conversion + +import "testing" + +var binaryTestCases = map[string]int{ + "0": 0, "1": 1, "10": 2, "11": 3, "100": 4, + "101": 5, "110": 6, "111": 7, "1000": 8, "1001": 9, + "1010": 10, "1011": 11, "1100": 12, "1101": 13, "1110": 14, + "1111": 15, "10000": 16, "10001": 17, "10010": 18, "10011": 19, + "10100": 20, "10101": 21, "10110": 22, "10111": 23, "11000": 24, + "11001": 25, "11010": 26, "11011": 27, "11100": 28, "11101": 29, + "11110": 30, "11111": 31, "100000": 32, "100001": 33, "100010": 34, + "100011": 35, "100100": 36, "100101": 37, "100110": 38, "100111": 39, + "101000": 40, "101001": 41, "101010": 42, "101011": 43, "101100": 44, + "101101": 45, "101110": 46, "101111": 47, "110000": 48, "110001": 49, + "110010": 50, "110011": 51, "110100": 52, "110101": 53, "110110": 54, + "110111": 55, "111000": 56, "111001": 57, "111010": 58, "111011": 59, + "111100": 60, "111101": 61, "111110": 62, "111111": 63, "1000000": 64, + "1000001": 65, "1000010": 66, "1000011": 67, "1000100": 68, "1000101": 69, + "1000110": 70, "1000111": 71, "1001000": 72, "1001001": 73, "1001010": 74, + "1001011": 75, "1001100": 76, "1001101": 77, "1001110": 78, "1001111": 79, + "1010000": 80, "1010001": 81, "1010010": 82, "1010011": 83, "1010100": 84, + "1010101": 85, "1010110": 86, "1010111": 87, "1011000": 88, "1011001": 89, + "1011010": 90, "1011011": 91, "1011100": 92, "1011101": 93, "1011110": 94, + "1011111": 95, "1100000": 96, "1100001": 97, "1100010": 98, "1100011": 99, + "1100100": 100, +} + +func TestBinaryToDecimal(t *testing.T) { + for input, expected := range binaryTestCases { + out, err := BinaryToDecimal(input) + if err != nil { + t.Errorf("BinaryToDecimal(%s) returned an error %s", input, err.Error()) + } + if out != expected { + t.Errorf("BinaryToDecimal(%s) = %d; want %d", input, out, expected) + } + } +} + +func BenchmarkBinaryToDecimal(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _, _ = BinaryToDecimal("1100100") + } +} diff --git a/conversion/conversion_test.go b/conversion/conversion_test.go new file mode 100644 index 000000000..34eec8f96 --- /dev/null +++ b/conversion/conversion_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package conversion diff --git a/conversion/decimaltobinary.go b/conversion/decimaltobinary.go new file mode 100644 index 000000000..54153b0d2 --- /dev/null +++ b/conversion/decimaltobinary.go @@ -0,0 +1,47 @@ +/* +Author: Motasim +GitHub: https://github.com/motasimmakki +Date: 14-Oct-2021 +*/ + +// This algorithm will convert any Decimal (+ve integer) number to Binary number. +// https://en.wikipedia.org/wiki/Binary_number +// Function receives a integer as a Decimal number and returns the Binary number. +// Supported integer value range is 0 to 2^(31 -1). +// time complexity: O(log(n)) +// space complexity: O(1) + +package conversion + +// Importing necessary package. +import ( + "errors" + "strconv" +) + +// Reverse() function that will take string, +// and returns the reverse of that string. +func Reverse(str string) string { + rStr := []rune(str) + for i, j := 0, len(rStr)-1; i < len(rStr)/2; i, j = i+1, j-1 { + rStr[i], rStr[j] = rStr[j], rStr[i] + } + return string(rStr) +} + +// DecimalToBinary() function that will take Decimal number as int, +// and return its Binary equivalent as a string. +func DecimalToBinary(num int) (string, error) { + if num < 0 { + return "", errors.New("integer must have +ve value") + } + if num == 0 { + return "0", nil + } + var result string = "" + for num > 0 { + result += strconv.Itoa(num & 1) + num >>= 1 + } + return Reverse(result), nil +} diff --git a/conversion/decimaltobinary_test.go b/conversion/decimaltobinary_test.go new file mode 100644 index 000000000..d8ec05fca --- /dev/null +++ b/conversion/decimaltobinary_test.go @@ -0,0 +1,46 @@ +package conversion + +import "testing" + +var decimalTestCases = map[int]string{ + 0: "0", 1: "1", 2: "10", 3: "11", 4: "100", + 5: "101", 6: "110", 7: "111", 8: "1000", 9: "1001", + 10: "1010", 11: "1011", 12: "1100", 13: "1101", 14: "1110", + 15: "1111", 16: "10000", 17: "10001", 18: "10010", 19: "10011", + 20: "10100", 21: "10101", 22: "10110", 23: "10111", 24: "11000", + 25: "11001", 26: "11010", 27: "11011", 28: "11100", 29: "11101", + 30: "11110", 31: "11111", 32: "100000", 33: "100001", 34: "100010", + 35: "100011", 36: "100100", 37: "100101", 38: "100110", 39: "100111", + 40: "101000", 41: "101001", 42: "101010", 43: "101011", 44: "101100", + 45: "101101", 46: "101110", 47: "101111", 48: "110000", 49: "110001", + 50: "110010", 51: "110011", 52: "110100", 53: "110101", 54: "110110", + 55: "110111", 56: "111000", 57: "111001", 58: "111010", 59: "111011", + 60: "111100", 61: "111101", 62: "111110", 63: "111111", 64: "1000000", + 65: "1000001", 66: "1000010", 67: "1000011", 68: "1000100", 69: "1000101", + 70: "1000110", 71: "1000111", 72: "1001000", 73: "1001001", 74: "1001010", + 75: "1001011", 76: "1001100", 77: "1001101", 78: "1001110", 79: "1001111", + 80: "1010000", 81: "1010001", 82: "1010010", 83: "1010011", 84: "1010100", + 85: "1010101", 86: "1010110", 87: "1010111", 88: "1011000", 89: "1011001", + 90: "1011010", 91: "1011011", 92: "1011100", 93: "1011101", 94: "1011110", + 95: "1011111", 96: "1100000", 97: "1100001", 98: "1100010", 99: "1100011", + 100: "1100100", +} + +func TestDecimalToBinary(t *testing.T) { + for input, expected := range decimalTestCases { + out, err := DecimalToBinary(input) + if err != nil { + t.Errorf("DecimalToBinary(%d) returned an error %s", input, err.Error()) + } + if out != expected { + t.Errorf("DecimalToBinary(%d) = %s; want %s", input, out, expected) + } + } +} + +func BenchmarkDecimalToBinary(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _, _ = DecimalToBinary(100) + } +} diff --git a/conversion/doc.go b/conversion/doc.go new file mode 100644 index 000000000..f5cc05779 --- /dev/null +++ b/conversion/doc.go @@ -0,0 +1,2 @@ +// Package conversion is a package of implementations which converts one data structure to another. +package conversion diff --git a/conversion/hexadecimaltobinary.go b/conversion/hexadecimaltobinary.go new file mode 100644 index 000000000..a0d262df6 --- /dev/null +++ b/conversion/hexadecimaltobinary.go @@ -0,0 +1,78 @@ +/* +Author: mapcrafter2048 +GitHub: https://github.com/mapcrafter2048 +*/ + +// This algorithm will convert any Hexadecimal number(0-9, A-F, a-f) to Binary number(0 or 1). +// https://en.wikipedia.org/wiki/Hexadecimal +// https://en.wikipedia.org/wiki/Binary_number +// Function receives a Hexadecimal Number as string and returns the Binary number as string. +// Supported Hexadecimal number range is 0 to 7FFFFFFFFFFFFFFF. + +package conversion + +import ( + "errors" + "regexp" + "strings" +) + +var isValidHex = regexp.MustCompile("^[0-9A-Fa-f]+$").MatchString + +// hexToBinary() function that will take Hexadecimal number as string, +// and return its Binary equivalent as a string. +func hexToBinary(hex string) (string, error) { + // Trim any leading or trailing whitespace + hex = strings.TrimSpace(hex) + + // Check if the hexadecimal string is empty + if hex == "" { + return "", errors.New("input string is empty") + } + + // Check if the hexadecimal string is valid + if !isValidHex(hex) { + return "", errors.New("invalid hexadecimal string: " + hex) + } + + // Parse the hexadecimal string to an integer + var decimal int64 + for i := 0; i < len(hex); i++ { + char := hex[i] + var value int64 + if char >= '0' && char <= '9' { + value = int64(char - '0') + } else if char >= 'A' && char <= 'F' { + value = int64(char - 'A' + 10) + } else if char >= 'a' && char <= 'f' { + value = int64(char - 'a' + 10) + } else { + return "", errors.New("invalid character in hexadecimal string: " + string(char)) + } + decimal = decimal*16 + value + } + + // Convert the integer to a binary string without using predefined functions + var binaryBuilder strings.Builder + if decimal == 0 { + binaryBuilder.WriteString("0") + } else { + for decimal > 0 { + bit := decimal % 2 + if bit == 0 { + binaryBuilder.WriteString("0") + } else { + binaryBuilder.WriteString("1") + } + decimal = decimal / 2 + } + } + + // Reverse the binary string since the bits are added in reverse order + binaryRunes := []rune(binaryBuilder.String()) + for i, j := 0, len(binaryRunes)-1; i < j; i, j = i+1, j-1 { + binaryRunes[i], binaryRunes[j] = binaryRunes[j], binaryRunes[i] + } + + return string(binaryRunes), nil +} diff --git a/conversion/hexadecimaltobinary_test.go b/conversion/hexadecimaltobinary_test.go new file mode 100644 index 000000000..c2dee9712 --- /dev/null +++ b/conversion/hexadecimaltobinary_test.go @@ -0,0 +1,46 @@ +package conversion + +import ( + "testing" +) + +func TestHexToBinary(t *testing.T) { + tests := []struct { + hex string + want string + wantErr bool + }{ + {"", "", true}, + {"G123", "", true}, + {"12XZ", "", true}, + {"1", "1", false}, + {"A", "1010", false}, + {"10", "10000", false}, + {"1A", "11010", false}, + {"aB", "10101011", false}, + {"0Ff", "11111111", false}, + {" 1A ", "11010", false}, + {"0001A", "11010", false}, + {"7FFFFFFFFFFFFFFF", "111111111111111111111111111111111111111111111111111111111111111", false}, + } + + for _, tt := range tests { + t.Run(tt.hex, func(t *testing.T) { + got, err := hexToBinary(tt.hex) + if (err != nil) != tt.wantErr { + t.Errorf("hexToBinary(%q) error = %v, wantErr %v", tt.hex, err, tt.wantErr) + return + } + if got != tt.want { + t.Errorf("hexToBinary(%q) = %v, want %v", tt.hex, got, tt.want) + } + }) + } +} + +func BenchmarkHexToBinary(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _, _ = hexToBinary("7FFFFFFFFFFFFFFF") + } +} diff --git a/conversion/hexadecimaltodecimal.go b/conversion/hexadecimaltodecimal.go new file mode 100644 index 000000000..f0d7a81d3 --- /dev/null +++ b/conversion/hexadecimaltodecimal.go @@ -0,0 +1,57 @@ +/* +Author: mapcrafter2048 +GitHub: https://github.com/mapcrafter2048 +*/ + +// This algorithm will convert any Hexadecimal number(0-9, A-F, a-f) to Decimal number(0-9). +// https://en.wikipedia.org/wiki/Hexadecimal +// https://en.wikipedia.org/wiki/Decimal +// Function receives a Hexadecimal Number as string and returns the Decimal number as integer. +// Supported Hexadecimal number range is 0 to 7FFFFFFFFFFFFFFF. + +package conversion + +import ( + "fmt" + "regexp" + "strings" +) + +var isValidHexadecimal = regexp.MustCompile("^[0-9A-Fa-f]+$").MatchString + +// hexToDecimal converts a hexadecimal string to a decimal integer. +func hexToDecimal(hexStr string) (int64, error) { + + hexStr = strings.TrimSpace(hexStr) + + if len(hexStr) == 0 { + return 0, fmt.Errorf("input string is empty") + } + + // Check if the string has a valid hexadecimal prefix + if len(hexStr) > 2 && (hexStr[:2] == "0x" || hexStr[:2] == "0X") { + hexStr = hexStr[2:] + } + + // Validate the hexadecimal string + if !isValidHexadecimal(hexStr) { + return 0, fmt.Errorf("invalid hexadecimal string") + } + + var decimalValue int64 + for _, char := range hexStr { + var digit int64 + if char >= '0' && char <= '9' { + digit = int64(char - '0') + } else if char >= 'A' && char <= 'F' { + digit = int64(char - 'A' + 10) + } else if char >= 'a' && char <= 'f' { + digit = int64(char - 'a' + 10) + } else { + return 0, fmt.Errorf("invalid character in hexadecimal string: %c", char) + } + decimalValue = decimalValue*16 + digit + } + + return decimalValue, nil +} diff --git a/conversion/hexadecimaltodecimal_test.go b/conversion/hexadecimaltodecimal_test.go new file mode 100644 index 000000000..4f399fe46 --- /dev/null +++ b/conversion/hexadecimaltodecimal_test.go @@ -0,0 +1,52 @@ +package conversion + +import ( + "testing" +) + +func TestHexToDecimal(t *testing.T) { + tests := []struct { + hex string + want int64 + wantErr bool + }{ + {"", 0, true}, + {"G123", 0, true}, + {"123Z", 0, true}, + {"1", 1, false}, + {"A", 10, false}, + {"10", 16, false}, + {"1A", 26, false}, + {"aB", 171, false}, + {"0Ff", 255, false}, + {" 1A ", 26, false}, + {"0x1A", 26, false}, + {"0X1A", 26, false}, + {"1A", 26, false}, + {"7FFFFFFFFFFFFFFF", 9223372036854775807, false}, + {"0001A", 26, false}, + {"0000007F", 127, false}, + {"0", 0, false}, + {"0x0", 0, false}, + } + + for _, tt := range tests { + t.Run(tt.hex, func(t *testing.T) { + got, err := hexToDecimal(tt.hex) + if (err != nil) != tt.wantErr { + t.Errorf("hexToDecimal(%q) error = %v, wantErr %v", tt.hex, err, tt.wantErr) + return + } + if got != tt.want { + t.Errorf("hexToDecimal(%q) = %v, want %v", tt.hex, got, tt.want) + } + }) + } +} + +func BenchmarkHexToDecimal(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _, _ = hexToDecimal("7FFFFFFFFFFFFFFF") + } +} diff --git a/conversion/inttoroman.go b/conversion/inttoroman.go new file mode 100644 index 000000000..1b9c39a0e --- /dev/null +++ b/conversion/inttoroman.go @@ -0,0 +1,42 @@ +// inttoroman.go +// description: Convert an integer to a roman numeral +// details: This program converts an integer to a roman numeral. The program uses a lookup array to convert the integer to a roman numeral. +// time complexity: O(1) +// space complexity: O(1) + +package conversion + +import ( + "errors" +) + +var ( + // lookup arrays used for converting from an int to a roman numeral extremely quickly. + r0 = []string{"", "I", "II", "III", "IV", "V", "VI", "VII", "VIII", "IX"} // 1 - 9 + r1 = []string{"", "X", "XX", "XXX", "XL", "L", "LX", "LXX", "LXXX", "XC"} // 10 - 90 + r2 = []string{"", "C", "CC", "CCC", "CD", "D", "DC", "DCC", "DCCC", "CM"} // 100 - 900 + r3 = []string{"", "M", "MM", "MMM"} // 1,000 - 3,000 +) + +// IntToRoman converts an integer value to a roman numeral string. An error is +// returned if the integer is not between 1 and 3999. +func IntToRoman(n int) (string, error) { + if n < 1 || n > 3999 { + return "", errors.New("integer must be between 1 and 3999") + } + // Concatenate strings for each of 4 lookup array categories. + // + // Key behavior to note here is how math with integers is handled. Values are floored to the + // nearest int, not rounded up. For example, 26/10 = 2 even though the actual result is 2.6. + // + // For example, lets use an input value of 126: + // `r3[n%1e4/1e3]` --> 126 % 10_000 = 126 --> 126 / 1_000 = 0.126 (0 as int) --> r3[0] = "" + // `r2[n%1e3/1e2]` --> 126 % 1_000 = 126 --> 126 / 100 = 1.26 (1 as int) --> r2[1] = "C" + // `r1[n%100/10]` --> 126 % 100 = 26 --> 26 / 10 = 2.6 (2 as int) --> r1[2] = "XX" + // `r0[n%10]` --> 126 % 10 = 6 --> r0[6] = "VI" + // FINAL --> "" + "C" + "XX" + "VI" = "CXXVI" + // + // This is efficient in Go. The 4 operands are evaluated, + // then a single allocation is made of the exact size needed for the result. + return r3[n%1e4/1e3] + r2[n%1e3/1e2] + r1[n%100/10] + r0[n%10], nil +} diff --git a/conversion/inttoroman_test.go b/conversion/inttoroman_test.go new file mode 100644 index 000000000..20bb24999 --- /dev/null +++ b/conversion/inttoroman_test.go @@ -0,0 +1,30 @@ +package conversion + +import "testing" + +func TestIntToRoman(t *testing.T) { + for expected, input := range romanTestCases { + out, err := IntToRoman(input) + if err != nil { + t.Errorf("IntToRoman(%d) returned an error %s", input, err.Error()) + } + if out != expected { + t.Errorf("IntToRoman(%d) = %s; want %s", input, out, expected) + } + } + _, err := IntToRoman(100000) + if err == nil { + t.Errorf("IntToRoman(%d) expected an error", 100000) + } + _, err = IntToRoman(0) + if err == nil { + t.Errorf("IntToRoman(%d) expected an error", 0) + } +} + +func BenchmarkIntToRoman(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _, _ = IntToRoman(3999) + } +} diff --git a/conversion/rgbhex.go b/conversion/rgbhex.go new file mode 100644 index 000000000..3d7265d2c --- /dev/null +++ b/conversion/rgbhex.go @@ -0,0 +1,55 @@ +// rgbhex.go +// description: convert hex input to red, green and blue and vice versa +// time complexity: O(1) +// space complexity: O(1) +// author(s) [darmiel](https://github.com/darmiel) +// see rgbhex_test.go + +package conversion + +// HEXToRGB splits an RGB input (e.g. a color in hex format; 0x) +// into the individual components: red, green and blue +func HEXToRGB(hex uint) (red, green, blue byte) { + // A hex code is structured like this: + // #3498db (light blue) - converted to binary: + // 00110100 10011000 11011011 + // + + // To get the blue value we use the bit operation AND with the bit mask 0xFF (in binary: 11111111) + // 00110100 10011000 <11011011> & + // 00000000 00000000 11111111 = + // 00000000 00000000 <11011011> = + blue = byte(hex & 0xFF) + + // To get the green value, we first shift the value 8 bits to the right: + // 00110100 <10011000> 11011011 >> 8 = + // 00000000 00110100 <10011000> & + // 00000000 00000000 11111111 = + // 00000000 00000000 <10011000> = + green = byte((hex >> 8) & 0xFF) + + // Same as green value, only this time shift 16 to the right + // Alternatively, you can apply a bitmask first and then shift it. + // <00110100> 10011000 11011011 & + // 11111111 00000000 00000000 = + // <00110100> 00000000 00000000 >> 16 + // 00000000 00000000 <00110100> = + red = byte((hex >> 16) & 0xFF) + return +} + +// RGBToHEX does exactly the opposite of HEXToRGB: +// it combines the three components red, green and blue to an RGB value, which can be converted to e.g. Hex +func RGBToHEX(red, green, blue byte) (hex uint) { + // Sets the bits of blue in position 1-8, green in 9-16 and red in 17-24 + + // Red: 00110100 + // Green: 10011000 + // Blue: 11011011 + // RGB: + // R << 16: [00110100] 00000000 00000000 | + // G << 8 : 00000000 {10011000} 00000000 | + // B : 00000000 00000000 <11011011> = + // [00110100] {10011000} <11011011> + return (uint(red) << 16) | (uint(green) << 8) | uint(blue) +} diff --git a/conversion/rgbhex_test.go b/conversion/rgbhex_test.go new file mode 100644 index 000000000..7b56cbe4d --- /dev/null +++ b/conversion/rgbhex_test.go @@ -0,0 +1,51 @@ +package conversion + +import "testing" + +var HEX = []uint{ + 0x1abc9c, + 0x3498db, + 0x9b59b6, +} + +var RGB = [][]byte{ + {26, 188, 156}, + {52, 152, 219}, + {155, 89, 182}, +} + +func TestHEXToRGB(t *testing.T) { + for i := 0; i < len(HEX); i++ { + hex := HEX[i] + expected := RGB[i] + resultR, resultG, resultB := HEXToRGB(hex) + if resultR != expected[0] || resultG != expected[1] || resultB != expected[2] { + t.Errorf("HEXToRGB(%d) = %d,%d,%d; want %d,%d,%d", + hex, resultR, resultG, resultB, expected[0], expected[1], expected[2]) + } + } +} + +func BenchmarkHEXToRGB(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _, _ = HEXToRGB(0xdeadbe) + } +} + +func TestRGBToHEX(t *testing.T) { + for i := 0; i < len(RGB); i++ { + args := RGB[i] + expected := HEX[i] + result := RGBToHEX(args[0], args[1], args[2]) + if result != expected { + t.Errorf("RGBToHEX(%d,%d,%d) = %d; want %d", + args[0], args[1], args[2], result, expected) + } + } +} + +func BenchmarkRGBToHEX(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = RGBToHEX(222, 173, 190) + } +} diff --git a/conversion/romantoint.go b/conversion/romantoint.go new file mode 100644 index 000000000..629952320 --- /dev/null +++ b/conversion/romantoint.go @@ -0,0 +1,59 @@ +// This algorithm will convert a standard roman number to an integer +// https://en.wikipedia.org/wiki/Roman_numerals +// Function receives a string as a roman number and outputs an integer +// Maximum output will be 3999 +// Only standard form is supported +// time complexity: O(n) +// space complexity: O(1) + +package conversion + +import ( + "errors" + "strings" +) + +// numeral describes the value and symbol of a single roman numeral +type numeral struct { + val int + sym string +} + +// lookup array for numeral values sorted by largest to smallest +var nums = []numeral{ + {1000, "M"}, + {900, "CM"}, + {500, "D"}, + {400, "CD"}, + {100, "C"}, + {90, "XC"}, + {50, "L"}, + {40, "XL"}, + {10, "X"}, + {9, "IX"}, + {5, "V"}, + {4, "IV"}, + {1, "I"}, +} + +// RomanToInt converts a roman numeral string to an integer. Roman numerals for numbers +// outside the range 1 to 3,999 will return an error. Nil or empty string return 0 +// with no error thrown. +func RomanToInt(input string) (int, error) { + if input == "" { + return 0, nil + } + var output int + for _, n := range nums { + for strings.HasPrefix(input, n.sym) { + output += n.val + input = input[len(n.sym):] + } + } + // if we are still left with input string values then the + // input was invalid and an error is returned. + if len(input) > 0 { + return 0, errors.New("invalid roman numeral") + } + return output, nil +} diff --git a/conversion/romantoint_test.go b/conversion/romantoint_test.go new file mode 100644 index 000000000..0fd34b2c3 --- /dev/null +++ b/conversion/romantoint_test.go @@ -0,0 +1,53 @@ +package conversion + +import "testing" + +var romanTestCases = map[string]int{ + "I": 1, "II": 2, "III": 3, "IV": 4, "V": 5, "VI": 6, + "VII": 7, "VIII": 8, "IX": 9, "X": 10, "XI": 11, "XII": 12, + "XIII": 13, "XIV": 14, "XV": 15, "XVI": 16, "XVII": 17, + "XVIII": 18, "XIX": 19, "XX": 20, "XXXI": 31, "XXXII": 32, + "XXXIII": 33, "XXXIV": 34, "XXXV": 35, "XXXVI": 36, "XXXVII": 37, + "XXXVIII": 38, "XXXIX": 39, "XL": 40, "XLI": 41, "XLII": 42, + "XLIII": 43, "XLIV": 44, "XLV": 45, "XLVI": 46, "XLVII": 47, + "XLVIII": 48, "XLIX": 49, "L": 50, "LXXXIX": 89, "XC": 90, + "XCI": 91, "XCII": 92, "XCIII": 93, "XCIV": 94, "XCV": 95, + "XCVI": 96, "XCVII": 97, "XCVIII": 98, "XCIX": 99, "C": 100, + "CI": 101, "CII": 102, "CIII": 103, "CIV": 104, "CV": 105, + "CVI": 106, "CVII": 107, "CVIII": 108, "CIX": 109, "CXLIX": 149, + "CCCXLIX": 349, "CDLVI": 456, "D": 500, "DCIV": 604, "DCCLXXXIX": 789, + "DCCCXLIX": 849, "CMIV": 904, "M": 1000, "MVII": 1007, "MLXVI": 1066, + "MCCXXXIV": 1234, "MDCCLXXVI": 1776, "MMXXI": 2021, "MMDCCCVI": 2806, + "MMCMXCIX": 2999, "MMM": 3000, "MMMCMLXXIX": 3979, "MMMCMXCIX": 3999, +} + +func TestRomanToInt(t *testing.T) { + for input, expected := range romanTestCases { + out, err := RomanToInt(input) + if err != nil { + t.Errorf("RomanToInt(%s) returned an error %s", input, err.Error()) + } + if out != expected { + t.Errorf("RomanToInt(%s) = %d; want %d", input, out, expected) + } + } + _, err := RomanToInt("IVCMXCIX") + if err == nil { + t.Error("RomanToInt(IVCMXCIX) expected an error") + } + + val, err := RomanToInt("") + if val != 0 { + t.Errorf("RomanToInt(\"\") = %d; want 0", val) + } + if err != nil { + t.Errorf("RomanToInt(\"\") returned an error %s", err.Error()) + } +} + +func BenchmarkRomanToInt(b *testing.B) { + b.ReportAllocs() + for i := 0; i < b.N; i++ { + _, _ = RomanToInt("MMMCMXCIX") + } +} diff --git a/data-structures/binary-tree/binary-search-tree.go b/data-structures/binary-tree/binary-search-tree.go deleted file mode 100644 index 1ce14349c..000000000 --- a/data-structures/binary-tree/binary-search-tree.go +++ /dev/null @@ -1,122 +0,0 @@ -// Binary search tree -// https://en.wikipedia.org/wiki/Binary_search_tree - -package binarySearchTree - -// package main - -import "fmt" - -type node struct { - val int - left *node - right *node -} - -type btree struct { - root *node -} - -func max(a, b int) int { - if a > b { - return a - } - return b -} - -func newNode(val int) *node { - return &node{val, nil, nil} -} - -func inorder(n *node) { - if n != nil { - inorder(n.left) - fmt.Print(n.val, " ") - inorder(n.right) - } -} - -func insert(root *node, val int) *node { - if root == nil { - return newNode(val) - } - if val < root.val { - root.left = insert(root.left, val) - } else { - root.right = insert(root.right, val) - } - return root -} - -func inorderSuccessor(root *node) *node { - cur := root - for cur.left != nil { - cur = cur.left - } - return cur -} - -func bst_delete(root *node, val int) *node { - if root == nil { - return nil - } - if val < root.val { - root.left = bst_delete(root.left, val) - } else if val > root.val { - root.right = bst_delete(root.right, val) - } else { - // this is the node to delete - - // node with one child - if root.left == nil { - root = root.right - } else if root.right == nil { - root = root.left - } else { - // node with two children - d := inorderSuccessor(root) - root.val = d.val - root.right = bst_delete(root.right, d.val) - } - } - return root -} - -// helper function for t.depth -func _calculate_depth(n *node, depth int) int { - if n == nil { - return depth - } - return max(_calculate_depth(n.left, depth+1), _calculate_depth(n.right, depth+1)) -} - -func (t *btree) depth() int { - return _calculate_depth(t.root, 0) -} - -/* -func main() { - t := &btree{nil} - inorder(t.root) - t.root = insert(t.root, 10) - t.root = insert(t.root, 20) - t.root = insert(t.root, 15) - t.root = insert(t.root, 30) - fmt.Print(t.depth(), "\n") - inorder(t.root) - fmt.Print("\n") - t.root = bst_delete(t.root, 10) - inorder(t.root) - fmt.Print("\n") - t.root = bst_delete(t.root, 30) - inorder(t.root) - fmt.Print("\n") - t.root = bst_delete(t.root, 15) - inorder(t.root) - fmt.Print("\n") - t.root = bst_delete(t.root, 20) - inorder(t.root) - fmt.Print("\n") - fmt.Print(t.depth(), "\n") -} -*/ diff --git a/data-structures/binary-tree/binary-tree.go b/data-structures/binary-tree/binary-tree.go deleted file mode 100644 index 80a88c6d4..000000000 --- a/data-structures/binary-tree/binary-tree.go +++ /dev/null @@ -1,110 +0,0 @@ -// basic binary tree and related operations - -package binarytree - -// package main - -import "fmt" - -type node struct { - val int - left *node - right *node -} - -type btree struct { - root *node -} - -func max(a, b int) int { - if a > b { - return a - } - return b -} - -func newNode(val int) *node { - n := &node{val, nil, nil} - return n -} - -func inorder(n *node) { - if n == nil { - return - } - inorder(n.left) - fmt.Print(n.val, " ") - inorder(n.right) -} - -func preorder(n *node) { - if n == nil { - return - } - fmt.Print(n.val, " ") - inorder(n.left) - inorder(n.right) -} - -func postorder(n *node) { - if n == nil { - return - } - inorder(n.left) - inorder(n.right) - fmt.Print(n.val, " ") -} - -func levelorder(root *node) { - var q []*node // queue - var n *node // temporary node - - q = append(q, root) - - for len(q) != 0 { - n, q = q[0], q[1:] - fmt.Print(n.val, " ") - if n.left != nil { - q = append(q, n.left) - } - if n.right != nil { - q = append(q, n.right) - } - } -} - -// helper function for t.depth -func _calculate_depth(n *node, depth int) int { - if n == nil { - return depth - } - return max(_calculate_depth(n.left, depth+1), _calculate_depth(n.right, depth+1)) -} - -func (t *btree) depth() int { - return _calculate_depth(t.root, 0) -} - -/* -func main() { - t := btree{nil} - t.root = newNode(0) - t.root.left = newNode(1) - t.root.right = newNode(2) - t.root.left.left = newNode(3) - t.root.left.right = newNode(4) - t.root.right.left = newNode(5) - t.root.right.right = newNode(6) - t.root.right.right.right = newNode(10) - - inorder(t.root) - fmt.Print("\n") - preorder(t.root) - fmt.Print("\n") - postorder(t.root) - fmt.Print("\n") - levelorder(t.root) - fmt.Print("\n") - fmt.Print(t.depth(), "\n") -} -*/ diff --git a/data-structures/dynamic-array/dynamic_array.go b/data-structures/dynamic-array/dynamic_array.go deleted file mode 100644 index 70b11b38e..000000000 --- a/data-structures/dynamic-array/dynamic_array.go +++ /dev/null @@ -1,114 +0,0 @@ -package dynamic-array - -import ( - "errors" -) - -var defaultCapacity = 10 - -type dynamicArray struct { - size int - capacity int - elementData []interface{} -} - -func (da *dynamicArray) put(index int, element interface{}) error { - err := da.checkRangeFromIndex(index) - - if err != nil { - return err - } - - da.elementData[index] = element - - return nil -} - -func (da *dynamicArray) add(element interface{}) { - if da.size == da.capacity { - da.newCapacity() - } - - da.elementData[da.size] = element - da.size++ -} - -func (da *dynamicArray) remove(index int) error { - err := da.checkRangeFromIndex(index) - - if err != nil { - return err - } - - copy(da.elementData[index:], da.elementData[index+1:da.size]) - da.elementData[da.size-1] = nil - - da.size-- - - return nil -} - -func (da *dynamicArray) get(index int) (interface{}, error) { - err := da.checkRangeFromIndex(index) - - if err != nil { - return nil, err - } - - return da.elementData[index], nil -} - -func (da *dynamicArray) isEmpty() bool { - return da.size == 0 -} - -func (da *dynamicArray) getData() []interface{} { - return da.elementData[:da.size] -} - -func (da *dynamicArray) checkRangeFromIndex(index int) error { - if index >= da.size || index < 0 { - return errors.New("index out of range") - } - return nil -} - -func (da *dynamicArray) newCapacity() { - if da.capacity == 0 { - da.capacity = defaultCapacity - } else { - da.capacity = da.capacity << 1 - } - - newDataElement := make([]interface{}, da.capacity) - - copy(newDataElement, da.elementData) - - da.elementData = newDataElement -} - -// func main() { -// numbers := dynamicArray{} -// fmt.Println(numbers.isEmpty()) - -// numbers.add(10) -// numbers.add(20) -// numbers.add(30) -// numbers.add(40) -// numbers.add(50) - -// fmt.Println(numbers.isEmpty()) - -// fmt.Println(numbers.getData()) - -// numbers.remove(1) - -// fmt.Println(numbers.getData()) - -// numberFound, _ := numbers.get(1) -// fmt.Println(numberFound) - -// numbers.put(0, 100) -// fmt.Println(numbers.getData()) -// } - diff --git a/data-structures/linked-list/Linkedlist.go b/data-structures/linked-list/Linkedlist.go deleted file mode 100644 index 6bad5c840..000000000 --- a/data-structures/linked-list/Linkedlist.go +++ /dev/null @@ -1,102 +0,0 @@ -package main - -import "fmt" - -/* v is the value of node; next is the pointer to next node */ -type node struct { - v int - next *node -} - -/* first node, called head. It points from first node to last node */ -var head *node = nil - -func (l *node) pushFront(val int) *node { - /* if there's no nodes, head points to l (first node) */ - if head == nil { - l.v = val - l.next = nil - head = l - return l - } else { - /* create a new node equals to head */ - nnode := new(node) - nnode = head - /* create a second node with new value and `next -> nnode` - * is this way, nnode2 is before nnode - */ - nnode2 := &node { - v: val, - next: nnode, - } - /* now head is equals nnode2 */ - head = nnode2 - return head - } -} - -func (l *node) pushBack(val int) *node { - /* if there's no nodes, head points to l (first node) */ - if head == nil { - l.v = val - l.next = nil - head = l - return l - } else { - /* read all list to last node */ - for l.next != nil { - l = l.next - } - /* allocate a new portion of memory */ - l.next = new(node) - l.next.v = val - l.next.next = nil - return l - } -} - -func (l *node) popFront() *node { - if head == nil { - return head - } - /* create a new node equals to first node pointed by head */ - cpnode := new(node) - cpnode = head.next - - /* now head is equals cpnode (second node) */ - head = cpnode - - return head -} - -func (l *node) popBack() *node { - if head == nil { - return head - } - /* create a new node equals to head */ - cpnode := new(node) - cpnode = head - - /* read list to the penultimate node */ - for cpnode.next.next != nil { - cpnode = cpnode.next - } - /* the penultimate node points to null. In this way the last node is deleted */ - cpnode.next = nil - return head -} - -func main() { - lista := new(node) - lista.pushBack(25).pushBack(24).pushBack(32) /* lista: 25 24 32 */ - lista.pushBack(56) /* lista: 25 24 32 56 */ - lista.pushFront(36) /* lista: 36 25 24 32 56 */ - lista.popFront() /* lista: 25 24 32 56 */ - lista.popBack() /* lista: 25 24 32 */ - - /* read the list until head is not nil */ - for head != nil { - fmt.Printf("%d ",head.v) - head = head.next /*head points to next node */ - } -} diff --git a/data-structures/linked-list/double-linkedlist.go b/data-structures/linked-list/double-linkedlist.go deleted file mode 100644 index c87f9003b..000000000 --- a/data-structures/linked-list/double-linkedlist.go +++ /dev/null @@ -1,156 +0,0 @@ -// demonstration of doubly linked list in golang - -package doublelinkedlist - -// package main - -import "fmt" - -type node struct { - val int - next *node - prev *node -} - -type doublelinkedlist struct { - head *node -} - -// to avoid mistakes when using pointer vs struct for new node creation -func newNode(val int) *node { - n := &node{} - n.val = val - n.next = nil - n.prev = nil - return n -} - -func (ll *doublelinkedlist) addAtBeg(val int) { - n := newNode(val) - n.next = ll.head - ll.head = n -} - -func (ll *doublelinkedlist) addAtEnd(val int) { - n := newNode(val) - - if ll.head == nil { - ll.head = n - return - } - - cur := ll.head - for ; cur.next != nil; cur = cur.next { - } - cur.next = n - n.prev = cur -} - -func (ll *doublelinkedlist) delAtBeg() int { - if ll.head == nil { - return -1 - } - - cur := ll.head - ll.head = cur.next - - if ll.head != nil { - ll.head.prev = nil - } - - return cur.val -} - -func (ll *doublelinkedlist) delAtEnd() int { - // no item - if ll.head == nil { - return -1 - } - - // only one item - if ll.head.next == nil { - return ll.delAtBeg() - } - - // more than one, go to second last - cur := ll.head - for ; cur.next.next != nil; cur = cur.next { - } - - retval := cur.next.val - cur.next = nil - return retval -} - -func (ll *doublelinkedlist) count() int { - var ctr int = 0 - - for cur := ll.head; cur != nil; cur = cur.next { - ctr += 1 - } - - return ctr -} - -func (ll *doublelinkedlist) reverse() { - var prev, next *node - cur := ll.head - - for cur != nil { - next = cur.next - cur.next = prev - cur.prev = next - prev = cur - cur = next - } - - ll.head = prev -} - -func (ll *doublelinkedlist) display() { - for cur := ll.head; cur != nil; cur = cur.next { - fmt.Print(cur.val, " ") - } - - fmt.Print("\n") -} - -func (ll *doublelinkedlist) displayReverse() { - if ll.head == nil { - return - } - var cur *node - for cur = ll.head; cur.next != nil; cur = cur.next { - } - - for ; cur != nil; cur = cur.prev { - fmt.Print(cur.val, " ") - } - - fmt.Print("\n") -} - -/* -func main() { - ll := doublelinkedlist{} - - ll.addAtBeg(10) - ll.addAtEnd(20) - ll.display() - ll.addAtBeg(30) - ll.display() - - ll.reverse() - ll.display() - ll.displayReverse() - - fmt.Print(ll.delAtBeg(), "\n") - fmt.Print(ll.delAtEnd(), "\n") - fmt.Print("Display") - ll.display() - fmt.Print(ll.delAtBeg(), "\n") - ll.display() - fmt.Print(ll.delAtBeg(), "\n") - ll.display() -} -*/ diff --git a/data-structures/linked-list/single-linkedlist.go b/data-structures/linked-list/single-linkedlist.go deleted file mode 100644 index bbcfb46ac..000000000 --- a/data-structures/linked-list/single-linkedlist.go +++ /dev/null @@ -1,123 +0,0 @@ -// demonstration of singly linked list in golang - -package singlelinkedlist - -// package main - -import "fmt" - -type node struct { - val int - next *node -} - -type singlelinkedlist struct { - head *node -} - -// to avoid mistakes when using pointer vs struct for new node creation -func newNode(val int) *node { - return &node{val, nil} -} - -func (ll *singlelinkedlist) addAtBeg(val int) { - n := newNode(val) - n.next = ll.head - ll.head = n -} - -func (ll *singlelinkedlist) addAtEnd(val int) { - n := newNode(val) - - if ll.head == nil { - ll.head = n - return - } - - cur := ll.head - for ; cur.next != nil; cur = cur.next { - } - cur.next = n -} - -func (ll *singlelinkedlist) delAtBeg() int { - if ll.head == nil { - return -1 - } - - cur := ll.head - ll.head = cur.next - - return cur.val -} - -func (ll *singlelinkedlist) delAtEnd() int { - if ll.head == nil { - return -1 - } - - if ll.head.next == nil { - return ll.delAtBeg() - } - - cur := ll.head - - for ; cur.next.next != nil; cur = cur.next { - } - - retval := cur.next.val - cur.next = nil - return retval - -} - -func (ll *singlelinkedlist) count() int { - var ctr int = 0 - - for cur := ll.head; cur != nil; cur = cur.next { - ctr += 1 - } - - return ctr -} - -func (ll *singlelinkedlist) reverse() { - var prev, next *node - cur := ll.head - - for cur != nil { - next = cur.next - cur.next = prev - prev = cur - cur = next - } - - ll.head = prev -} - -func (ll *singlelinkedlist) display() { - for cur := ll.head; cur != nil; cur = cur.next { - fmt.Print(cur.val, " ") - } - - fmt.Print("\n") -} - -// func main() { -// ll := singlelinkedlist{} - -// ll.addAtBeg(10) -// ll.addAtEnd(20) -// ll.display() -// ll.addAtBeg(30) -// ll.display() -// ll.reverse() -// ll.display() - -// fmt.Print(ll.delAtBeg(), "\n") -// ll.display() - -// fmt.Print(ll.delAtEnd(), "\n") -// ll.display() - -// } diff --git a/data-structures/trie/trie.go b/data-structures/trie/trie.go deleted file mode 100644 index df3c87ae3..000000000 --- a/data-structures/trie/trie.go +++ /dev/null @@ -1,46 +0,0 @@ -// Package trie provides Trie data structures in golang. -// -// Wikipedia: https://en.wikipedia.org/wiki/Trie -package trie - -// Node represents each node in Trie. -type Node struct { - children map[rune]*Node // map children nodes - isLeaf bool // current node value -} - -// NewNode creates a new Trie node with initialized -// children map. -func NewNode() *Node { - n := &Node{} - n.children = make(map[rune]*Node) - n.isLeaf = false - return n -} - -// Insert inserts words at a Trie node. -func (n *Node) Insert(s string) { - curr := n - for _, c := range s { - next, ok := curr.children[c] - if !ok { - next = NewNode() - curr.children[c] = next - } - curr = next - } - curr.isLeaf = true -} - -// Find finds words at a Trie node. -func (n *Node) Find(s string) bool { - curr := n - for _, c := range s { - next, ok := curr.children[c] - if !ok { - return false - } - curr = next - } - return true -} diff --git a/data-structures/trie/trie_test.go b/data-structures/trie/trie_test.go deleted file mode 100644 index 4c6c94901..000000000 --- a/data-structures/trie/trie_test.go +++ /dev/null @@ -1,70 +0,0 @@ -package trie - -import ( - "testing" -) - -func TestTrie(t *testing.T) { - n := NewNode() - - insertWords := [...]string{ - "nikola", - "tesla", - } - checkWords := map[string]bool{ - "thomas": false, - "edison": false, - "nikola": true, - } - - for _, w := range insertWords { - n.insert(w) - t.Logf( - "added \"%s\" to the Trie.", - w, - ) - } - - for k, v := range checkWords { - ok := n.find(k) - if ok != v { - t.Fatalf( - "\"%s\" is supposed to be %sin the Trie.", - k, - map[bool]string{true: "", false: "NOT "}[v], - ) - } - t.Logf( - "\"%s\" is %sin the Trie.", - k, - map[bool]string{true: "", false: "NOT "}[ok], - ) - } -} - -func BenchmarkTrie(b *testing.B) { - for i := 0; i < b.N; i++ { - n := NewNode() - - n.insert("nikola") - n.insert("tesla") - - n.find("thomas") - n.find("edison") - n.find("nikola") - } -} - -func ExampleNode() { - // creates a new node - node := NewNode() - - // adds words - node.insert("nikola") - node.insert("tesla") - - // finds words - node.find("thomas") // false - node.find("edison") // false - node.find("nikola") // true -} diff --git a/dynamic/abbreviation.go b/dynamic/abbreviation.go new file mode 100644 index 000000000..e5b7ad6e9 --- /dev/null +++ b/dynamic/abbreviation.go @@ -0,0 +1,47 @@ +// File: abbreviation.go +// Description: Abbreviation problem +// Details: +// https://www.hackerrank.com/challenges/abbr/problem +// Problem description (from hackerrank): +// You can perform the following operations on the string, a: +// 1. Capitalize zero or more of a's lowercase letters. +// 2. Delete all of the remaining lowercase letters in a. +// Given 2 strings a and b, determine if it's possible to make a equal to be using above operations. +// Example: +// Given a = "ABcde" and b = "ABCD" +// We can capitalize "c" and "d" in a to get "ABCde" then delete all the lowercase letters (which is only "e") in a to get "ABCD" which equals b. +// Author: [duongoku](https://github.com/duongoku) +// Time Complexity: O(n*m) where n is the length of a and m is the length of b +// Space Complexity: O(n*m) where n is the length of a and m is the length of b +// See abbreviation_test.go for test cases + +package dynamic + +// strings for getting uppercases and lowercases +import ( + "strings" +) + +// Returns true if it is possible to make a equals b (if b is an abbreviation of a), returns false otherwise +func Abbreviation(a string, b string) bool { + dp := make([][]bool, len(a)+1) + for i := range dp { + dp[i] = make([]bool, len(b)+1) + } + dp[0][0] = true + + for i := 0; i < len(a); i++ { + for j := 0; j <= len(b); j++ { + if dp[i][j] { + if j < len(b) && strings.ToUpper(string(a[i])) == string(b[j]) { + dp[i+1][j+1] = true + } + if string(a[i]) == strings.ToLower(string(a[i])) { + dp[i+1][j] = true + } + } + } + } + + return dp[len(a)][len(b)] +} diff --git a/dynamic/abbreviation_test.go b/dynamic/abbreviation_test.go new file mode 100644 index 000000000..38824d33a --- /dev/null +++ b/dynamic/abbreviation_test.go @@ -0,0 +1,41 @@ +package dynamic + +import ( + "fmt" + "testing" +) + +func TestAbbreviation(t *testing.T) { + tests := []struct { + a string + b string + expected bool + }{ + {"uOHlGMdUBc", "uOalGMdUBCasdcavsdf", false}, + {"kotgDIUagj", "DIU", true}, + {"WPTffVkSNl", "WPTVSN", true}, + {"CoJsPURrVX", "CPUVX", false}, + {"xasreDHndqvCnFfX", "DHndqvCnFX", false}, + {"XFEaWCxpeepGjOnCCsFh", "XFEAWCPEPGOCCSF", true}, + {"", "", true}, + {"a", "", true}, + {"a", "b", false}, + {"a", "a", false}, + {"A", "A", true}, + } + count := len(tests) + for i := 0; i < count; i++ { + name := fmt.Sprintf( + "Test case #%d: string a = \"%s\", string b = \"%s\"", + i+1, + tests[i].a, + tests[i].b, + ) + t.Run(name, func(t *testing.T) { + result := Abbreviation(tests[i].a, tests[i].b) + if result != tests[i].expected { + t.Errorf("Expected the %t, got %t", tests[i].expected, result) + } + }) + } +} diff --git a/dynamic/binomialcoefficient.go b/dynamic/binomialcoefficient.go new file mode 100644 index 000000000..fed664fd5 --- /dev/null +++ b/dynamic/binomialcoefficient.go @@ -0,0 +1,43 @@ +// binomialcoefficient.go +// description: Implementation of the binomial coefficient using dynamic programming +// details: The binomial coefficient C(n, k) is the number of ways to choose a subset of k elements from a set of n elements. The binomial coefficient is calculated using the formula C(n, k) = C(n-1, k-1) + C(n-1, k) with base cases C(n, 0) = C(n, n) = 1. +// time complexity: O(n*k) where n is the number of elements and k is the number of elements to choose +// space complexity: O(n*k) where n is the number of elements and k is the number of elements to choose +package dynamic + +import "github.com/TheAlgorithms/Go/math/min" + +// func main() { +// myArrayOfK := [4]int{5, 6, 7, 8} +// var x int + +// fmt.Println("\nBinomial Coefficient Using Dynamic Programming:", bin2(50, 5)) +// for _, element := range myArrayOfK { +// start := time.Now() +// x = bin2(50, element) +// elapsed := time.Since(start) +// fmt.Println("bin2 (50,", element, ") = ", x, " took ", elapsed) + +// } + +// } + +// Bin2 function +func Bin2(n int, k int) int { + var i, j int + B := make([][]int, (n + 1)) + for i := range B { + B[i] = make([]int, k+1) + } + + for i = 0; i <= n; i++ { + for j = 0; j <= min.Int(i, k); j++ { + if j == 0 || j == i { + B[i][j] = 1 + } else { + B[i][j] = B[i-1][j-1] + B[i-1][j] + } + } + } + return B[n][k] +} diff --git a/dynamic/binomialcoefficient_test.go b/dynamic/binomialcoefficient_test.go new file mode 100644 index 000000000..109a5b955 --- /dev/null +++ b/dynamic/binomialcoefficient_test.go @@ -0,0 +1,32 @@ +package dynamic_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +func TestBin2(t *testing.T) { + td := []struct { + n, k, expected int + }{ + {0, 0, 1}, + {1, 1, 1}, + {2, 0, 1}, {2, 1, 2}, {2, 2, 1}, + {3, 0, 1}, {3, 1, 3}, {3, 2, 3}, {3, 3, 1}, + {4, 0, 1}, {4, 1, 4}, {4, 2, 6}, {4, 3, 4}, {4, 4, 1}, + {5, 0, 1}, {5, 1, 5}, {5, 2, 10}, {5, 3, 10}, {5, 4, 5}, {5, 5, 1}, + {10, 2, 45}, + {15, 10, 3003}, + } + for _, tc := range td { + name := fmt.Sprintf("binomial coefficient of (%d, %d)", tc.n, tc.k) + t.Run(name, func(t *testing.T) { + actual := dynamic.Bin2(tc.n, tc.k) + if actual != tc.expected { + t.Errorf("expecting binomial coefficient of (%d, %d) to be %d but got %d", tc.n, tc.k, tc.expected, actual) + } + }) + } +} diff --git a/dynamic/burstballoons.go b/dynamic/burstballoons.go new file mode 100644 index 000000000..492b00d8c --- /dev/null +++ b/dynamic/burstballoons.go @@ -0,0 +1,31 @@ +package dynamic + +import "github.com/TheAlgorithms/Go/math/max" + +// MaxCoins returns the maximum coins we can collect by bursting the balloons +func MaxCoins(nums []int) int { + n := len(nums) + if n == 0 { + return 0 + } + + nums = append([]int{1}, nums...) + nums = append(nums, 1) + + dp := make([][]int, n+2) + for i := range dp { + dp[i] = make([]int, n+2) + } + + for length := 1; length <= n; length++ { + for left := 1; left+length-1 <= n; left++ { + right := left + length - 1 + for k := left; k <= right; k++ { + coins := nums[left-1] * nums[k] * nums[right+1] + dp[left][right] = max.Int(dp[left][right], dp[left][k-1]+dp[k+1][right]+coins) + } + } + } + + return dp[1][n] +} diff --git a/dynamic/burstballoons_test.go b/dynamic/burstballoons_test.go new file mode 100644 index 000000000..c36e08824 --- /dev/null +++ b/dynamic/burstballoons_test.go @@ -0,0 +1,33 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseBurstBalloons struct { + nums []int + expected int +} + +func getBurstBalloonsTestCases() []testCaseBurstBalloons { + return []testCaseBurstBalloons{ + {[]int{3, 1, 5, 8}, 167}, // Maximum coins from [3,1,5,8] + {[]int{1, 5}, 10}, // Maximum coins from [1,5] + {[]int{1}, 1}, // Single balloon + {[]int{}, 0}, // No balloons + } + +} + +func TestMaxCoins(t *testing.T) { + t.Run("Burst Balloons test cases", func(t *testing.T) { + for _, tc := range getBurstBalloonsTestCases() { + actual := dynamic.MaxCoins(tc.nums) + if actual != tc.expected { + t.Errorf("MaxCoins(%v) = %d; expected %d", tc.nums, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/catalan.go b/dynamic/catalan.go new file mode 100644 index 000000000..2f53c3edb --- /dev/null +++ b/dynamic/catalan.go @@ -0,0 +1,33 @@ +//The Catalan numbers are a sequence of positive integers that appear in many counting +// problems in combinatorics. +// time complexity: O(n²) +// space complexity: O(n) +//reference: https://brilliant.org/wiki/catalan-numbers/ + +package dynamic + +import "fmt" + +var errCatalan = fmt.Errorf("can't have a negative n-th catalan number") + +// NthCatalan returns the n-th Catalan Number +// Complexity: O(n²) +func NthCatalanNumber(n int) (int64, error) { + if n < 0 { + //doesn't accept negative number + return 0, errCatalan + } + + var catalanNumberList []int64 + catalanNumberList = append(catalanNumberList, 1) //first value is 1 + + for i := 1; i <= n; i++ { + catalanNumberList = append(catalanNumberList, 0) //append 0 and calculate + + for j := 0; j < i; j++ { + catalanNumberList[i] += catalanNumberList[j] * catalanNumberList[i-j-1] + } + } + + return catalanNumberList[n], nil +} diff --git a/dynamic/catalan_test.go b/dynamic/catalan_test.go new file mode 100644 index 000000000..4867053d8 --- /dev/null +++ b/dynamic/catalan_test.go @@ -0,0 +1,46 @@ +package dynamic + +import ( + "fmt" + "testing" +) + +func TestCatalanNumbers(t *testing.T) { + var testCatalanNumbersData = []struct { + nthCatalanNumber int + expectedCatalanNumber int64 + expectedError error + }{ + {nthCatalanNumber: -1000, expectedCatalanNumber: 0, expectedError: errCatalan}, + {nthCatalanNumber: -1, expectedCatalanNumber: 0, expectedError: errCatalan}, + {nthCatalanNumber: 0, expectedCatalanNumber: 1, expectedError: nil}, + {nthCatalanNumber: 1, expectedCatalanNumber: 1, expectedError: nil}, + {nthCatalanNumber: 2, expectedCatalanNumber: 2, expectedError: nil}, + {nthCatalanNumber: 3, expectedCatalanNumber: 5, expectedError: nil}, + {nthCatalanNumber: 4, expectedCatalanNumber: 14, expectedError: nil}, + {nthCatalanNumber: 5, expectedCatalanNumber: 42, expectedError: nil}, + {nthCatalanNumber: 6, expectedCatalanNumber: 132, expectedError: nil}, + {nthCatalanNumber: 7, expectedCatalanNumber: 429, expectedError: nil}, + {nthCatalanNumber: 8, expectedCatalanNumber: 1430, expectedError: nil}, + {nthCatalanNumber: 9, expectedCatalanNumber: 4862, expectedError: nil}, + {nthCatalanNumber: 10, expectedCatalanNumber: 16796, expectedError: nil}, + {nthCatalanNumber: 1000, expectedCatalanNumber: 4233371109654655040, expectedError: nil}, + } + + for i := range testCatalanNumbersData { + t.Run(fmt.Sprintf("the %dth Catalan Number", testCatalanNumbersData[i].nthCatalanNumber), func(t *testing.T) { + nthCatalanNumber := testCatalanNumbersData[i].nthCatalanNumber + result, err := NthCatalanNumber(nthCatalanNumber) + expectedCatalanNumber := testCatalanNumbersData[i].expectedCatalanNumber + expectedError := testCatalanNumbersData[i].expectedError + + if err != expectedError { + t.Errorf("Expected %dth Catalan Number error: %d\nFound: %d\n", nthCatalanNumber, expectedError, err) + } + + if result != expectedCatalanNumber { + t.Errorf("Expected %dth Catalan Number: %d\nFound: %d\n", nthCatalanNumber, expectedCatalanNumber, result) + } + }) + } +} diff --git a/dynamic/coinchange.go b/dynamic/coinchange.go new file mode 100644 index 000000000..2ba6064ab --- /dev/null +++ b/dynamic/coinchange.go @@ -0,0 +1,23 @@ +// coinchange.go +// description: Implementation of the coin change problem using dynamic programming +// details: The coin change problem is a problem that asks for the number of ways to make change for a given amount of money using a given set of coins. The problem can be solved using dynamic programming. +// time complexity: O(n*m) where n is the number of coins and m is the amount of money +// space complexity: O(m) where m is the amount of money + +package dynamic + +// CoinChange finds the number of possible combinations of coins +// of different values which can get to the target amount. +func CoinChange(coins []int32, amount int32) int32 { + combination := make([]int32, amount) + combination[0] = 1 + + for _, c := range coins { + for i := c; i < amount; i++ { + + combination[i] += combination[i-c] + } + } + + return combination[amount-1] +} diff --git a/dynamic/coinchange_test.go b/dynamic/coinchange_test.go new file mode 100644 index 000000000..174a702f8 --- /dev/null +++ b/dynamic/coinchange_test.go @@ -0,0 +1,31 @@ +package dynamic_test + +import ( + "fmt" + "github.com/TheAlgorithms/Go/dynamic" + "testing" +) + +func TestCoinChange(t *testing.T) { + coinCombination := []int32{1, 2, 5, 10} + targets := []struct { + target int32 + expected int32 + }{ + {4, 2}, + {5, 3}, + {10, 8}, + {15, 19}, + {20, 34}, + } + + for _, v := range targets { + t.Run(fmt.Sprintf("target: %d ", v.target), func(t *testing.T) { + result := dynamic.CoinChange(coinCombination, v.target) + if result != v.expected { + t.Errorf("target: %d Expected %d, got %d", v.target, v.expected, result) + } + }) + } + +} diff --git a/dynamic/dicethrow.go b/dynamic/dicethrow.go new file mode 100644 index 000000000..69711ca14 --- /dev/null +++ b/dynamic/dicethrow.go @@ -0,0 +1,33 @@ +// dicethrow.go +// description: Solves the Dice Throw Problem using dynamic programming +// reference: https://www.geeksforgeeks.org/dice-throw-problem/ +// time complexity: O(m * n) +// space complexity: O(m * n) + +package dynamic + +// DiceThrow returns the number of ways to get sum `sum` using `m` dice with `n` faces +func DiceThrow(m, n, sum int) int { + dp := make([][]int, m+1) + for i := range dp { + dp[i] = make([]int, sum+1) + } + + for i := 1; i <= n; i++ { + if i <= sum { + dp[1][i] = 1 + } + } + + for i := 2; i <= m; i++ { + for j := 1; j <= sum; j++ { + for k := 1; k <= n; k++ { + if j-k >= 0 { + dp[i][j] += dp[i-1][j-k] + } + } + } + } + + return dp[m][sum] +} diff --git a/dynamic/dicethrow_test.go b/dynamic/dicethrow_test.go new file mode 100644 index 000000000..dad25e533 --- /dev/null +++ b/dynamic/dicethrow_test.go @@ -0,0 +1,42 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseDiceThrow struct { + numDice int + numFaces int + targetSum int + expected int +} + +// getDiceThrowTestCases provides the test cases for DiceThrow +func getDiceThrowTestCases() []testCaseDiceThrow { + return []testCaseDiceThrow{ + {2, 6, 7, 6}, // Two dice, six faces each, sum = 7 + {1, 6, 3, 1}, // One die, six faces, sum = 3 + {3, 4, 5, 6}, // Three dice, four faces each, sum = 5 + {1, 6, 1, 1}, // One die, six faces, sum = 1 + {2, 6, 12, 1}, // Two dice, six faces each, sum = 12 + {3, 6, 18, 1}, // Three dice, six faces each, sum = 18 + {2, 6, 20, 0}, // Two dice, six faces each, sum = 20 (impossible) + {1, 1, 1, 1}, // One die, one face, sum = 1 + {1, 1, 2, 0}, // One die, one face, sum = 2 (impossible) + {2, 1, 2, 1}, // Two dice, one face each, sum = 2 + } +} + +// TestDiceThrow tests the DiceThrow function with basic test cases +func TestDiceThrow(t *testing.T) { + t.Run("Basic test cases", func(t *testing.T) { + for _, tc := range getDiceThrowTestCases() { + actual := dynamic.DiceThrow(tc.numDice, tc.numFaces, tc.targetSum) + if actual != tc.expected { + t.Errorf("DiceThrow(%d, %d, %d) = %d; expected %d", tc.numDice, tc.numFaces, tc.targetSum, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/doc.go b/dynamic/doc.go new file mode 100644 index 000000000..c6ff7e596 --- /dev/null +++ b/dynamic/doc.go @@ -0,0 +1,2 @@ +// Package dynamic is a package of certain implementations of dynamically run algorithms. +package dynamic diff --git a/dynamic/dynamic_test.go b/dynamic/dynamic_test.go new file mode 100644 index 000000000..965718118 --- /dev/null +++ b/dynamic/dynamic_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package dynamic diff --git a/dynamic/editdistance.go b/dynamic/editdistance.go new file mode 100644 index 000000000..6d4778a3e --- /dev/null +++ b/dynamic/editdistance.go @@ -0,0 +1,71 @@ +// EDIT DISTANCE PROBLEM +// time complexity: O(m * n) where m and n are lengths of the strings, first and second respectively. +// space complexity: O(m * n) where m and n are lengths of the strings, first and second respectively. +// https://www.geeksforgeeks.org/edit-distance-dp-5/ +// https://leetcode.com/problems/edit-distance/ + +package dynamic + +import "github.com/TheAlgorithms/Go/math/min" + +// EditDistanceRecursive is a naive implementation with exponential time complexity. +func EditDistanceRecursive(first string, second string, pointerFirst int, pointerSecond int) int { + + if pointerFirst == 0 { + return pointerSecond + } + + if pointerSecond == 0 { + return pointerFirst + } + + // Characters match, so we recur for the remaining portions + if first[pointerFirst-1] == second[pointerSecond-1] { + return EditDistanceRecursive(first, second, pointerFirst-1, pointerSecond-1) + } + + // We have three choices, all with cost of 1 unit + return 1 + min.Int(EditDistanceRecursive(first, second, pointerFirst, pointerSecond-1), // Insert + EditDistanceRecursive(first, second, pointerFirst-1, pointerSecond), // Delete + EditDistanceRecursive(first, second, pointerFirst-1, pointerSecond-1)) // Replace +} + +// EditDistanceDP is an optimised implementation which builds on the ideas of the recursive implementation. +// We use dynamic programming to compute the DP table where dp[i][j] denotes the edit distance value +// of first[0..i-1] and second[0..j-1]. Time complexity is O(m * n) where m and n are lengths of the strings, +// first and second respectively. +func EditDistanceDP(first string, second string) int { + + m := len(first) + n := len(second) + + // Create the DP table + dp := make([][]int, m+1) + for i := 0; i <= m; i++ { + dp[i] = make([]int, n+1) + } + + for i := 0; i <= m; i++ { + for j := 0; j <= n; j++ { + + if i == 0 { + dp[i][j] = j + continue + } + + if j == 0 { + dp[i][j] = i + continue + } + + if first[i-1] == second[j-1] { + dp[i][j] = dp[i-1][j-1] + continue + } + + dp[i][j] = 1 + min.Int(dp[i][j-1], dp[i-1][j], dp[i-1][j-1]) + } + } + + return dp[m][n] +} diff --git a/dynamic/editdistance_test.go b/dynamic/editdistance_test.go new file mode 100644 index 000000000..188591413 --- /dev/null +++ b/dynamic/editdistance_test.go @@ -0,0 +1,35 @@ +package dynamic + +import ( + "fmt" + "testing" +) + +func Test_EditDistance(t *testing.T) { + + var testCases = []struct { + first string + second string + expected int + }{ + {"", "", 0}, + {"horse", "ros", 3}, + {"intention", "execution", 5}, + {"abcdxabcde", "abcdeabcdx", 2}, + {"sunday", "saturday", 3}, + {"food", "money", 4}, + {"voldemort", "dumbledore", 7}, + } + + for i := range testCases { + + t.Run(fmt.Sprintf("Word 1: %s, Word 2: %s", testCases[i].first, testCases[i].second), func(t *testing.T) { + + computed := EditDistanceDP(testCases[i].first, testCases[i].second) + + if computed != testCases[i].expected { + t.Errorf("Word 1: %s, Word 2: %s, Expected: %d, Computed: %d", testCases[i].first, testCases[i].second, testCases[i].expected, computed) + } + }) + } +} diff --git a/dynamic/eggdropping.go b/dynamic/eggdropping.go new file mode 100644 index 000000000..b6d379389 --- /dev/null +++ b/dynamic/eggdropping.go @@ -0,0 +1,47 @@ +package dynamic + +import ( + "github.com/TheAlgorithms/Go/math/max" + "github.com/TheAlgorithms/Go/math/min" +) + +// EggDropping finds the minimum number of attempts needed to find the critical floor +// with `eggs` number of eggs and `floors` number of floors +func EggDropping(eggs, floors int) int { + // Edge case: If there are no floors, no attempts needed + if floors == 0 { + return 0 + } + // Edge case: If there is one floor, one attempt needed + if floors == 1 { + return 1 + } + // Edge case: If there is one egg, need to test all floors one by one + if eggs == 1 { + return floors + } + + // Initialize DP table + dp := make([][]int, eggs+1) + for i := range dp { + dp[i] = make([]int, floors+1) + } + + // Fill the DP table for 1 egg + for j := 1; j <= floors; j++ { + dp[1][j] = j + } + + // Fill the DP table for more than 1 egg + for i := 2; i <= eggs; i++ { + for j := 2; j <= floors; j++ { + dp[i][j] = int(^uint(0) >> 1) // initialize with a large number + for x := 1; x <= j; x++ { + // Recurrence relation to fill the DP table + res := max.Int(dp[i-1][x-1], dp[i][j-x]) + 1 + dp[i][j] = min.Int(dp[i][j], res) + } + } + } + return dp[eggs][floors] +} diff --git a/dynamic/eggdropping_test.go b/dynamic/eggdropping_test.go new file mode 100644 index 000000000..5e3232f70 --- /dev/null +++ b/dynamic/eggdropping_test.go @@ -0,0 +1,35 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseEggDropping struct { + eggs int + floors int + expected int +} + +func getEggDroppingTestCases() []testCaseEggDropping { + return []testCaseEggDropping{ + {1, 10, 10}, // One egg, need to test all floors + {2, 10, 4}, // Two eggs and ten floors + {3, 14, 4}, // Three eggs and fourteen floors + {2, 36, 8}, // Two eggs and thirty-six floors + {2, 0, 0}, // Two eggs, zero floors + } + +} + +func TestEggDropping(t *testing.T) { + t.Run("Egg Dropping test cases", func(t *testing.T) { + for _, tc := range getEggDroppingTestCases() { + actual := dynamic.EggDropping(tc.eggs, tc.floors) + if actual != tc.expected { + t.Errorf("EggDropping(%d, %d) = %d; expected %d", tc.eggs, tc.floors, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/fibonacci.go b/dynamic/fibonacci.go new file mode 100644 index 000000000..6025b59f0 --- /dev/null +++ b/dynamic/fibonacci.go @@ -0,0 +1,25 @@ +// fibonacci.go +// description: Implementation of the Fibonacci sequence using dynamic programming +// time complexity: O(n) +// space complexity: O(1) +package dynamic + +// https://www.geeksforgeeks.org/program-for-nth-fibonacci-number/ + +// NthFibonacci returns the nth Fibonacci Number +func NthFibonacci(n uint) uint { + if n == 0 { + return 0 + } + + // n1 and n2 are the (i-1)th and ith Fibonacci numbers, respectively + var n1, n2 uint = 0, 1 + + for i := uint(1); i < n; i++ { + n3 := n1 + n2 + n1 = n2 + n2 = n3 + } + + return n2 +} diff --git a/dynamic/fibonacci_test.go b/dynamic/fibonacci_test.go new file mode 100644 index 000000000..db8aebae6 --- /dev/null +++ b/dynamic/fibonacci_test.go @@ -0,0 +1,42 @@ +package dynamic + +import ( + "fmt" + "testing" +) + +func Test_NthFibonacci(t *testing.T) { + // source: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html + var fibonacciNumbers = []struct { + nth uint + fibonacci uint + }{ + {0, 0}, + {1, 1}, + {2, 1}, + {3, 2}, + {4, 3}, + {5, 5}, + {6, 8}, + {7, 13}, + {8, 21}, + {9, 34}, + {10, 55}, + {20, 6765}, + {30, 832040}, + {40, 102334155}, + {50, 12586269025}, + {60, 1548008755920}, + {70, 190392490709135}, + {80, 23416728348467685}, + {90, 2880067194370816120}, + } + for i := range fibonacciNumbers { + t.Run(fmt.Sprintf("the %dth Fibonacci number", fibonacciNumbers[i].nth), func(t *testing.T) { + result := NthFibonacci(fibonacciNumbers[i].nth) + if result != fibonacciNumbers[i].fibonacci { + t.Errorf("Expected the %dth Fibonacci number to be %d, got %d", fibonacciNumbers[i].nth, fibonacciNumbers[i].fibonacci, result) + } + }) + } +} diff --git a/dynamic/interleavingstrings.go b/dynamic/interleavingstrings.go new file mode 100644 index 000000000..da13840b2 --- /dev/null +++ b/dynamic/interleavingstrings.go @@ -0,0 +1,36 @@ +// interleavingstrings.go +// description: Solves the Interleaving Strings problem using dynamic programming +// reference: https://en.wikipedia.org/wiki/Interleaving_strings +// time complexity: O(m*n) +// space complexity: O(m*n) + +package dynamic + +// IsInterleave checks if string `s1` and `s2` can be interleaved to form string `s3` +func IsInterleave(s1, s2, s3 string) bool { + if len(s1)+len(s2) != len(s3) { + return false + } + + dp := make([][]bool, len(s1)+1) + for i := range dp { + dp[i] = make([]bool, len(s2)+1) + } + + dp[0][0] = true + for i := 1; i <= len(s1); i++ { + dp[i][0] = dp[i-1][0] && s1[i-1] == s3[i-1] + } + + for j := 1; j <= len(s2); j++ { + dp[0][j] = dp[0][j-1] && s2[j-1] == s3[j-1] + } + + for i := 1; i <= len(s1); i++ { + for j := 1; j <= len(s2); j++ { + dp[i][j] = (dp[i-1][j] && s1[i-1] == s3[i+j-1]) || (dp[i][j-1] && s2[j-1] == s3[i+j-1]) + } + } + + return dp[len(s1)][len(s2)] +} diff --git a/dynamic/interleavingstrings_test.go b/dynamic/interleavingstrings_test.go new file mode 100644 index 000000000..a1559e932 --- /dev/null +++ b/dynamic/interleavingstrings_test.go @@ -0,0 +1,38 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseInterleaving struct { + s1, s2, s3 string + expected bool +} + +func getInterleavingTestCases() []testCaseInterleaving { + return []testCaseInterleaving{ + {"aab", "axy", "aaxaby", true}, // Valid interleaving + {"aab", "axy", "abaaxy", false}, // Invalid interleaving + {"", "", "", true}, // All empty strings + {"abc", "", "abc", true}, // Only s1 matches s3 + {"", "xyz", "xyz", true}, // Only s2 matches s3 + {"abc", "xyz", "abxcyz", true}, // Valid interleaving + {"aaa", "aaa", "aaaaaa", true}, // Identical strings + {"aaa", "aaa", "aaaaaaa", false}, // Extra character + {"abc", "def", "abcdef", true}, // Concatenation order + {"abc", "def", "adbcef", true}, // Valid mixed interleaving + } +} + +func TestIsInterleave(t *testing.T) { + t.Run("Interleaving Strings test cases", func(t *testing.T) { + for _, tc := range getInterleavingTestCases() { + actual := dynamic.IsInterleave(tc.s1, tc.s2, tc.s3) + if actual != tc.expected { + t.Errorf("IsInterleave(%q, %q, %q) = %v; expected %v", tc.s1, tc.s2, tc.s3, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/knapsack.go b/dynamic/knapsack.go new file mode 100644 index 000000000..6b637ca54 --- /dev/null +++ b/dynamic/knapsack.go @@ -0,0 +1,52 @@ +package dynamic + +// Knapsack Problem +// https://www.geeksforgeeks.org/0-1-knapsack-problem-dp-10/ +// https://en.wikipedia.org/wiki/Knapsack_problem +// time complexity: O(n*maxWeight) +// space complexity: O(n*maxWeight) + +import ( + "math" +) + +// Max function - possible duplicate +func Max(a, b int) int { + return int(math.Max(float64(a), float64(b))) +} + +// Knapsack solves knapsack problem +// return maxProfit +func Knapsack(maxWeight int, weights, values []int) int { + n := len(weights) + m := maxWeight + // create dp data structure + dp := make([][]int, n+1) + for i := range dp { + dp[i] = make([]int, m+1) + } + for i := 0; i < len(weights); i++ { + for j := 0; j <= maxWeight; j++ { + if weights[i] > j { + dp[i+1][j] = dp[i][j] + } else { + dp[i+1][j] = Max(dp[i][j-weights[i]]+values[i], dp[i][j]) + } + } + } + return dp[n][m] +} + +/* +func main() { + maxWeight := 50 + values := []int{ + 60, 100, 120, + } + weights := []int{ + 10, 20, 30, + } + maxProfit := Knapsack(maxWeight, weights, values) + fmt.Println(maxProfit) +} +*/ diff --git a/dynamic/knapsack_test.go b/dynamic/knapsack_test.go new file mode 100644 index 000000000..aaa7a579b --- /dev/null +++ b/dynamic/knapsack_test.go @@ -0,0 +1,38 @@ +package dynamic_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +func TestKnapsack(t *testing.T) { + td := []struct { + maxWeight int + weights []int + values []int + expected int + }{ + {0, []int{0}, []int{0}, 0}, + {10, []int{1, 2, 3}, []int{1, 1, 1}, 3}, // picks all + {10, []int{1, 2, 3, 4, 5, 6}, []int{1, 1, 1, 1, 1, 1}, 4}, // picks 1,2,3,4 + {10, []int{1, 2, 3, 4, 5, 6}, []int{1, 1, 1, 1, 1, 5}, 7}, // picks 1,3,6 + {10, []int{1, 2, 3, 4, 5, 6}, []int{-1, 10, -3, -4, 10, 1}, 20}, // picks 2,5 + {10, []int{1, 2, 3, 4, 5, 6}, []int{-10, -10, -10, -10, 10, 10}, 10}, // picks 5 or 6 + } + for _, tc := range td { + name := fmt.Sprintf("Knapsack problem with (maxWeight: %d, weights: %v, values: %v)", tc.maxWeight, tc.weights, tc.values) + t.Run(name, func(t *testing.T) { + actual := dynamic.Knapsack(tc.maxWeight, tc.weights, tc.values) + if actual != tc.expected { + t.Errorf("expecting knapsack with (maxWeight: %d, weights: %v, values: %v) to return %d but got %d", tc.maxWeight, tc.weights, tc.values, tc.expected, actual) + } + }) + } +} + +func ExampleKnapsack() { + fmt.Print(dynamic.Knapsack(10, []int{4, 5, 8}, []int{50, 15, 60})) + //Output:65 +} diff --git a/dynamic/longestarithmeticsubsequence.go b/dynamic/longestarithmeticsubsequence.go new file mode 100644 index 000000000..a187b9cea --- /dev/null +++ b/dynamic/longestarithmeticsubsequence.go @@ -0,0 +1,34 @@ +// longestarithmeticsubsequence.go +// description: Implementation of the Longest Arithmetic Subsequence problem +// reference: https://en.wikipedia.org/wiki/Longest_arithmetic_progression +// time complexity: O(n^2) +// space complexity: O(n^2) + +package dynamic + +// LongestArithmeticSubsequence returns the length of the longest arithmetic subsequence +func LongestArithmeticSubsequence(nums []int) int { + n := len(nums) + if n <= 1 { + return n + } + + dp := make([]map[int]int, n) + for i := range dp { + dp[i] = make(map[int]int) + } + + maxLength := 1 + + for i := 1; i < n; i++ { + for j := 0; j < i; j++ { + diff := nums[i] - nums[j] + dp[i][diff] = dp[j][diff] + 1 + if dp[i][diff]+1 > maxLength { + maxLength = dp[i][diff] + 1 + } + } + } + + return maxLength +} diff --git a/dynamic/longestarithmeticsubsequence_test.go b/dynamic/longestarithmeticsubsequence_test.go new file mode 100644 index 000000000..2a971fbd7 --- /dev/null +++ b/dynamic/longestarithmeticsubsequence_test.go @@ -0,0 +1,38 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseLongestArithmeticSubsequence struct { + nums []int + expected int +} + +func getLongestArithmeticSubsequenceTestCases() []testCaseLongestArithmeticSubsequence { + return []testCaseLongestArithmeticSubsequence{ + {[]int{3, 6, 9, 12}, 4}, // Arithmetic sequence of length 4 + {[]int{9, 4, 7, 2, 10}, 3}, // Arithmetic sequence of length 3 + {[]int{20, 1, 15, 3, 10, 5, 8}, 4}, // Arithmetic sequence of length 4 + {[]int{1, 2, 3, 4, 5}, 5}, // Arithmetic sequence of length 5 + {[]int{10, 7, 4, 1}, 4}, // Arithmetic sequence of length 4 + {[]int{1, 5, 7, 8, 5, 3, 4, 3, 1, 2}, 4}, // Arithmetic sequence of length 4 + {[]int{1, 3, 5, 7, 9}, 5}, // Arithmetic sequence of length 5 + {[]int{5, 10, 15, 20}, 4}, // Arithmetic sequence of length 4 + {[]int{1}, 1}, // Single element, length is 1 + {[]int{}, 0}, // Empty array, length is 0 + } +} + +func TestLongestArithmeticSubsequence(t *testing.T) { + t.Run("Longest Arithmetic Subsequence test cases", func(t *testing.T) { + for _, tc := range getLongestArithmeticSubsequenceTestCases() { + actual := dynamic.LongestArithmeticSubsequence(tc.nums) + if actual != tc.expected { + t.Errorf("LongestArithmeticSubsequence(%v) = %v; expected %v", tc.nums, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/longestcommonsubsequence.go b/dynamic/longestcommonsubsequence.go new file mode 100644 index 000000000..087d986e0 --- /dev/null +++ b/dynamic/longestcommonsubsequence.go @@ -0,0 +1,40 @@ +// LONGEST COMMON SUBSEQUENCE +// DP - 4 +// https://www.geeksforgeeks.org/longest-common-subsequence-dp-4/ +// https://leetcode.com/problems/longest-common-subsequence/ +// time complexity: O(m*n) where m and n are lengths of the strings +// space complexity: O(m*n) where m and n are lengths of the strings + +package dynamic + +func strToRuneSlice(s string) (r []rune, size int) { + r = []rune(s) + return r, len(r) +} + +// LongestCommonSubsequence function +func LongestCommonSubsequence(a string, b string) int { + aRunes, aLen := strToRuneSlice(a) + bRunes, bLen := strToRuneSlice(b) + + // here we are making a 2d slice of size (aLen+1)*(bLen+1) + lcs := make([][]int, aLen+1) + for i := 0; i <= aLen; i++ { + lcs[i] = make([]int, bLen+1) + } + + // block that implements LCS + for i := 0; i <= aLen; i++ { + for j := 0; j <= bLen; j++ { + if i == 0 || j == 0 { + lcs[i][j] = 0 + } else if aRunes[i-1] == bRunes[j-1] { + lcs[i][j] = lcs[i-1][j-1] + 1 + } else { + lcs[i][j] = Max(lcs[i-1][j], lcs[i][j-1]) + } + } + } + // returning the length of longest common subsequence + return lcs[aLen][bLen] +} diff --git a/dynamic/longestcommonsubsequence_test.go b/dynamic/longestcommonsubsequence_test.go new file mode 100644 index 000000000..5112f1270 --- /dev/null +++ b/dynamic/longestcommonsubsequence_test.go @@ -0,0 +1,54 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseLCS struct { + stringA string + stringB string + expected int +} + +func getLCSTestCases() []testCaseLCS { + return []testCaseLCS{ + {"ABCDGH", "AEDFHR", 3}, + {"AGGTAB", "GXTXAYB", 4}, + {"programming", "gaming", 6}, + {"physics", "smartphone", 2}, + {"computer", "food", 1}, + {"123", "12345", 3}, + {"XYZ", "XYZ", 3}, + {"XYZ", "XYZa", 3}, + {"XYZ", "aXYZ", 3}, + {"0123", "abc", 0}, + {"abcdef", "aXbXcXXXdeXXf", 6}, + {"", "abc", 0}, + {"", "", 0}, + {"££", "££", 2}, + {"x笑x笑", "aaa笑a笑", 2}, + {"xYxY", "aaaYaY", 2}, + } +} + +func TestLongestCommonSubsequence(t *testing.T) { + t.Run("Simple test", func(t *testing.T) { + for _, tc := range getLCSTestCases() { + actual := dynamic.LongestCommonSubsequence(tc.stringA, tc.stringB) + if actual != tc.expected { + t.Errorf("expected: %d, but got: %d", tc.expected, actual) + } + } + }) + + t.Run("Symmetry test", func(t *testing.T) { + for _, tc := range getLCSTestCases() { + actual := dynamic.LongestCommonSubsequence(tc.stringB, tc.stringA) + if actual != tc.expected { + t.Errorf("expected: %d, but got: %d", tc.expected, actual) + } + } + }) +} diff --git a/dynamic/longestincreasingsubsequence.go b/dynamic/longestincreasingsubsequence.go new file mode 100644 index 000000000..a1e70e53f --- /dev/null +++ b/dynamic/longestincreasingsubsequence.go @@ -0,0 +1,33 @@ +// longestincreasingsubsequence.go +// description: Implementation of the Longest Increasing Subsequence using dynamic programming +// reference: https://en.wikipedia.org/wiki/Longest_increasing_subsequence +// time complexity: O(n^2) +// space complexity: O(n) + +package dynamic + +import ( + "github.com/TheAlgorithms/Go/math/max" +) + +// LongestIncreasingSubsequence returns the longest increasing subsequence +// where all elements of the subsequence are sorted in increasing order +func LongestIncreasingSubsequence(elements []int) int { + n := len(elements) + lis := make([]int, n) + for i := range lis { + lis[i] = 1 + } + for i := range lis { + for j := 0; j < i; j++ { + if elements[i] > elements[j] && lis[i] < lis[j]+1 { + lis[i] = lis[j] + 1 + } + } + } + res := 0 + for _, value := range lis { + res = max.Int(res, value) + } + return res +} diff --git a/dynamic/longestincreasingsubsequence_test.go b/dynamic/longestincreasingsubsequence_test.go new file mode 100644 index 000000000..81ea2fcde --- /dev/null +++ b/dynamic/longestincreasingsubsequence_test.go @@ -0,0 +1,38 @@ +package dynamic_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +func longestIncreasingSubsequenceTest(t *testing.T, algorithm func(nums []int) int) { + td := []struct { + elements []int + expectedLen int + }{ + {[]int{1, 2, 3, 4, 5, 10}, 6}, + {[]int{1, 7, 3, 4, 5}, 4}, // 1,3,4,5 + {[]int{1, 3, 5}, 3}, + {[]int{7, 1, 6}, 2}, + {[]int{4, 1, 6, 2}, 2}, + {[]int{11, 9, 6}, 1}, + } + for _, tc := range td { + t.Run(fmt.Sprint("test with", tc.elements), func(t *testing.T) { + actualLen := algorithm(tc.elements) + if tc.expectedLen != actualLen { + t.Fatalf("expecting a sequence of len %d to be found but the actual len was %d; input: %v", tc.expectedLen, actualLen, tc.elements) + } + }) + } +} + +func TestLongestIncreasingSubsequence(t *testing.T) { + longestIncreasingSubsequenceTest(t, dynamic.LongestIncreasingSubsequence) +} + +func TestLongestIncreasingSubsequenceGreedy(t *testing.T) { + longestIncreasingSubsequenceTest(t, dynamic.LongestIncreasingSubsequenceGreedy) +} diff --git a/dynamic/longestincreasingsubsequencegreedy.go b/dynamic/longestincreasingsubsequencegreedy.go new file mode 100644 index 000000000..bb039468a --- /dev/null +++ b/dynamic/longestincreasingsubsequencegreedy.go @@ -0,0 +1,43 @@ +package dynamic + +// LongestIncreasingSubsequenceGreedy is a function to find the longest increasing +// subsequence in a given array using a greedy approach. +// The dynamic programming approach is implemented alongside this one. +// Worst Case Time Complexity: O(nlogn) +// Auxiliary Space: O(n), where n is the length of the array(slice). +// Reference: https://www.geeksforgeeks.org/construction-of-longest-monotonically-increasing-subsequence-n-log-n/ +func LongestIncreasingSubsequenceGreedy(nums []int) int { + longestIncreasingSubsequence := make([]int, 0) + + for _, num := range nums { + // find the leftmost index in longestIncreasingSubsequence with value >= num + leftmostIndex := lowerBound(longestIncreasingSubsequence, num) + + if leftmostIndex == len(longestIncreasingSubsequence) { + longestIncreasingSubsequence = append(longestIncreasingSubsequence, num) + } else { + longestIncreasingSubsequence[leftmostIndex] = num + } + } + + return len(longestIncreasingSubsequence) +} + +// Function to find the leftmost index in arr with value >= val, mimicking the inbuild lower_bound function in C++ +// Time Complexity: O(logn) +// Auxiliary Space: O(1) +func lowerBound(arr []int, val int) int { + searchWindowLeft, searchWindowRight := 0, len(arr)-1 + + for searchWindowLeft <= searchWindowRight { + middle := (searchWindowLeft + searchWindowRight) / 2 + + if arr[middle] < val { + searchWindowLeft = middle + 1 + } else { + searchWindowRight = middle - 1 + } + } + + return searchWindowRight + 1 +} diff --git a/dynamic-programming/longest-palindromic-subsequence.go b/dynamic/longestpalindromicsubsequence.go similarity index 59% rename from dynamic-programming/longest-palindromic-subsequence.go rename to dynamic/longestpalindromicsubsequence.go index 5cbfcd764..700fb8f87 100644 --- a/dynamic-programming/longest-palindromic-subsequence.go +++ b/dynamic/longestpalindromicsubsequence.go @@ -1,18 +1,9 @@ // longest palindromic subsequence +// time complexity: O(n^2) +// space complexity: O(n^2) // http://www.geeksforgeeks.org/dynamic-programming-set-12-longest-palindromic-subsequence/ -package longestPalindromicSubsequence - -// package main - -import "fmt" - -func max(a, b int) int { - if a > b { - return a - } - return b -} +package dynamic func lpsRec(word string, i, j int) int { if i == j { @@ -24,10 +15,16 @@ func lpsRec(word string, i, j int) int { if word[i] == word[j] { return 2 + lpsRec(word, i+1, j-1) } - return max(lpsRec(word, i, j-1), lpsRec(word, i+1, j)) + return Max(lpsRec(word, i, j-1), lpsRec(word, i+1, j)) } -func lpsDp(word string) int { +// LpsRec function +func LpsRec(word string) int { + return lpsRec(word, 0, len(word)-1) +} + +// LpsDp function +func LpsDp(word string) int { N := len(word) dp := make([][]int, N) @@ -47,19 +44,10 @@ func lpsDp(word string) int { dp[i][j] = 2 + dp[i+1][j-1] } } else { - dp[i][j] = max(dp[i+1][j], dp[i][j-1]) + dp[i][j] = Max(dp[i+1][j], dp[i][j-1]) } } } - return dp[1][N-1] -} - -/* -func main() { - // word := "aaabbbbababbabbabbabf" - word := "aaaabbbba" - fmt.Printf("%d\n", lpsRec(word, 0, len(word)-1)) - fmt.Printf("%d\n", lpsDp(word)) + return dp[0][N-1] } -*/ diff --git a/dynamic/longestpalindromicsubsequence_test.go b/dynamic/longestpalindromicsubsequence_test.go new file mode 100644 index 000000000..34a8f2590 --- /dev/null +++ b/dynamic/longestpalindromicsubsequence_test.go @@ -0,0 +1,40 @@ +package dynamic_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +func lpsTestTemplate(t *testing.T, algorithm func(input string) int) { + testCases := []struct { + input string + expected int + }{ + {"BBABCBCAB", 7}, + {"BBBAB", 4}, + {"ABBD", 2}, + {"GEEKSFORGEEKS", 5}, + {"abcdefgh", 1}, + {"bbbab", 4}, + {"cbbd", 2}, + {"racexyzcxar", 7}, + } + for _, tc := range testCases { + t.Run(fmt.Sprint("test with ", tc.input), func(t *testing.T) { + result := algorithm(tc.input) + if tc.expected != result { + t.Fatalf("expected %d, got %d", tc.expected, result) + } + }) + } +} + +func TestLpsRec(t *testing.T) { + lpsTestTemplate(t, dynamic.LpsRec) +} + +func TestLpsDp(t *testing.T) { + lpsTestTemplate(t, dynamic.LpsDp) +} diff --git a/dynamic/longestpalindromicsubstring.go b/dynamic/longestpalindromicsubstring.go new file mode 100644 index 000000000..01d105629 --- /dev/null +++ b/dynamic/longestpalindromicsubstring.go @@ -0,0 +1,43 @@ +// longestpalindromicsubstring.go +// description: Implementation of finding the longest palindromic substring +// reference: https://en.wikipedia.org/wiki/Longest_palindromic_substring +// time complexity: O(n^2) +// space complexity: O(n^2) + +package dynamic + +// LongestPalindromicSubstring returns the longest palindromic substring in the input string +func LongestPalindromicSubstring(s string) string { + n := len(s) + if n == 0 { + return "" + } + + dp := make([][]bool, n) + for i := range dp { + dp[i] = make([]bool, n) + } + + start := 0 + maxLength := 1 + for i := 0; i < n; i++ { + dp[i][i] = true + } + + for length := 2; length <= n; length++ { + for i := 0; i < n-length+1; i++ { + j := i + length - 1 + if length == 2 { + dp[i][j] = (s[i] == s[j]) + } else { + dp[i][j] = (s[i] == s[j]) && dp[i+1][j-1] + } + + if dp[i][j] && length > maxLength { + maxLength = length + start = i + } + } + } + return s[start : start+maxLength] +} diff --git a/dynamic/longestpalindromicsubstring_test.go b/dynamic/longestpalindromicsubstring_test.go new file mode 100644 index 000000000..e8424eabe --- /dev/null +++ b/dynamic/longestpalindromicsubstring_test.go @@ -0,0 +1,37 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseLongestPalindromicSubstring struct { + s string + expected string +} + +func getLongestPalindromicSubstringTestCases() []testCaseLongestPalindromicSubstring { + return []testCaseLongestPalindromicSubstring{ + {"babad", "bab"}, // Example with multiple palindromes + {"cbbd", "bb"}, // Example with longest even palindrome + {"a", "a"}, // Single character, palindrome is itself + {"", ""}, // Empty string, no palindrome + {"racecar", "racecar"}, // Whole string is a palindrome + {"abcba", "abcba"}, // Palindrome in the middle + {"aabbcc", "aa"}, // Multiple substrings, longest "aa" + {"madam", "madam"}, // Full palindrome string + {"forgeeksskeegfor", "geeksskeeg"}, // Complex palindrome in the middle + } +} + +func TestLongestPalindromicSubstring(t *testing.T) { + t.Run("Longest Palindromic Substring test cases", func(t *testing.T) { + for _, tc := range getLongestPalindromicSubstringTestCases() { + actual := dynamic.LongestPalindromicSubstring(tc.s) + if actual != tc.expected { + t.Errorf("LongestPalindromicSubstring(%q) = %q; expected %q", tc.s, actual, tc.expected) + } + } + }) +} diff --git a/dynamic-programming/matrix-multiplication.go b/dynamic/matrixmultiplication.go similarity index 64% rename from dynamic-programming/matrix-multiplication.go rename to dynamic/matrixmultiplication.go index dc77ee0a6..10fccdbda 100644 --- a/dynamic-programming/matrix-multiplication.go +++ b/dynamic/matrixmultiplication.go @@ -1,34 +1,29 @@ // matrix chain multiplication problem // https://en.wikipedia.org/wiki/Matrix_chain_multiplication -// www.geeksforgeeks.org/dynamic-programming-set-8-matrix-chain-multiplication/ +// www.geeksforgeeks.org/dynamic_programming-set-8-matrix-chain-multiplication/ +// time complexity: O(n^3) +// space complexity: O(n^2) -// package main -package matrixChainMultiplication +package dynamic -import "fmt" +import "github.com/TheAlgorithms/Go/math/min" -func min(a, b int) int { - if a > b { - return b - } else { - return a - } -} - -func matrixChainRec(D []int, i, j int) int { +// MatrixChainRec function +func MatrixChainRec(D []int, i, j int) int { // d[i-1] x d[i] : dimension of matrix i if i == j { return 0 } q := 1 << 32 for k := i; k < j; k++ { - prod := matrixChainRec(D, i, k) + matrixChainRec(D, k+1, j) + D[i-1]*D[k]*D[j] - q = min(prod, q) + prod := MatrixChainRec(D, i, k) + MatrixChainRec(D, k+1, j) + D[i-1]*D[k]*D[j] + q = min.Int(prod, q) } return q } -func matrixChainDp(D []int) int { +// MatrixChainDp function +func MatrixChainDp(D []int) int { // d[i-1] x d[i] : dimension of matrix i N := len(D) @@ -44,7 +39,7 @@ func matrixChainDp(D []int) int { dp[i][j] = 1 << 31 for k := i; k < j; k++ { prod := dp[i][k] + dp[k+1][j] + D[i-1]*D[k]*D[j] - dp[i][j] = min(prod, dp[i][j]) + dp[i][j] = min.Int(prod, dp[i][j]) } } } diff --git a/dynamic/maxsubarraysum.go b/dynamic/maxsubarraysum.go new file mode 100644 index 000000000..4e283e1b9 --- /dev/null +++ b/dynamic/maxsubarraysum.go @@ -0,0 +1,22 @@ +// maxsubarraysum.go +// description: Implementation of Kadane's algorithm for Maximum Subarray Sum +// reference: https://en.wikipedia.org/wiki/Maximum_subarray_problem +// time complexity: O(n) +// space complexity: O(1) + +package dynamic + +import "github.com/TheAlgorithms/Go/math/max" + +// MaxSubArraySum returns the sum of the maximum subarray in the input array +func MaxSubArraySum(nums []int) int { + maxSum := nums[0] + currentSum := nums[0] + + for i := 1; i < len(nums); i++ { + currentSum = max.Int(nums[i], currentSum+nums[i]) + maxSum = max.Int(maxSum, currentSum) + } + + return maxSum +} diff --git a/dynamic/maxsubarraysum_test.go b/dynamic/maxsubarraysum_test.go new file mode 100644 index 000000000..20492c3f7 --- /dev/null +++ b/dynamic/maxsubarraysum_test.go @@ -0,0 +1,37 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseMaxSubArraySum struct { + nums []int + expected int +} + +func getMaxSubArraySumTestCases() []testCaseMaxSubArraySum { + return []testCaseMaxSubArraySum{ + {[]int{-2, -3, 4, -1, -2, 1, 5, -3}, 7}, // Kadane's algorithm example + {[]int{-1, -2, -3, -4}, -1}, // All negative numbers, max single element + {[]int{5, 4, -1, 7, 8}, 23}, // Positive numbers with a large sum + {[]int{-2, 1, -3, 4, -1, 2, 1, -5, 4}, 6}, // Mixed with a maximum subarray of length 4 + {[]int{1, 2, 3, 4, 5}, 15}, // All positive numbers, sum is the entire array + {[]int{-1, -2, -3, -4, -5}, -1}, // Only negative numbers, largest single element + {[]int{0, 0, 0, 0, 0}, 0}, // Array of zeros, maximum subarray is zero + {[]int{3}, 3}, // Single positive number + {[]int{-1}, -1}, // Single negative number + } +} + +func TestMaxSubArraySum(t *testing.T) { + t.Run("Max SubArray Sum test cases", func(t *testing.T) { + for _, tc := range getMaxSubArraySumTestCases() { + actual := dynamic.MaxSubArraySum(tc.nums) + if actual != tc.expected { + t.Errorf("MaxSubArraySum(%v) = %v; expected %v", tc.nums, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/optimalbst.go b/dynamic/optimalbst.go new file mode 100644 index 000000000..b80f2163c --- /dev/null +++ b/dynamic/optimalbst.go @@ -0,0 +1,61 @@ +package dynamic + +import "github.com/TheAlgorithms/Go/math/min" + +// OptimalBST returns the minimum cost of constructing a Binary Search Tree +func OptimalBST(keys []int, freq []int, n int) int { + // Initialize DP table with size n x n + dp := make([][]int, n) + for i := range dp { + dp[i] = make([]int, n) + } + + // Base case: single key cost + for i := 0; i < n; i++ { + dp[i][i] = freq[i] + } + + // Build the DP table for sequences of length 2 to n + for length := 2; length <= n; length++ { + for i := 0; i < n-length+1; i++ { + j := i + length - 1 + dp[i][j] = int(^uint(0) >> 1) // Initialize with a large value + sum := sum(freq, i, j) + + // Try every key as root and compute cost + for k := i; k <= j; k++ { + // Left cost: dp[i][k-1] is valid only if k > i + var leftCost int + if k > i { + leftCost = dp[i][k-1] + } else { + leftCost = 0 + } + + // Right cost: dp[k+1][j] is valid only if k < j + var rightCost int + if k < j { + rightCost = dp[k+1][j] + } else { + rightCost = 0 + } + + // Total cost for root k + cost := sum + leftCost + rightCost + + // Update dp[i][j] with the minimum cost + dp[i][j] = min.Int(dp[i][j], cost) + } + } + } + return dp[0][n-1] +} + +// Helper function to sum the frequencies +func sum(freq []int, i, j int) int { + total := 0 + for k := i; k <= j; k++ { + total += freq[k] + } + return total +} diff --git a/dynamic/optimalbst_test.go b/dynamic/optimalbst_test.go new file mode 100644 index 000000000..362b45449 --- /dev/null +++ b/dynamic/optimalbst_test.go @@ -0,0 +1,35 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseOptimalBST struct { + keys []int + freq []int + n int + expected int +} + +func getOptimalBSTTestCases() []testCaseOptimalBST { + return []testCaseOptimalBST{ + {[]int{10, 12, 20}, []int{34, 8, 50}, 3, 142}, // Example with 3 keys + {[]int{10, 20, 30, 40, 50}, []int{10, 20, 30, 40, 50}, 5, 300}, // Example with 5 keys + {[]int{10}, []int{100}, 1, 100}, // Single key case + } +} + +func TestOptimalBST(t *testing.T) { + t.Run("Optimal Binary Search Tree test cases", func(t *testing.T) { + for _, tc := range getOptimalBSTTestCases() { + t.Run("testing optimal BST", func(t *testing.T) { + actual := dynamic.OptimalBST(tc.keys, tc.freq, tc.n) + if actual != tc.expected { + t.Errorf("OptimalBST(%v, %v, %d) = %d; expected %d", tc.keys, tc.freq, tc.n, actual, tc.expected) + } + }) + } + }) +} diff --git a/dynamic/partitionproblem.go b/dynamic/partitionproblem.go new file mode 100644 index 000000000..bb3ca5496 --- /dev/null +++ b/dynamic/partitionproblem.go @@ -0,0 +1,30 @@ +// partitionproblem.go +// description: Solves the Partition Problem using dynamic programming +// reference: https://en.wikipedia.org/wiki/Partition_problem +// time complexity: O(n*sum) +// space complexity: O(n*sum) + +package dynamic + +// PartitionProblem checks whether the given set can be partitioned into two subsets +// such that the sum of the elements in both subsets is the same. +func PartitionProblem(nums []int) bool { + sum := 0 + for _, num := range nums { + sum += num + } + if sum%2 != 0 { + return false + } + + target := sum / 2 + dp := make([]bool, target+1) + dp[0] = true + + for _, num := range nums { + for i := target; i >= num; i-- { + dp[i] = dp[i] || dp[i-num] + } + } + return dp[target] +} diff --git a/dynamic/partitionproblem_test.go b/dynamic/partitionproblem_test.go new file mode 100644 index 000000000..c85742ecf --- /dev/null +++ b/dynamic/partitionproblem_test.go @@ -0,0 +1,39 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +// testCasePartitionProblem holds the test cases for the Partition Problem +type testCasePartitionProblem struct { + nums []int + expected bool +} + +// getPartitionProblemTestCases returns a list of test cases for the Partition Problem +func getPartitionProblemTestCases() []testCasePartitionProblem { + return []testCasePartitionProblem{ + {[]int{1, 5, 11, 5}, true}, // Example with a partitionable set + {[]int{1, 2, 3, 5}, false}, // Example where partition is not possible + {[]int{1, 2, 5}, false}, // Set cannot be partitioned into two subsets + {[]int{2, 2, 2, 2}, true}, // Even split possible with equal elements + {[]int{7, 3, 2, 1}, false}, // Set cannot be partitioned + {[]int{}, true}, // Empty set, can be partitioned trivially + {[]int{1}, false}, // Single element, cannot be partitioned + {[]int{10, 10, 10, 10}, true}, // Equal elements, partitionable + } +} + +// TestPartitionProblem tests the PartitionProblem function with different test cases +func TestPartitionProblem(t *testing.T) { + t.Run("Partition Problem test cases", func(t *testing.T) { + for _, tc := range getPartitionProblemTestCases() { + actual := dynamic.PartitionProblem(tc.nums) + if actual != tc.expected { + t.Errorf("PartitionProblem(%v) = %v; expected %v", tc.nums, actual, tc.expected) + } + } + }) +} diff --git a/dynamic-programming/rod-cutting.go b/dynamic/rodcutting.go similarity index 64% rename from dynamic-programming/rod-cutting.go rename to dynamic/rodcutting.go index 8abc4e441..4d37f4ecc 100644 --- a/dynamic-programming/rod-cutting.go +++ b/dynamic/rodcutting.go @@ -1,44 +1,33 @@ // Solution to Rod cutting problem // https://en.wikipedia.org/wiki/Cutting_stock_problem // http://www.geeksforgeeks.org/dynamic-programming-set-13-cutting-a-rod/ +// time complexity: O(n^2) +// space complexity: O(n) -package dpRodCutting +package dynamic -// package main - -import "fmt" - -func max(a, b int) int { - if a > b { - return a - } else { - return b - } - -} - -// solve the problem recursively: initial approach -func cutRodRec(price []int, length int) int { +// CutRodRec solve the problem recursively: initial approach +func CutRodRec(price []int, length int) int { if length == 0 { return 0 } q := -1 for i := 1; i <= length; i++ { - q = max(q, price[i]+cutRodRec(price, length-i)) + q = Max(q, price[i]+CutRodRec(price, length-i)) } return q } -// solve the same problem using dynamic programming -func cutRodDp(price []int, length int) int { +// CutRodDp solve the same problem using dynamic programming +func CutRodDp(price []int, length int) int { r := make([]int, length+1) // a.k.a the memoization array r[0] = 0 // cost of 0 length rod is 0 for j := 1; j <= length; j++ { // for each length (subproblem) q := -1 for i := 1; i <= j; i++ { - q = max(q, price[i]+r[j-i]) // avoiding recursive call + q = Max(q, price[i]+r[j-i]) // avoiding recursive call } r[j] = q } diff --git a/dynamic/rodcutting_test.go b/dynamic/rodcutting_test.go new file mode 100644 index 000000000..96321df40 --- /dev/null +++ b/dynamic/rodcutting_test.go @@ -0,0 +1,39 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type rodCuttingTestCase struct { + price []int + length int + expected int +} + +func getRodCuttingTestCases() []rodCuttingTestCase { + return []rodCuttingTestCase{ + {[]int{0, 1, 5, 8, 9}, 4, 10}, + {[]int{0, 2, 5, 7, 8, 0}, 5, 12}, + {[]int{0, 1, 5, 8, 9, 10, 17, 17, 20}, 8, 22}, + {[]int{0, 3, 5, 8, 9, 10, 17, 17, 20}, 8, 24}, + } +} + +func cutRodSolTestFunc(t *testing.T, cutRodSolFunc func([]int, int) int) { + for _, tc := range getRodCuttingTestCases() { + actual := cutRodSolFunc(tc.price, tc.length) + if actual != tc.expected { + t.Errorf("expected: %d, got: %d", tc.expected, actual) + } + } +} + +func TestCutRodRec(t *testing.T) { + cutRodSolTestFunc(t, dynamic.CutRodRec) +} + +func TestCutRodDp(t *testing.T) { + cutRodSolTestFunc(t, dynamic.CutRodDp) +} diff --git a/dynamic/subsetsum.go b/dynamic/subsetsum.go new file mode 100644 index 000000000..db04c32de --- /dev/null +++ b/dynamic/subsetsum.go @@ -0,0 +1,56 @@ +//Given a set of non-negative integers, and a (positive) value sum, +//determine if there is a subset of the given set with sum +//equal to given sum. +// time complexity: O(n*sum) +// space complexity: O(n*sum) +//references: https://www.geeksforgeeks.org/subset-sum-problem-dp-25/ + +package dynamic + +import "fmt" + +var ErrInvalidPosition = fmt.Errorf("invalid position in subset") +var ErrNegativeSum = fmt.Errorf("negative sum is not allowed") + +func IsSubsetSum(array []int, sum int) (bool, error) { + if sum < 0 { + //not allow negative sum + return false, ErrNegativeSum + } + + //create subset matrix + arraySize := len(array) + subset := make([][]bool, arraySize+1) + for i := 0; i <= arraySize; i++ { + subset[i] = make([]bool, sum+1) + } + + for i := 0; i <= arraySize; i++ { + //sum 0 is always true + subset[i][0] = true + } + + for i := 1; i <= sum; i++ { + //empty set is false when sum is not 0 + subset[0][i] = false + } + + for i := 1; i <= arraySize; i++ { + for j := 1; j <= sum; j++ { + if array[i-1] > j { + subset[i][j] = subset[i-1][j] + } + + if array[i-1] <= j { + if j-array[i-1] < 0 || j-array[i-1] > sum { + //out of bounds + return false, ErrInvalidPosition + } + + subset[i][j] = subset[i-1][j] || subset[i-1][j-array[i-1]] + } + } + } + + return subset[arraySize][sum], nil +} diff --git a/dynamic/subsetsum_test.go b/dynamic/subsetsum_test.go new file mode 100644 index 000000000..acb24f18e --- /dev/null +++ b/dynamic/subsetsum_test.go @@ -0,0 +1,93 @@ +package dynamic + +import "testing" + +func TestSubsetSum(t *testing.T) { + + var subsetSumTestData = []struct { + description string + array []int + sum int + expectedResult bool + expectedError error + }{ + { + description: "array of size 0 and sum 0", + array: []int{}, + sum: 0, + expectedResult: true, + expectedError: nil, + }, + { + description: "array of size 0 and non-zero sum", + array: []int{}, + sum: 2, + expectedResult: false, + expectedError: nil, + }, + { + description: "array of size 2 and sum 0", + array: []int{1, 2}, + sum: 0, + expectedResult: true, + expectedError: nil, + }, + { + description: "array of size 5 and sum 6", + array: []int{1, 2, 3, 4, 5}, + sum: 6, + expectedResult: true, + expectedError: nil, + }, + { + description: "array of size 5 and sum 7", + array: []int{1, 2, 3, 4, 5}, + sum: 7, + expectedResult: true, + expectedError: nil, + }, + { + description: "array of size 5 and sum 17", + array: []int{1, 2, 3, 4, 5}, + sum: 17, + expectedResult: false, + expectedError: nil, + }, + { + description: "array of size 6 negative values and sum positive", + array: []int{-1, -2, -3, -4, -5, -6}, + sum: 1, + expectedResult: false, + expectedError: ErrInvalidPosition, + }, + { + description: "array of size 6 with positive and negative values, also with a negative sum", + array: []int{-1, -1, 3, 4, 5, 6}, + sum: -2, + expectedResult: false, + expectedError: ErrNegativeSum, + }, + } + + for i := range subsetSumTestData { + + t.Run(subsetSumTestData[i].description, func(t *testing.T) { + array := subsetSumTestData[i].array + sum := subsetSumTestData[i].sum + + expectedResult := subsetSumTestData[i].expectedResult + result, err := IsSubsetSum(array, sum) + expectedError := subsetSumTestData[i].expectedError + + if err != expectedError { + t.Logf("FAIL: %s", subsetSumTestData[i].description) + t.Fatalf("Expected error:%t\nFound: %t", expectedError, err) + } + + if result != expectedResult { + t.Logf("FAIL: %s", subsetSumTestData[i].description) + t.Fatalf("Expected result:%t\nFound: %t", expectedResult, result) + } + }) + } +} diff --git a/dynamic/tilingproblem.go b/dynamic/tilingproblem.go new file mode 100644 index 000000000..0407f320d --- /dev/null +++ b/dynamic/tilingproblem.go @@ -0,0 +1,22 @@ +// tilingproblem.go +// description: Solves the Tiling Problem using dynamic programming +// reference: https://en.wikipedia.org/wiki/Tiling_problem +// time complexity: O(n) +// space complexity: O(n) + +package dynamic + +// TilingProblem returns the number of ways to tile a 2xN grid using 2x1 dominoes +func TilingProblem(n int) int { + if n <= 1 { + return 1 + } + dp := make([]int, n+1) + dp[0] = 1 + dp[1] = 1 + + for i := 2; i <= n; i++ { + dp[i] = dp[i-1] + dp[i-2] + } + return dp[n] +} diff --git a/dynamic/tilingproblem_test.go b/dynamic/tilingproblem_test.go new file mode 100644 index 000000000..4f103cd21 --- /dev/null +++ b/dynamic/tilingproblem_test.go @@ -0,0 +1,38 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseTilingProblem struct { + n int + expected int +} + +func getTilingProblemTestCases() []testCaseTilingProblem { + return []testCaseTilingProblem{ + {1, 1}, // Base case: 1 way to tile a 2x1 grid + {2, 2}, // 2 ways to tile a 2x2 grid + {3, 3}, // 3 ways to tile a 2x3 grid + {4, 5}, // 5 ways to tile a 2x4 grid + {5, 8}, // 8 ways to tile a 2x5 grid + {6, 13}, // 13 ways to tile a 2x6 grid + {10, 89}, // 89 ways to tile a 2x10 grid + {0, 1}, // Edge case: 1 way to tile a 2x0 grid (no tiles) + {7, 21}, // 21 ways to tile a 2x7 grid + {8, 34}, // 34 ways to tile a 2x8 grid + } +} + +func TestTilingProblem(t *testing.T) { + t.Run("Tiling Problem test cases", func(t *testing.T) { + for _, tc := range getTilingProblemTestCases() { + actual := dynamic.TilingProblem(tc.n) + if actual != tc.expected { + t.Errorf("TilingProblem(%d) = %d; expected %d", tc.n, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/traprainwater.go b/dynamic/traprainwater.go new file mode 100644 index 000000000..3b1c6a966 --- /dev/null +++ b/dynamic/traprainwater.go @@ -0,0 +1,43 @@ +// filename: traprainwater.go +// description: Provides a function to calculate the amount of trapped rainwater between bars represented by an elevation map using dynamic programming. +// details: +// The TrapRainWater function calculates the amount of trapped rainwater between the bars represented by the given elevation map. +// It uses dynamic programming to precompute the maximum height of bars to the left and right of each position. +// Then, it iterates through the array to calculate the amount of trapped rainwater at each position based on the minimum of the left and right maximum heights. +// Finally, it sums up the trapped rainwater for all positions and returns the total amount. +// time complexity: O(n) +// space complexity: O(n) +// author(s) [TruongNhanNguyen (SOZEL)](https://github.com/TruongNhanNguyen) +package dynamic + +import "math" + +// TrapRainWater calculates the amount of trapped rainwater between the bars represented by the given elevation map. +// It uses dynamic programming to precompute the maximum height of bars to the left and right of each position. +// Then, it iterates through the array to calculate the amount of trapped rainwater at each position based on the minimum of the left and right maximum heights. +// Finally, it sums up the trapped rainwater for all positions and returns the total amount. +func TrapRainWater(height []int) int { + if len(height) == 0 { + return 0 + } + + leftMax := make([]int, len(height)) + rightMax := make([]int, len(height)) + + leftMax[0] = height[0] + for i := 1; i < len(height); i++ { + leftMax[i] = int(math.Max(float64(leftMax[i-1]), float64(height[i]))) + } + + rightMax[len(height)-1] = height[len(height)-1] + for i := len(height) - 2; i >= 0; i-- { + rightMax[i] = int(math.Max(float64(rightMax[i+1]), float64(height[i]))) + } + + trappedWater := 0 + for i := 0; i < len(height); i++ { + trappedWater += int(math.Min(float64(leftMax[i]), float64(rightMax[i]))) - height[i] + } + + return trappedWater +} diff --git a/dynamic/traprainwater_test.go b/dynamic/traprainwater_test.go new file mode 100644 index 000000000..a031a3077 --- /dev/null +++ b/dynamic/traprainwater_test.go @@ -0,0 +1,34 @@ +package dynamic_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +func TestTrapRainWater(t *testing.T) { + heights := [][]int{ + {}, + {0, 1, 0, 2, 1, 0, 1, 3, 2, 1, 2, 1}, + {4, 2, 0, 3, 2, 5}, + {3, 1, 2, 4, 0, 1, 3, 2, 4}, + } + + expectedResults := []int{ + 0, + 6, + 9, + 13, + } + + for i, height := range heights { + expected := expectedResults[i] + t.Run(fmt.Sprintf("Case %d", i+1), func(t *testing.T) { + result := dynamic.TrapRainWater(height) + if result != expected { + t.Errorf("Expected %d, but got %d", expected, result) + } + }) + } +} diff --git a/dynamic/uniquepaths.go b/dynamic/uniquepaths.go new file mode 100644 index 000000000..978a81c7e --- /dev/null +++ b/dynamic/uniquepaths.go @@ -0,0 +1,33 @@ +// See https://leetcode.com/problems/unique-paths/ +// time complexity: O(m*n) where m and n are the dimensions of the grid +// space complexity: O(m*n) where m and n are the dimensions of the grid +// author: Rares Mateizer (https://github.com/rares985) +package dynamic + +// UniquePaths implements the solution to the "Unique Paths" problem +func UniquePaths(m, n int) int { + if m <= 0 || n <= 0 { + return 0 + } + + grid := make([][]int, m) + for i := range grid { + grid[i] = make([]int, n) + } + + for i := 0; i < m; i++ { + grid[i][0] = 1 + } + + for j := 0; j < n; j++ { + grid[0][j] = 1 + } + + for i := 1; i < m; i++ { + for j := 1; j < n; j++ { + grid[i][j] = grid[i-1][j] + grid[i][j-1] + } + } + + return grid[m-1][n-1] +} diff --git a/dynamic/uniquepaths_test.go b/dynamic/uniquepaths_test.go new file mode 100644 index 000000000..ac5accbb4 --- /dev/null +++ b/dynamic/uniquepaths_test.go @@ -0,0 +1,28 @@ +package dynamic + +import ( + "testing" +) + +func TestUniquePaths(t *testing.T) { + testCases := map[string]struct { + m int + n int + want int + }{ + "negative sizes": {-1, -1, 0}, + "empty matrix both dimensions": {0, 0, 0}, + "empty matrix one dimension": {0, 1, 0}, + "one element": {1, 1, 1}, + "small matrix": {2, 2, 2}, + "stress test": {1000, 1000, 2874513998398909184}, + } + + for name, test := range testCases { + t.Run(name, func(t *testing.T) { + if got := UniquePaths(test.m, test.n); got != test.want { + t.Errorf("UniquePaths(%v, %v) = %v, want %v", test.m, test.n, got, test.want) + } + }) + } +} diff --git a/dynamic/wildcardmatching.go b/dynamic/wildcardmatching.go new file mode 100644 index 000000000..26b4530af --- /dev/null +++ b/dynamic/wildcardmatching.go @@ -0,0 +1,33 @@ +// wildcardmatching.go +// description: Solves the Wildcard Matching problem using dynamic programming +// reference: https://en.wikipedia.org/wiki/Wildcard_matching +// time complexity: O(m*n) +// space complexity: O(m*n) + +package dynamic + +// IsMatch checks if the string `s` matches the wildcard pattern `p` +func IsMatch(s, p string) bool { + dp := make([][]bool, len(s)+1) + for i := range dp { + dp[i] = make([]bool, len(p)+1) + } + + dp[0][0] = true + for j := 1; j <= len(p); j++ { + if p[j-1] == '*' { + dp[0][j] = dp[0][j-1] + } + } + + for i := 1; i <= len(s); i++ { + for j := 1; j <= len(p); j++ { + if p[j-1] == s[i-1] || p[j-1] == '?' { + dp[i][j] = dp[i-1][j-1] + } else if p[j-1] == '*' { + dp[i][j] = dp[i-1][j] || dp[i][j-1] + } + } + } + return dp[len(s)][len(p)] +} diff --git a/dynamic/wildcardmatching_test.go b/dynamic/wildcardmatching_test.go new file mode 100644 index 000000000..cc6cd4fde --- /dev/null +++ b/dynamic/wildcardmatching_test.go @@ -0,0 +1,44 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +// testCaseWildcardMatching holds the test cases for the Wildcard Matching problem +type testCaseWildcardMatching struct { + s string + p string + expected bool +} + +// getWildcardMatchingTestCases returns a list of test cases for the Wildcard Matching problem +func getWildcardMatchingTestCases() []testCaseWildcardMatching { + return []testCaseWildcardMatching{ + {"aa", "a*", true}, // '*' can match zero or more characters + {"aa", "a", false}, // No match due to no wildcard + {"ab", "?*", true}, // '?' matches any single character, '*' matches remaining + {"abcd", "a*d", true}, // '*' matches the characters between 'a' and 'd' + {"abcd", "a*c", false}, // No match as 'c' doesn't match the last character 'd' + {"abc", "*", true}, // '*' matches the entire string + {"abc", "a*c", true}, // '*' matches 'b' + {"abc", "a?c", true}, // '?' matches 'b' + {"abc", "a?d", false}, // '?' cannot match 'd' + {"", "", true}, // Both strings empty, so they match + {"a", "?", true}, // '?' matches any single character + {"a", "*", true}, // '*' matches any number of characters, including one + } +} + +// TestIsMatch tests the IsMatch function with various test cases +func TestIsMatch(t *testing.T) { + t.Run("Wildcard Matching test cases", func(t *testing.T) { + for _, tc := range getWildcardMatchingTestCases() { + actual := dynamic.IsMatch(tc.s, tc.p) + if actual != tc.expected { + t.Errorf("IsMatch(%q, %q) = %v; expected %v", tc.s, tc.p, actual, tc.expected) + } + } + }) +} diff --git a/dynamic/wordbreak.go b/dynamic/wordbreak.go new file mode 100644 index 000000000..6d7ad5d58 --- /dev/null +++ b/dynamic/wordbreak.go @@ -0,0 +1,28 @@ +// wordbreak.go +// description: Solves the Word Break Problem using dynamic programming +// reference: https://en.wikipedia.org/wiki/Word_break_problem +// time complexity: O(n^2) +// space complexity: O(n) + +package dynamic + +// WordBreak checks if the input string can be segmented into words from a dictionary +func WordBreak(s string, wordDict []string) bool { + wordSet := make(map[string]bool) + for _, word := range wordDict { + wordSet[word] = true + } + + dp := make([]bool, len(s)+1) + dp[0] = true + + for i := 1; i <= len(s); i++ { + for j := 0; j < i; j++ { + if dp[j] && wordSet[s[j:i]] { + dp[i] = true + break + } + } + } + return dp[len(s)] +} diff --git a/dynamic/wordbreak_test.go b/dynamic/wordbreak_test.go new file mode 100644 index 000000000..afcf62cb6 --- /dev/null +++ b/dynamic/wordbreak_test.go @@ -0,0 +1,40 @@ +package dynamic_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/dynamic" +) + +type testCaseWordBreak struct { + s string + wordDict []string + expected bool +} + +func getWordBreakTestCases() []testCaseWordBreak { + return []testCaseWordBreak{ + {"leetcode", []string{"leet", "code"}, true}, // "leetcode" can be segmented into "leet" and "code" + {"applepenapple", []string{"apple", "pen"}, true}, // "applepenapple" can be segmented into "apple", "pen", "apple" + {"catsanddog", []string{"cats", "dog", "sand", "and", "cat"}, true}, // "catsanddog" can be segmented into "cats", "and", "dog" + {"bb", []string{"a", "b", "bbb", "aaaa", "aaa"}, true}, // "bb" can be segmented into "b" and "b" + {"", []string{"cat", "dog", "sand", "and"}, true}, // Empty string can always be segmented (empty words) + {"applepie", []string{"apple", "pie"}, true}, // "applepie" can be segmented into "apple" and "pie" + {"catsandog", []string{"cats", "dog", "sand", "and", "cat"}, false}, // "catsandog" cannot be segmented + {"ilovecoding", []string{"i", "love", "coding"}, true}, // "ilovecoding" can be segmented into "i", "love", "coding" + {"cars", []string{"car", "ca", "rs"}, true}, // "cars" can be segmented into "car" and "s" + {"pen", []string{"pen", "pencil"}, true}, // "pen" is a direct match + {"apple", []string{"orange", "banana"}, false}, // "apple" is not in the word dictionary + } +} + +func TestWordBreak(t *testing.T) { + t.Run("Word Break test cases", func(t *testing.T) { + for _, tc := range getWordBreakTestCases() { + actual := dynamic.WordBreak(tc.s, tc.wordDict) + if actual != tc.expected { + t.Errorf("WordBreak(%q, %v) = %v; expected %v", tc.s, tc.wordDict, actual, tc.expected) + } + } + }) +} diff --git a/go.mod b/go.mod new file mode 100644 index 000000000..5a3e15ba4 --- /dev/null +++ b/go.mod @@ -0,0 +1,3 @@ +module github.com/TheAlgorithms/Go + +go 1.19 diff --git a/go.sum b/go.sum new file mode 100644 index 000000000..e69de29bb diff --git a/graph/articulationpoints.go b/graph/articulationpoints.go new file mode 100644 index 000000000..26b3a6b78 --- /dev/null +++ b/graph/articulationpoints.go @@ -0,0 +1,89 @@ +// Package graph provides algorithms to analyze graph structures. +package graph + +import "github.com/TheAlgorithms/Go/math/min" + +// apHelper stores auxiliary data used to identify articulation points in a graph. +type apHelper struct { + isAP []bool + visited []bool + childCount []int + discoveryTime []int + earliestDiscovery []int +} + +// ArticulationPoint identifies articulation points in a graph. It returns a boolean slice +// where each element indicates whether a vertex is an articulation point. +// Worst Case Time Complexity: O(|V| + |E|) +// Auxiliary Space: O(|V|) +// Reference: https://en.wikipedia.org/wiki/Biconnected_component and https://cptalks.quora.com/Cut-Vertex-Articulation-point +func ArticulationPoint(graph *Graph) []bool { + // Time variable to keep track of the discovery time of a vertex + time := 0 + + // Initialize apHelper instance with the required data structures + apHelperInstance := &apHelper{ + isAP: make([]bool, graph.vertices), + visited: make([]bool, graph.vertices), + childCount: make([]int, graph.vertices), + discoveryTime: make([]int, graph.vertices), + earliestDiscovery: make([]int, graph.vertices), + } + + // Start traversal from the root (0) + articulationPointHelper(apHelperInstance, 0, -1, &time, graph) + + // Check if the root has only one child, making it non-articulate + if apHelperInstance.childCount[0] == 1 { + apHelperInstance.isAP[0] = false + } + + return apHelperInstance.isAP +} + +// articulationPointHelper recursively traverses the graph using DFS and marks articulation points. +// It updates `childCount`, `discoveryTime`, and `earliestDiscovery` slices for the given vertex. +func articulationPointHelper( + apHelperInstance *apHelper, + vertex int, + parent int, + time *int, + graph *Graph, +) { + apHelperInstance.visited[vertex] = true + + // Set discovery and earliest discovery times for the vertex + apHelperInstance.discoveryTime[vertex] = *time + apHelperInstance.earliestDiscovery[vertex] = *time + *time++ + + for nextVertex := range graph.edges[vertex] { + if nextVertex == parent { + continue + } + + if apHelperInstance.visited[nextVertex] { + // Update the earliest discovery time to the smallest reachable discovery time + apHelperInstance.earliestDiscovery[vertex] = min.Int( + apHelperInstance.earliestDiscovery[vertex], + apHelperInstance.discoveryTime[nextVertex], + ) + continue + } + + // Increment child count and perform recursive traversal for DFS + apHelperInstance.childCount[vertex]++ + articulationPointHelper(apHelperInstance, nextVertex, vertex, time, graph) + + // Update the earliest discovery time post DFS + apHelperInstance.earliestDiscovery[vertex] = min.Int( + apHelperInstance.earliestDiscovery[vertex], + apHelperInstance.earliestDiscovery[nextVertex], + ) + + // Mark vertex as articulation point if condition meets + if apHelperInstance.earliestDiscovery[nextVertex] >= apHelperInstance.discoveryTime[vertex] { + apHelperInstance.isAP[vertex] = true + } + } +} diff --git a/graph/articulationpoints_test.go b/graph/articulationpoints_test.go new file mode 100644 index 000000000..a9dca3e6d --- /dev/null +++ b/graph/articulationpoints_test.go @@ -0,0 +1,82 @@ +package graph + +import ( + "reflect" + "testing" +) + +func TestArticulationPoints(t *testing.T) { + var testCases = []struct { + description string + graph Graph + expected []bool + }{ + { + "Linear tree structure", + Graph{ + vertices: 5, + edges: map[int]map[int]int{ + 0: { + 1: 0, + }, + + 1: { + 0: 0, + 2: 0, + }, + + 2: { + 1: 0, + 3: 0, + }, + + 3: { + 2: 0, + 4: 0, + }, + }, + }, + []bool{false, true, true, true, false}, + }, { + "A complete graph", + Graph{ + vertices: 4, + edges: map[int]map[int]int{ + 0: { + 1: 0, + 2: 0, + 3: 0, + }, + + 1: { + 0: 0, + 2: 0, + 3: 0, + }, + + 2: { + 0: 0, + 1: 0, + 3: 0, + }, + + 3: { + 0: 0, + 1: 0, + 2: 0, + }, + }, + }, + []bool{false, false, false, false}, + }, + } + + for _, test := range testCases { + t.Run(test.description, func(t *testing.T) { + is_ap := ArticulationPoint(&test.graph) + if !reflect.DeepEqual(is_ap, test.expected) { + t.Logf("FAIL: %s", test.description) + } + }) + } +} diff --git a/graph/bellmanford.go b/graph/bellmanford.go new file mode 100644 index 000000000..d1db29c5c --- /dev/null +++ b/graph/bellmanford.go @@ -0,0 +1,51 @@ +// The Bellman–Ford algorithm is an algorithm that computes shortest paths from a +// single source vertex to all of the other vertices in a weighted directed graph. +// It is slower than Dijkstra but capable of handling negative edge weights. +// https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm +// Implementation is based on the book 'Introduction to Algorithms' (CLRS) +// time complexity: O(V*E) where V is the number of vertices and E is the number of edges in the graph +// space complexity: O(V) where V is the number of vertices in the graph + +package graph + +import ( + "errors" + "math" +) + +func (g *Graph) BellmanFord(start, end int) (isReachable bool, distance int, err error) { + INF := math.Inf(1) + distances := make([]float64, g.vertices) + + // Set all vertices to unreachable, initialize source + for i := 0; i < g.vertices; i++ { + distances[i] = INF + } + distances[start] = 0 + + // Making iterations equal to #vertices + for n := 0; n < g.vertices; n++ { + + // Looping over all edges + for u, adjacents := range g.edges { + for v, weightUV := range adjacents { + + // If new shorter distance is found, update distance value (relaxation step) + if newDistance := distances[u] + float64(weightUV); distances[v] > newDistance { + distances[v] = newDistance + } + } + } + } + + // Check for negative weight cycle + for u, adjacents := range g.edges { + for v, weightUV := range adjacents { + if newDistance := distances[u] + float64(weightUV); distances[v] > newDistance { + return false, -1, errors.New("negative weight cycle present") + } + } + } + + return distances[end] != INF, int(distances[end]), nil +} diff --git a/graph/bellmanford_test.go b/graph/bellmanford_test.go new file mode 100644 index 000000000..83364b5df --- /dev/null +++ b/graph/bellmanford_test.go @@ -0,0 +1,137 @@ +package graph + +import ( + "errors" + "fmt" + "math" + "testing" +) + +func TestBellmanford(t *testing.T) { + + var testCases = []struct { + name string + edges [][]int + vertices int + start int + end int + isReachable bool + distance int + err error + }{ + { + "single edge", + [][]int{ + {0, 1, 1}, + }, + 2, 0, 1, true, 1, nil, + }, + { + "negative weights", + [][]int{ + {0, 1, 1}, + {1, 2, -3}, + {2, 1, 4}, + {2, 3, 1}, + }, + 4, 0, 1, true, 1, nil, + }, + { + "negative cycle", + [][]int{ + {0, 1, 1}, + {1, 2, -3}, + {2, 1, 1}, + {2, 3, 1}, + }, + 4, 0, 1, false, -1, errors.New("negative weight cycle present"), + }, + { + "unreachable vertex", + [][]int{ + {0, 6, 771}, + {0, 9, 782}, + {1, 2, 454}, + {2, 8, 48}, + {3, 8, 249}, + {3, 9, 880}, + {3, 5, 280}, + {7, 1, 92}, + {7, 2, 497}, + {8, 1, 102}, + {8, 4, 977}, + }, + 10, 8, 3, false, int(math.Inf(1)), nil, + }, + { + "disconnected graph", + [][]int{ + {0, 1, 10}, + {2, 3, 15}, + {3, 5, 10}, + }, + 6, 0, 3, false, int(math.Inf(1)), nil, + }, + { + "multiple paths", + [][]int{ + {0, 1, 5}, + {1, 2, 10}, + {1, 3, 30}, + {2, 4, 10}, + {4, 5, 15}, + {3, 5, 10}, + }, + 6, 0, 5, true, 40, nil, + }, + { + "random 1", + [][]int{ + {0, 1, 10}, + {1, 2, 10}, + {0, 2, 100}, + {2, 0, -10}, + {1, 2, 1}, + }, + 3, 0, 1, true, 10, nil, + }, + { + "random 2", + [][]int{ + {0, 1, 5498}, + {2, 0, 7679}, + {0, 3, 4999}, + {1, 2, 8629}, + {1, 3, -948}, + {2, 3, 6231}, + }, + 4, 0, 3, true, 4550, nil, + }, + } + + for _, test := range testCases { + t.Run(fmt.Sprint(test.name), func(t *testing.T) { + // Initializing graph, adding edges + graph := New(test.vertices) + graph.Directed = true + for _, edge := range test.edges { + graph.AddWeightedEdge(edge[0], edge[1], edge[2]) + } + + resIsReachable, resDistance, resError := graph.BellmanFord(test.start, test.end) + if resDistance != test.distance { + t.Errorf("Distance, Expected: %d, Computed: %d", test.distance, resDistance) + } + if resIsReachable != test.isReachable { + t.Errorf("Reachable, Expected: %t, Computed: %t", test.isReachable, resIsReachable) + } + if !errors.Is(test.err, resError) { + if resError == nil || test.err == nil { + t.Errorf("Reachable, Expected: %s, Computed: %s", test.err, resError) + } else if resError.Error() != test.err.Error() { + t.Errorf("Reachable, Expected: %s, Computed: %s", test.err.Error(), resError.Error()) + } + } + }) + } +} diff --git a/graph/breadthfirstsearch.go b/graph/breadthfirstsearch.go new file mode 100644 index 000000000..bac2f04cc --- /dev/null +++ b/graph/breadthfirstsearch.go @@ -0,0 +1,28 @@ +package graph + +// BreadthFirstSearch is an algorithm for traversing and searching graph data structures. +// It starts at an arbitrary node of a graph, and explores all of the neighbor nodes +// at the present depth prior to moving on to the nodes at the next depth level. +// Worst-case performance O(|V|+|E|)=O(b^{d})}O(|V|+|E|)=O(b^{d}) where |V| is the number of vertices and |E| is the number of edges in the graph and b is the branching factor of the graph (the average number of successors of a node). d is the depth of the goal node. +// Worst-case space complexity O(|V|)=O(b^{d})}O(|V|)=O(b^{d}) where |V| is the number of vertices and |E| is the number of edges in the graph and b is the branching factor of the graph (the average number of successors of a node). d is the depth of the goal node. +// reference: https://en.wikipedia.org/wiki/Breadth-first_search +func BreadthFirstSearch(start, end, nodes int, edges [][]int) (isConnected bool, distance int) { + queue := make([]int, 0) + discovered := make([]int, nodes) + discovered[start] = 1 + queue = append(queue, start) + for len(queue) > 0 { + v := queue[0] + queue = queue[1:] + for i := 0; i < len(edges[v]); i++ { + if discovered[i] == 0 && edges[v][i] > 0 { + if i == end { + return true, discovered[v] + } + discovered[i] = discovered[v] + 1 + queue = append(queue, i) + } + } + } + return false, 0 +} diff --git a/graph/breadthfirstsearch_test.go b/graph/breadthfirstsearch_test.go new file mode 100644 index 000000000..a01db4fc1 --- /dev/null +++ b/graph/breadthfirstsearch_test.go @@ -0,0 +1,78 @@ +package graph + +import ( + "testing" +) + +func TestBreadthFirstSearch(t *testing.T) { + var bfsTestData = []struct { + description string + start int + end int + nodes int + edges [][]int + expected1 bool + expected2 int + }{ + { + "test 1 connected with distance 2", + 0, + 5, + 6, + [][]int{ + {0, 1, 1, 0, 0, 0}, + {1, 0, 0, 1, 0, 1}, + {1, 0, 0, 1, 0, 0}, + {0, 1, 1, 0, 1, 0}, + {0, 0, 0, 1, 0, 0}, + {0, 1, 0, 0, 0, 0}, + }, + true, + 2, + }, + { + "test 2 connected with distance 4", + 0, + 5, + 6, + [][]int{ + {0, 1, 1, 0, 0, 0}, + {1, 0, 0, 1, 0, 0}, + {1, 0, 0, 1, 0, 0}, + {0, 1, 1, 0, 1, 0}, + {0, 0, 0, 1, 0, 1}, + {0, 0, 0, 0, 1, 0}, + }, + true, + 4, + }, + { + "test 2 not connected", + 0, + 5, + 6, + [][]int{ + {0, 1, 1, 0, 0, 0}, + {1, 0, 0, 1, 0, 0}, + {1, 0, 0, 1, 0, 0}, + {0, 1, 1, 0, 1, 0}, + {0, 0, 0, 1, 0, 0}, + {0, 0, 0, 0, 0, 0}, + }, + false, + 0, + }, + } + for _, test := range bfsTestData { + t.Run(test.description, func(t *testing.T) { + r1, r2 := BreadthFirstSearch(test.start, test.end, + test.nodes, test.edges) + if r1 != test.expected1 || r2 != test.expected2 { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Nodes '%v' and Edges '%v' start from '%d' and end in '%d' "+ + "was expecting '%v' with distance '%d' but result was '%v','%d'", + test.nodes, test.edges, test.start, test.end, test.expected1, test.expected2, r1, r2) + } + }) + } +} diff --git a/graph/coloring/backtracking.go b/graph/coloring/backtracking.go new file mode 100644 index 000000000..885b79e28 --- /dev/null +++ b/graph/coloring/backtracking.go @@ -0,0 +1,52 @@ +// This file contains the graph coloring implementation using backtracking +// time complexity: O(V^V) where V is the number of vertices in the graph +// space complexity: O(V) where V is the number of vertices in the graph +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring + +// ColorUsingBacktracking will return the Color of each vertex and the +// total number of different colors used, using backtracking +func (g *Graph) ColorUsingBacktracking() (map[int]Color, int) { + vertexColors := make(map[int]Color, g.vertices) + g.colorVertex(0, vertexColors) + + colorsUsed := 0 + for _, cr := range vertexColors { + if colorsUsed < int(cr) { + colorsUsed = int(cr) + } + } + return vertexColors, colorsUsed +} + +// colorVertex will try to color provided vertex, v +func (g *Graph) colorVertex(v int, color map[int]Color) bool { + // If all vertices are colored, the colors store will be completely filled. + if len(color) == g.vertices { + return true + } + + // As the upper bound of no. of colors is the no. of vertices in graph, + // try assigning each color to the vertex v + for cr := Color(1); cr <= Color(g.vertices); cr++ { + // Use the color, cr for vertex, v if it is safe to use, by + // checking its neighbours + safe := true + for nb := range g.edges[v] { + // cr, color is not safe if color of nb, crnb is not equal to cr + if crnb, ok := color[nb]; ok && crnb == cr { + safe = false + break + } + } + if safe { + color[v] = cr + if g.colorVertex(v+1, color) { + return true + } + delete(color, v) + } + } + return false +} diff --git a/graph/coloring/backtracking_test.go b/graph/coloring/backtracking_test.go new file mode 100644 index 000000000..6bc735cca --- /dev/null +++ b/graph/coloring/backtracking_test.go @@ -0,0 +1,24 @@ +// This file provides tests for coloring using backtracking. +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring_test + +import ( + "strconv" + "testing" +) + +func TestGraphColorUsingBacktracking(t *testing.T) { + for i, tt := range getTestGraphs() { + t.Run(strconv.Itoa(i), func(t *testing.T) { + colorsOfVertices, colors := tt.Graph.ColorUsingBacktracking() + if colors != tt.ColorsUsed { + t.Errorf("ColorUsingBacktracking() return more number of colors: %v, want %v colors", colors, tt.ColorsUsed) + } + // check colors + if err := tt.Graph.ValidateColorsOfVertex(colorsOfVertices); err != nil { + t.Errorf("ColorUsingBacktracking() assigned colors are wrong, error = %v", err) + } + }) + } +} diff --git a/graph/coloring/bfs.go b/graph/coloring/bfs.go new file mode 100644 index 000000000..22f0bc899 --- /dev/null +++ b/graph/coloring/bfs.go @@ -0,0 +1,58 @@ +// This file contains the graph coloring implementation using BFS +// time complexity: O(V+E) where V is the number of vertices and E is the number of edges in the graph +// space complexity: O(V) where V is the number of vertices in the graph +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring + +import "container/list" + +// ColorUsingBFS will return the Color of each vertex and the +// total number of different colors used, using BFS +func (g *Graph) ColorUsingBFS() (map[int]Color, int) { + // Initially all vertices will have same color + vertexColors := make(map[int]Color, g.vertices) + for i := 0; i < g.vertices; i++ { + vertexColors[i] = 1 + } + + visited := make(map[int]struct{}) + // Run BFS from each non-visited vertex + for i := 0; i < g.vertices; i++ { + if _, ok := visited[i]; ok { + continue + } + visited[i] = struct{}{} + + queue := list.New() + queue.PushBack(i) + + for queue.Len() != 0 { + // front vertex in the queue + frontNode := queue.Front() + front := frontNode.Value.(int) + queue.Remove(frontNode) + + // Now, check all neighbours of front vertex, if they have same + // color as that of front, change their color + for nb := range g.edges[front] { + if vertexColors[nb] == vertexColors[front] { + vertexColors[nb]++ + } + // if the neighbour is not already visited, add it to the queue + if _, ok := visited[nb]; !ok { + visited[nb] = struct{}{} + queue.PushBack(nb) + } + } + } + } + + colorsUsed := 0 + for _, cr := range vertexColors { + if colorsUsed < int(cr) { + colorsUsed = int(cr) + } + } + return vertexColors, colorsUsed +} diff --git a/graph/coloring/bfs_test.go b/graph/coloring/bfs_test.go new file mode 100644 index 000000000..adfc502ce --- /dev/null +++ b/graph/coloring/bfs_test.go @@ -0,0 +1,24 @@ +// This file provides tests for coloring using BFS. +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring_test + +import ( + "strconv" + "testing" +) + +func TestGraphColorUsingBFS(t *testing.T) { + for i, tt := range getTestGraphs() { + t.Run(strconv.Itoa(i), func(t *testing.T) { + colorsOfVertices, colors := tt.Graph.ColorUsingBFS() + if colors != tt.ColorsUsed { + t.Errorf("ColorUsingBFS() return more number of colors: %v, want %v colors", colors, tt.ColorsUsed) + } + // check colors + if err := tt.Graph.ValidateColorsOfVertex(colorsOfVertices); err != nil { + t.Errorf("ColorUsingBFS() assigned colors are wrong, error = %v", err) + } + }) + } +} diff --git a/graph/coloring/bipartite.go b/graph/coloring/bipartite.go new file mode 100644 index 000000000..1f0e3c62c --- /dev/null +++ b/graph/coloring/bipartite.go @@ -0,0 +1,55 @@ +package coloring + +// Bipartite.go +// description: Implementation of the Bipartite graph coloring algorithm +// details: A bipartite graph is a graph whose vertices can be divided into two disjoint sets U and V such that every edge connects a vertex in U to one in V. The Bipartite graph coloring algorithm is used to determine if a graph is bipartite or not. +// time complexity: O(V+E) where V is the number of vertices and E is the number of edges in the graph +// space complexity: O(V) where V is the number of vertices in the graph + +func (g *Graph) TryBipartiteColoring() map[int]Color { + // 0 is uncolored, 1/2 are colors + colors := make(map[int]Color) + visited := make(map[int]bool) + + for i := range g.edges { + colors[i] = 0 + visited[i] = false + } + + var colorNode func(int) + colorNode = func(s int) { + visited[s] = true + coloring := []Color{0, 2, 1} + + for n := range g.edges[s] { + if colors[n] == 0 { + colors[n] = coloring[colors[s]] + } + if !visited[n] { + colorNode(n) + } + } + } + + for i := range g.edges { + if colors[i] == 0 { + colors[i] = 1 + colorNode(i) + } + } + + return colors +} + +// basically tries to color the graph in two colors if each edge +// connects 2 differently colored nodes the graph can be considered bipartite +func BipartiteCheck(N int, edges [][]int) bool { + var graph Graph + for i := 0; i < N; i++ { + graph.AddVertex(i) + } + for _, e := range edges { + graph.AddEdge(e[0], e[1]) + } + return graph.ValidateColorsOfVertex(graph.TryBipartiteColoring()) == nil +} diff --git a/graph/coloring/bipartite_test.go b/graph/coloring/bipartite_test.go new file mode 100644 index 000000000..0b60ae79b --- /dev/null +++ b/graph/coloring/bipartite_test.go @@ -0,0 +1,32 @@ +package coloring + +import ( + "testing" +) + +var testCases = []struct { + name string + N int + isBipartite bool + edges [][]int +}{ + { + "basic true", 2, true, + [][]int{{1, 0}}, + }, + { + "basic false", 3, false, + [][]int{{0, 1}, {1, 2}, {2, 0}}, + }, +} + +func TestBipartite(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := BipartiteCheck(tc.N, tc.edges) + if tc.isBipartite != actual { + t.Errorf("failed %s: %v", tc.name, tc.edges) + } + }) + } +} diff --git a/graph/coloring/doc.go b/graph/coloring/doc.go new file mode 100644 index 000000000..849144dcc --- /dev/null +++ b/graph/coloring/doc.go @@ -0,0 +1,5 @@ +// Package coloring provides implementation of different graph coloring +// algorithms, e.g. coloring using BFS, using Backtracking, using greedy +// approach. +// Author(s): [Shivam](https://github.com/Shivam010) +package coloring diff --git a/graph/coloring/graph.go b/graph/coloring/graph.go new file mode 100644 index 000000000..d8065cb10 --- /dev/null +++ b/graph/coloring/graph.go @@ -0,0 +1,57 @@ +// This file contains the simple structural implementation of undirected +// graph, used in coloring algorithms. +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring + +import "errors" + +// Color provides a type for vertex color +type Color int + +// Graph provides a structure to store an undirected graph. +// It is safe to use its empty object. +type Graph struct { + vertices int + edges map[int]map[int]struct{} +} + +// AddVertex will add a new vertex in the graph, if the vertex already +// exist it will do nothing +func (g *Graph) AddVertex(v int) { + if g.edges == nil { + g.edges = make(map[int]map[int]struct{}) + } + + // Check if vertex is present or not + if _, ok := g.edges[v]; !ok { + g.vertices++ + g.edges[v] = make(map[int]struct{}) + } +} + +// AddEdge will add a new edge between the provided vertices in the graph +func (g *Graph) AddEdge(one, two int) { + // Add vertices: one and two to the graph if they are not present + g.AddVertex(one) + g.AddVertex(two) + + // and finally add the edges: one->two and two->one for undirected graph + g.edges[one][two] = struct{}{} + g.edges[two][one] = struct{}{} +} + +func (g *Graph) ValidateColorsOfVertex(colors map[int]Color) error { + if g.vertices != len(colors) { + return errors.New("coloring: not all vertices of graph are colored") + } + // check colors + for vertex, neighbours := range g.edges { + for nb := range neighbours { + if colors[vertex] == colors[nb] { + return errors.New("coloring: same colors of neighbouring vertex") + } + } + } + return nil +} diff --git a/graph/coloring/graph_test.go b/graph/coloring/graph_test.go new file mode 100644 index 000000000..839d9f261 --- /dev/null +++ b/graph/coloring/graph_test.go @@ -0,0 +1,153 @@ +// This file provides tests for graph coloring validations. +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring_test + +import ( + "github.com/TheAlgorithms/Go/graph/coloring" + "strconv" + "testing" +) + +type testGraph struct { + Graph *coloring.Graph + ColorsUsed int + VertexColors map[int]coloring.Color +} + +func getTestGraphs() (list []*testGraph) { + // Graph 0th: + // 1---2 + // | / \ + // 4---3 0 + // Min number of colors required = 3 + g0 := &testGraph{ + Graph: &coloring.Graph{}, + ColorsUsed: 3, + VertexColors: map[int]coloring.Color{ + 1: 1, 4: 1, 0: 1, + 2: 2, + 3: 3, + }, + } + list = append(list, g0) + g0.Graph.AddEdge(4, 3) + g0.Graph.AddEdge(3, 1) + g0.Graph.AddEdge(3, 2) + g0.Graph.AddEdge(1, 2) + g0.Graph.AddEdge(2, 0) + + // Graph 1st: + // 1---2 + // | / | + // 4---3---0 + // Min number of colors required = 3 + g1 := &testGraph{ + Graph: &coloring.Graph{}, + ColorsUsed: 3, + VertexColors: map[int]coloring.Color{ + 1: 1, 4: 1, 0: 1, + 2: 2, + 3: 3, + }, + } + list = append(list, g1) + g1.Graph.AddEdge(4, 3) + g1.Graph.AddEdge(3, 1) + g1.Graph.AddEdge(3, 2) + g1.Graph.AddEdge(1, 2) + g1.Graph.AddEdge(2, 0) + g1.Graph.AddEdge(3, 0) + + // Graph 2nd: + // 1---2 + // | + // 4---3 0 + // Min number of colors required = 2 + g2 := &testGraph{ + Graph: &coloring.Graph{}, + ColorsUsed: 2, + VertexColors: map[int]coloring.Color{ + 1: 1, 4: 1, 0: 1, + 2: 2, 3: 2, + }, + } + list = append(list, g2) + g2.Graph.AddVertex(0) + g2.Graph.AddEdge(4, 3) + g2.Graph.AddEdge(3, 1) + g2.Graph.AddEdge(1, 2) + + // Graph 3rd: + // 1---2 4 + // | | | + // 0---3 5 + // Min number of colors required = 2 + g3 := &testGraph{ + Graph: &coloring.Graph{}, + ColorsUsed: 2, + VertexColors: map[int]coloring.Color{ + 1: 1, 3: 1, 4: 1, + 0: 2, 2: 2, 5: 2, + }, + } + list = append(list, g3) + g3.Graph.AddEdge(0, 3) + g3.Graph.AddEdge(1, 2) + g3.Graph.AddEdge(1, 0) + g3.Graph.AddEdge(3, 2) + g3.Graph.AddEdge(4, 5) + + // Graph 4th: + // Completely Connected graph of vertex 4 + // Min number of colors required = 2 + g4 := &testGraph{ + Graph: &coloring.Graph{}, + ColorsUsed: 4, + VertexColors: map[int]coloring.Color{ + 0: 1, 1: 2, 2: 3, 4: 4, + }, + } + list = append(list, g4) + for i := 0; i < 4; i++ { + for j := i + 1; j < 4; j++ { + g4.Graph.AddEdge(i, j) + } + } + + return +} + +func TestGraph_ValidateColorsOfVertex(t *testing.T) { + for i, tt := range getTestGraphs() { + t.Run(strconv.Itoa(i), func(t *testing.T) { + if err := tt.Graph.ValidateColorsOfVertex(tt.VertexColors); err != nil { + t.Errorf("ValidateColorsOfVertex() error = %v, wantErr nil", err) + } + }) + } +} + +func getTestGraphsForNegativeTests() (list []*testGraph) { + list = getTestGraphs() + list[0].VertexColors = nil + list[1].VertexColors = map[int]coloring.Color{} + for v := range list[2].VertexColors { + in := len(list[2].VertexColors) - v - 1 + list[2].VertexColors[v] = list[2].VertexColors[in] + } + for v := range list[3].VertexColors { + list[3].VertexColors[v] = 1 + } + return list[:4] +} + +func TestGraphValidateColorsOfVertex_Negative(t *testing.T) { + for i, tt := range getTestGraphsForNegativeTests() { + t.Run(strconv.Itoa(i), func(t *testing.T) { + if err := tt.Graph.ValidateColorsOfVertex(tt.VertexColors); err == nil { + t.Errorf("ValidateColorsOfVertex() error = nil, want some err") + } + }) + } +} diff --git a/graph/coloring/greedy.go b/graph/coloring/greedy.go new file mode 100644 index 000000000..07ca6af1b --- /dev/null +++ b/graph/coloring/greedy.go @@ -0,0 +1,54 @@ +// This file contains the graph coloring implementation using Greedy Approach. +// time complexity: O(V^2) where V is the number of vertices in the graph +// space complexity: O(V) where V is the number of vertices in the graph +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring + +import "sort" + +// ColorUsingGreedyApproach will return the Color of each vertex and the +// total number of different colors used, using a greedy approach, based on +// the number of edges (or degree) from any vertex. +func (g *Graph) ColorUsingGreedyApproach() (map[int]Color, int) { + degreeOfVertex := make([]struct{ degree, vertex int }, 0, g.vertices) + for v, neighbours := range g.edges { + degreeOfVertex = append(degreeOfVertex, + struct{ degree, vertex int }{ + vertex: v, + degree: len(neighbours), + }, + ) + } + // sort the degreeOfVertex in decreasing order of degrees + sort.Slice(degreeOfVertex, func(i, j int) bool { + return degreeOfVertex[i].degree > degreeOfVertex[j].degree + }) + + vertexColors := make(map[int]Color, g.vertices) + // Start with a color and assign the color to all possible vertices in the degreeOfVertex slice + // and then, re-iterate with new color for all those which are left + for color := 1; color <= g.vertices; color++ { + vertexLoop: + for _, val := range degreeOfVertex { + // skip, if already assigned + if _, ok := vertexColors[val.vertex]; ok { + continue vertexLoop + } + // Check its neighbours + for ng := range g.edges[val.vertex] { + if vertexColors[ng] == Color(color) { + // not possible to use this color for val.vertex + continue vertexLoop + } + } + // Assign color to the vertex + vertexColors[val.vertex] = Color(color) + } + // continue till all the vertices are colored + if len(vertexColors) == g.vertices { + return vertexColors, color + } + } + return vertexColors, g.vertices +} diff --git a/graph/coloring/greedy_test.go b/graph/coloring/greedy_test.go new file mode 100644 index 000000000..cd55d7d38 --- /dev/null +++ b/graph/coloring/greedy_test.go @@ -0,0 +1,24 @@ +// This file provides tests for coloring using Greedy approach. +// Author(s): [Shivam](https://github.com/Shivam010) + +package coloring_test + +import ( + "strconv" + "testing" +) + +func TestGraphColorUsingGreedyApproach(t *testing.T) { + for i, tt := range getTestGraphs() { + t.Run(strconv.Itoa(i), func(t *testing.T) { + colorsOfVertices, colors := tt.Graph.ColorUsingGreedyApproach() + if colors != tt.ColorsUsed { + t.Errorf("ColorUsingGreedyApproach() return more number of colors: %v, want %v colors", colors, tt.ColorsUsed) + } + // check colors + if err := tt.Graph.ValidateColorsOfVertex(colorsOfVertices); err != nil { + t.Errorf("ColorUsingGreedyApproach() assigned colors are wrong, error = %v", err) + } + }) + } +} diff --git a/graph/cycle.go b/graph/cycle.go new file mode 100644 index 000000000..c55cd6bed --- /dev/null +++ b/graph/cycle.go @@ -0,0 +1,112 @@ +// cycle.go +// this file handle algorithm that related to cycle in graph +// time complexity: O(V+E) where V is the number of vertices and E is the number of edges in the graph +// space complexity: O(V) where V is the number of vertices in the graph +// reference: https://en.wikipedia.org/wiki/Cycle_(graph_theory) +// [kiarash hajian](https://github.com/kiarash8112) + +package graph + +func (g *Graph) HasCycle() bool { + //this implimetation referred as 3-color too + all := map[int]struct{}{} + visiting := map[int]struct{}{} + visited := map[int]struct{}{} + + for v := range g.edges { + all[v] = struct{}{} + } + + for current := range all { + if g.hasCycleHelper(current, all, visiting, visited) { + return true + } + } + + return false + +} + +func (g Graph) hasCycleHelper(v int, all, visiting, visited map[int]struct{}) bool { + delete(all, v) + visiting[v] = struct{}{} + + neighbors := g.edges[v] + for v := range neighbors { + if _, ok := visited[v]; ok { + continue + } else if _, ok := visiting[v]; ok { + return true + } else if g.hasCycleHelper(v, all, visiting, visited) { + return true + } + } + delete(visiting, v) + visited[v] = struct{}{} + return false +} + +// this function can do HasCycle() job but it is slower +func (g *Graph) FindAllCycles() []Graph { + all := map[int]struct{}{} + visiting := map[int]struct{}{} + visited := map[int]struct{}{} + + allCycles := []Graph{} + + for v := range g.edges { + all[v] = struct{}{} + } + + for current := range all { + foundCycle, parents := g.findAllCyclesHelper(current, all, visiting, visited) + + if foundCycle { + foundCycleFromCurrent := false + //this loop remove additional vertex from detected cycle + //using foundCycleFromCurrent bool to make sure after removing vertex we still have cycle + for i := len(parents) - 1; i > 0; i-- { + if parents[i][1] == parents[0][0] { + parents = parents[:i+1] + foundCycleFromCurrent = true + } + } + if foundCycleFromCurrent { + graph := Graph{Directed: true} + for _, edges := range parents { + graph.AddEdge(edges[1], edges[0]) + } + allCycles = append(allCycles, graph) + } + + } + + } + + return allCycles + +} + +func (g Graph) findAllCyclesHelper(current int, all, visiting, visited map[int]struct{}) (bool, [][]int) { + parents := [][]int{} + + delete(all, current) + visiting[current] = struct{}{} + + neighbors := g.edges[current] + for v := range neighbors { + if _, ok := visited[v]; ok { + continue + } else if _, ok := visiting[v]; ok { + parents = append(parents, []int{v, current}) + return true, parents + } else if ok, savedParents := g.findAllCyclesHelper(v, all, visiting, visited); ok { + parents = append(parents, savedParents...) + parents = append(parents, []int{v, current}) + return true, parents + } + } + delete(visiting, current) + visited[current] = struct{}{} + return false, parents +} diff --git a/graph/cycle_test.go b/graph/cycle_test.go new file mode 100644 index 000000000..0ac7dfdbe --- /dev/null +++ b/graph/cycle_test.go @@ -0,0 +1,53 @@ +package graph + +import ( + "testing" +) + +func TestHasCycle(t *testing.T) { + graph := Graph{Directed: true} + edges := [][]int{{0, 1}, {1, 2}, {2, 0}, {4, 0}} + for _, edge := range edges { + graph.AddEdge(edge[0], edge[1]) + } + if !graph.HasCycle() { + t.Error("answer of hasCycle is not correct") + } + + graph = Graph{Directed: true} + edges = [][]int{{0, 1}, {1, 2}, {2, 6}, {4, 0}} + for _, edge := range edges { + graph.AddEdge(edge[0], edge[1]) + } + if graph.HasCycle() { + t.Error("answer of hasCycle is not correct") + } +} + +func TestFindAllCycles(t *testing.T) { + graph := Graph{Directed: true} + edges := [][]int{{0, 4}, {1, 3}, {2, 3}, {3, 4}, {4, 7}, {5, 2}, {6, 3}, {7, 3}} + for _, edge := range edges { + graph.AddEdge(edge[0], edge[1]) + } + + res := graph.FindAllCycles() + + if len(res) != 1 { + t.Error("number of cycles is not correct") + } + + firstCycle := res[0] + if len(firstCycle.edges) != 3 { + t.Error("number of vertex in cycle is not correct") + } + if _, ok := firstCycle.edges[3][4]; !ok { + t.Error("connection in cycle is not correct") + } + if _, ok := firstCycle.edges[4][7]; !ok { + t.Error("connection in cycle is not correct") + } + if _, ok := firstCycle.edges[7][3]; !ok { + t.Error("connection in cycle is not correct") + } +} diff --git a/graph/depthfirstsearch.go b/graph/depthfirstsearch.go new file mode 100644 index 000000000..76bed3106 --- /dev/null +++ b/graph/depthfirstsearch.go @@ -0,0 +1,85 @@ +// depthfirstsearch.go +// description: this file contains the implementation of the depth first search algorithm +// details: Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node and explores as far as possible along each branch before backtracking. +// time complexity: O(n) +// space complexity: O(n) + +package graph + +func GetIdx(target int, nodes []int) int { + for i := 0; i < len(nodes); i++ { + if nodes[i] == target { + return i + } + } + return -1 +} + +func NotExist(target int, slice []int) bool { + for i := 0; i < len(slice); i++ { + if slice[i] == target { + return false + } + } + return true +} + +func DepthFirstSearchHelper(start, end int, nodes []int, edges [][]bool, showroute bool) ([]int, bool) { + var route []int + var stack []int + startIdx := GetIdx(start, nodes) + stack = append(stack, startIdx) + for len(stack) > 0 { + now := stack[len(stack)-1] + route = append(route, nodes[now]) + if len(stack) > 1 { + stack = stack[:len(stack)-1] + } else { + stack = stack[:len(stack)-1] + } + for i := 0; i < len(edges[now]); i++ { + if edges[now][i] && NotExist(i, stack) { + stack = append(stack, i) + } + edges[now][i] = false + edges[i][now] = false + } + if route[len(route)-1] == end { + return route, true + } + } + + if showroute { + return route, false + } else { + return nil, false + } +} + +func DepthFirstSearch(start, end int, nodes []int, edges [][]bool) ([]int, bool) { + return DepthFirstSearchHelper(start, end, nodes, edges, false) +} + +// func main() { +// nodes := []int{ +// 1, 2, 3, 4, 5, 6, +// } +// /* +// sample graph +// ①-② +// | | +// ③-④-⑤-⑥ +// */ +// edges := [][]bool{ +// {false, true, true, false, false, false}, +// {true, false, false, true, false, false}, +// {true, false, false, true, false, false}, +// {false, true, true, false, true, false}, +// {false, false, false, true, false, true}, +// {false, false, false, false, true, false}, +// } +// start := 1 +// end := 6 +// route, _ := dfs(start, end, nodes, edges) +// fmt.Println(route) +// } diff --git a/graph/depthfirstsearch_test.go b/graph/depthfirstsearch_test.go new file mode 100644 index 000000000..d63573ca1 --- /dev/null +++ b/graph/depthfirstsearch_test.go @@ -0,0 +1,64 @@ +package graph + +import ( + "reflect" + "testing" +) + +func TestDfsWhenPathIsFound(t *testing.T) { + nodes := []int{ + 1, 2, 3, 4, 5, 6, + } + + //Adjacency Matrix for connected nodes + edges := [][]bool{ + {false, true, true, false, false, false}, + {true, false, false, true, false, false}, + {true, false, false, true, false, false}, + {false, true, true, false, true, false}, + {false, false, false, true, false, true}, + {false, false, false, false, true, false}, + } + + start := 1 + end := 6 + + actual, actualIsFound := DepthFirstSearch(start, end, nodes, edges) + expected := []int{1, 3, 4, 5, 6} + expectedIsFound := true + t.Run("Test Dfs", func(t *testing.T) { + if !reflect.DeepEqual(expected, actual) || !reflect.DeepEqual(actualIsFound, expectedIsFound) { + t.Errorf("got route: %v, want route: %v", actual, expected) + t.Errorf("got isFound: %v, want isFound: %v", actualIsFound, expectedIsFound) + } + }) +} + +func TestDfsWhenPathIsNotFound(t *testing.T) { + nodes := []int{ + 1, 2, 3, 4, 5, 6, + } + + //Adjacency Matrix for connected nodes + edges := [][]bool{ + {false, true, true, false, false, false}, + {true, false, false, true, false, false}, + {true, false, false, true, false, false}, + {false, true, true, false, true, false}, + {false, false, false, true, false, true}, + {false, false, false, false, true, false}, + } + + start := 1 + end := 7 + + actual, actualIsFound := DepthFirstSearch(start, end, nodes, edges) + var expected []int + expectedIsFound := false + t.Run("Test Dfs", func(t *testing.T) { + if !reflect.DeepEqual(expected, actual) || !reflect.DeepEqual(actualIsFound, expectedIsFound) { + t.Errorf("got route: %v, want route: %v", actual, expected) + t.Errorf("got isFound: %v, want isFound: %v", actualIsFound, expectedIsFound) + } + }) +} diff --git a/graph/dijkstra.go b/graph/dijkstra.go new file mode 100644 index 000000000..ad7a8a778 --- /dev/null +++ b/graph/dijkstra.go @@ -0,0 +1,69 @@ +// dijkstra.go +// description: this file contains the implementation of the Dijkstra algorithm +// details: Dijkstra's algorithm is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later. The algorithm exists in many variants; Dijkstra's original variant found the shortest path between two nodes, but a more common variant fixes a single node as the "source" node and finds shortest paths from the source to all other nodes in the graph, producing a shortest-path tree. +// time complexity: O((V+E) log V) where V is the number of vertices and E is the number of edges in the graph +// space complexity: O(V) where V is the number of vertices in the graph +// reference: https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm + +package graph + +import "github.com/TheAlgorithms/Go/sort" + +type Item struct { + node int + dist int +} + +func (a Item) More(b any) bool { + // reverse direction for minheap + return a.dist < b.(Item).dist +} +func (a Item) Idx() int { + return a.node +} + +func (g *Graph) Dijkstra(start, end int) (int, bool) { + visited := make(map[int]bool) + nodes := make(map[int]*Item) + + nodes[start] = &Item{ + dist: 0, + node: start, + } + pq := sort.MaxHeap{} + pq.Init(nil) + pq.Push(*nodes[start]) + + visit := func(curr Item) { + visited[curr.node] = true + for n, d := range g.edges[curr.node] { + if visited[n] { + continue + } + + item := nodes[n] + dist2 := curr.dist + d + if item == nil { + nodes[n] = &Item{node: n, dist: dist2} + pq.Push(*nodes[n]) + } else if item.dist > dist2 { + item.dist = dist2 + pq.Update(*item) + } + } + } + + for pq.Size() > 0 { + curr := pq.Pop().(Item) + if curr.node == end { + break + } + visit(curr) + } + + item := nodes[end] + if item == nil { + return -1, false + } + return item.dist, true +} diff --git a/graph/dijkstra_test.go b/graph/dijkstra_test.go new file mode 100644 index 000000000..168c7da69 --- /dev/null +++ b/graph/dijkstra_test.go @@ -0,0 +1,51 @@ +package graph + +import ( + "testing" +) + +var tc_dijkstra = []struct { + name string + edges [][]int + node0 int + node1 int + expected int +}{ + { + "straight line graph", + [][]int{{0, 1, 5}, {1, 2, 2}}, + 0, 2, 7, + }, + { + "unconnected node", + [][]int{{0, 1, 5}}, + 0, 2, -1, + }, + { + "double paths", + [][]int{{0, 1, 5}, {1, 3, 5}, {0, 2, 5}, {2, 3, 4}}, + 0, 3, 9, + }, + { + "double paths extended", + [][]int{{0, 1, 5}, {1, 3, 5}, {0, 2, 5}, {2, 3, 4}, {3, 4, 1}}, + 0, 4, 10, + }, +} + +func TestDijkstra(t *testing.T) { + for _, tc := range tc_dijkstra { + t.Run(tc.name, func(t *testing.T) { + var graph Graph + for _, edge := range tc.edges { + graph.AddWeightedEdge(edge[0], edge[1], edge[2]) + } + + actual, _ := graph.Dijkstra(tc.node0, tc.node1) + if actual != tc.expected { + t.Errorf("expected %d, got %d, from node %d to %d, with %v", + tc.expected, actual, tc.node0, tc.node1, tc.edges) + } + }) + } +} diff --git a/graph/doc.go b/graph/doc.go new file mode 100644 index 000000000..ec3d4c5ce --- /dev/null +++ b/graph/doc.go @@ -0,0 +1,3 @@ +// Package graph demonstrates Graph search algorithms +// reference: https://en.wikipedia.org/wiki/Tree_traversal +package graph diff --git a/graph/edmondkarp.go b/graph/edmondkarp.go new file mode 100644 index 000000000..f6917efcb --- /dev/null +++ b/graph/edmondkarp.go @@ -0,0 +1,93 @@ +// Edmond-Karp algorithm is an implementation of the Ford-Fulkerson method +// to compute max-flow between a pair of source-sink vertices in a weighted graph +// It uses BFS (Breadth First Search) to find the residual paths +// Time Complexity: O(V * E^2) where V is the number of vertices and E is the number of edges +// Space Complexity: O(V + E) Because we keep residual graph in size of the original graph +// Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. 2009. Introduction to Algorithms, Third Edition (3rd. ed.). The MIT Press. + +package graph + +import ( + "math" +) + +// Returns a mapping of vertices as path, if there is any from source to sink +// Otherwise, returns nil +func FindPath(rGraph WeightedGraph, source int, sink int) map[int]int { + queue := make([]int, 0) + marked := make([]bool, len(rGraph)) + marked[source] = true + queue = append(queue, source) + parent := make(map[int]int) + + // BFS loop with saving the path found + for len(queue) > 0 { + v := queue[0] + queue = queue[1:] + for i := 0; i < len(rGraph[v]); i++ { + if !marked[i] && rGraph[v][i] > 0 { + parent[i] = v + // Terminate the BFS, if we reach to sink + if i == sink { + return parent + } + marked[i] = true + queue = append(queue, i) + } + } + } + // source and sink are not in the same connected component + return nil +} + +func EdmondKarp(graph WeightedGraph, source int, sink int) float64 { + // Check graph emptiness + if len(graph) == 0 { + return 0.0 + } + + // Check correct dimensions of the graph slice + for i := 0; i < len(graph); i++ { + if len(graph[i]) != len(graph) { + return 0.0 + } + } + + rGraph := make(WeightedGraph, len(graph)) + for i := 0; i < len(graph); i++ { + rGraph[i] = make([]float64, len(graph)) + } + // Init the residual graph with the same capacities as the original graph + copy(rGraph, graph) + + maxFlow := 0.0 + + for { + parent := FindPath(rGraph, source, sink) + if parent == nil { + break + } + // Finding the max flow over the path returned by BFS + // i.e. finding minimum residual capacity amonth the path edges + pathFlow := math.MaxFloat64 + for v := sink; v != source; v = parent[v] { + u := parent[v] + if rGraph[u][v] < pathFlow { + pathFlow = rGraph[u][v] + } + } + + // update residual capacities of the edges and + // reverse edges along the path + for v := sink; v != source; v = parent[v] { + u := parent[v] + rGraph[u][v] -= pathFlow + rGraph[v][u] += pathFlow + } + + // Update the total flow found so far + maxFlow += pathFlow + } + + return maxFlow +} diff --git a/graph/edmondkarp_test.go b/graph/edmondkarp_test.go new file mode 100644 index 000000000..08e104652 --- /dev/null +++ b/graph/edmondkarp_test.go @@ -0,0 +1,79 @@ +package graph + +import ( + "testing" +) + +func TestEdmondKarp(t *testing.T) { + var edmondKarpTestData = []struct { + description string + graph WeightedGraph + source int + sink int + expected float64 + }{ + { + description: "test empty graph", + graph: nil, + source: 0, + sink: 0, + expected: 0.0, + }, + { + description: "test graph with wrong dimensions", + graph: WeightedGraph{ + {1, 2}, + {0}, + }, + source: 0, + sink: 1, + expected: 0.0, + }, + { + description: "test graph with no edges", + graph: WeightedGraph{ + {0, 0}, + {0, 0}, + }, + source: 0, + sink: 1, + expected: 0.0, + }, + { + description: "test graph with 4 vertices", + graph: WeightedGraph{ + {0, 1000000, 1000000, 0}, + {0, 0, 1, 1000000}, + {0, 0, 0, 1000000}, + {0, 0, 0, 0}, + }, + source: 0, + sink: 3, + expected: 2000000, + }, + { + description: "test graph with 6 vertices and some float64 weights", + graph: WeightedGraph{ + {0, 16, 13.8, 0, 0, 0}, + {0, 0, 10, 12.7, 0, 0}, + {0, 4.2, 0, 0, 14, 0}, + {0, 0, 9.1, 0, 0, 21.3}, + {0, 0, 0, 7.5, 0, 4}, + {0, 0, 0, 0, 0, 0}, + }, + source: 0, + sink: 5, + expected: 24.2, + }, + } + for _, test := range edmondKarpTestData { + t.Run(test.description, func(t *testing.T) { + result := EdmondKarp(test.graph, test.source, test.sink) + + if !almostEqual(test.expected, result) { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expected result:%f\nFound: %f", test.expected, result) + } + }) + } +} diff --git a/graph/floydwarshall.go b/graph/floydwarshall.go new file mode 100644 index 000000000..9544e587b --- /dev/null +++ b/graph/floydwarshall.go @@ -0,0 +1,55 @@ +// Floyd-Warshall algorithm +// time complexity: O(V^3) where V is the number of vertices in the graph +// space complexity: O(V^2) where V is the number of vertices in the graph +// https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm + +package graph + +import "math" + +// WeightedGraph defining matrix to use 2d array easier +type WeightedGraph [][]float64 + +// Defining maximum value. If two vertices share this value, it means they are not connected +var Inf = math.Inf(1) + +// FloydWarshall Returns all pair's shortest path using Floyd Warshall algorithm +func FloydWarshall(graph WeightedGraph) WeightedGraph { + // If graph is empty, returns nil + if len(graph) == 0 || len(graph) != len(graph[0]) { + return nil + } + + for i := 0; i < len(graph); i++ { + //If graph matrix width is different than the height, returns nil + if len(graph[i]) != len(graph) { + return nil + } + } + + numVertices := len(graph) + + // Initializing result matrix and filling it up with same values as given graph + result := make(WeightedGraph, numVertices) + + for i := 0; i < numVertices; i++ { + result[i] = make([]float64, numVertices) + for j := 0; j < numVertices; j++ { + result[i][j] = graph[i][j] + } + } + + // Running over the result matrix and following the algorithm + for k := 0; k < numVertices; k++ { + for i := 0; i < numVertices; i++ { + for j := 0; j < numVertices; j++ { + // If there is a less costly path from i to j node, remembering it + if result[i][j] > result[i][k]+result[k][j] { + result[i][j] = result[i][k] + result[k][j] + } + } + } + } + + return result +} diff --git a/graph/floydwarshall_test.go b/graph/floydwarshall_test.go new file mode 100644 index 000000000..a4a28aae5 --- /dev/null +++ b/graph/floydwarshall_test.go @@ -0,0 +1,110 @@ +package graph + +import ( + "math" + "testing" +) + +const float64EqualityThreshold = 1e-9 + +// almostEqual subtracts two float64 variables and returns true if they differ less then float64EqualityThreshold +// reference: https://stackoverflow.com/a/47969546 +func almostEqual(a, b float64) bool { + return math.Abs(a-b) <= float64EqualityThreshold +} + +// IsAlmostEqualTo verifies if two WeightedGraphs can be considered almost equal +func (a *WeightedGraph) IsAlmostEqualTo(b WeightedGraph) bool { + if len(*a) != len(b) { + return false + } + + for i := range *a { + if len((*a)[i]) != len(b[i]) { + return false + } + + for j := range (*a)[i] { + if (*a)[i][j] == Inf && b[i][j] == Inf { + continue + } + + if !almostEqual((*a)[i][j], b[i][j]) { + return false + } + } + } + + return true +} + +func TestFloydWarshall(t *testing.T) { + var floydWarshallTestData = []struct { + description string + graph [][]float64 + expected [][]float64 + }{ + { + description: "test empty graph", + graph: nil, + expected: nil, + }, + { + description: "test graph with wrong dimensions", + graph: [][]float64{ + {1, 2}, + {Inf}, + }, + expected: nil, + }, + { + description: "test graph with no edges", + graph: [][]float64{ + {Inf, Inf}, + {Inf, Inf}, + }, + expected: [][]float64{ + {Inf, Inf}, + {Inf, Inf}, + }, + }, + { + description: "test graph with only negative edges", + graph: [][]float64{ + {-3, -2}, + {-3, -2}, + }, + expected: [][]float64{ + {-17, -25}, + {-26, -34}, + }, + }, + { + description: "test graph with 5 vertices and self-loops", + graph: [][]float64{ + {1, 2, Inf, Inf, Inf}, + {Inf, Inf, 3, -4, Inf}, + {Inf, Inf, Inf, Inf, 5}, + {1, Inf, Inf, Inf, Inf}, + {Inf, Inf, Inf, 2, Inf}, + }, + expected: [][]float64{ + {-1, 1, 4, -3, 8}, + {-3, -1, 2, -5, 6}, + {7, 9, 12, 5, 5}, + {0, 2, 5, -2, 9}, + {2, 4, 7, 0, 9}, + }, + }, + } + for _, test := range floydWarshallTestData { + t.Run(test.description, func(t *testing.T) { + result := FloydWarshall(test.graph) + + if !result.IsAlmostEqualTo(test.expected) { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expected result:%f\nFound: %f", test.expected, result) + } + }) + } +} diff --git a/graph/graph.go b/graph/graph.go new file mode 100644 index 000000000..b6392c422 --- /dev/null +++ b/graph/graph.go @@ -0,0 +1,54 @@ +// This file contains the simple structural implementation of +// directed & undirected graphs used within the graph package +// Author(s): [Shivam](https://github.com/Shivam010), [Tahmeed](https://github.com/Tahmeed156) + +package graph + +// Graph provides a structure to store the graph. +// It is safe to use its empty object. +type Graph struct { + vertices int + edges map[int]map[int]int // Stores weight of an edge + Directed bool // Differentiate directed/undirected graphs +} + +// Constructor functions for graphs (undirected by default) +func New(v int) *Graph { + return &Graph{ + vertices: v, + } +} + +// AddVertex will add a new vertex in the graph. +// If the vertex already exists it will do nothing. +func (g *Graph) AddVertex(v int) { + if g.edges == nil { + g.edges = make(map[int]map[int]int) + } + + // Check if vertex is present or not + if _, ok := g.edges[v]; !ok { + g.edges[v] = make(map[int]int) + } +} + +// AddEdge will add a new edge between the provided vertices in the graph +func (g *Graph) AddEdge(one, two int) { + // Add an edge with 0 weight + g.AddWeightedEdge(one, two, 0) +} + +// AddWeightedEdge will add a new weighted edge between the provided vertices in the graph +func (g *Graph) AddWeightedEdge(one, two, weight int) { + // Add vertices: one and two to the graph if they are not present + g.AddVertex(one) + g.AddVertex(two) + + // And finally add the edges + // one->two and two->one for undirected graph + // one->two for directed graphs + g.edges[one][two] = weight + if !g.Directed { + g.edges[two][one] = weight + } +} diff --git a/graph/graph_test.go b/graph/graph_test.go new file mode 100644 index 000000000..032fcc529 --- /dev/null +++ b/graph/graph_test.go @@ -0,0 +1,131 @@ +// Tests for directed and undirected graphs + +package graph + +import ( + "fmt" + "testing" +) + +var graphTestCases = []struct { + name string + edges [][]int + vertices int +}{ + { + "single edge", + [][]int{ + {0, 1, 1}, + }, + 2, + }, + { + "many edges", + [][]int{ + {0, 1, 1}, + {0, 2, 2}, + {1, 3, 4}, + {3, 4, 3}, + {4, 8, 3}, + {4, 9, 1}, + {7, 8, 2}, + {8, 9, 2}, + }, + 10, + }, + { + "cycles", + [][]int{ + {0, 1, 1}, + {0, 2, 2}, + {1, 3, 4}, + {3, 4, 3}, + {4, 2, 1}, + }, + 5, + }, + { + "disconnected graphs", + [][]int{ + {0, 1, 5}, + {2, 4, 5}, + {3, 8, 5}, + }, + 2, + }, +} + +func TestDirectedGraph(t *testing.T) { + + // Testing self-loops separately only for directed graphs. + // For undirected graphs each edge already creates a self-loop. + directedGraphTestCases := append(graphTestCases, struct { + name string + edges [][]int + vertices int + }{ + "self-loops", + [][]int{ + {0, 1, 1}, + {1, 2, 2}, + {2, 1, 3}, + }, + 3, + }) + + for _, test := range directedGraphTestCases { + t.Run(fmt.Sprint(test.name), func(t *testing.T) { + // Initializing graph, adding edges + graph := New(test.vertices) + graph.Directed = true + for _, edge := range test.edges { + graph.AddWeightedEdge(edge[0], edge[1], edge[2]) + } + + if graph.vertices != test.vertices { + t.Errorf("Number of vertices, Expected: %d, Computed: %d", test.vertices, graph.vertices) + } + edgeCount := 0 + for _, e := range graph.edges { + edgeCount += len(e) + } + if edgeCount != len(test.edges) { + t.Errorf("Number of edges, Expected: %d, Computed: %d", len(test.edges), edgeCount) + } + for _, edge := range test.edges { + if val, found := graph.edges[edge[0]][edge[1]]; !found || val != edge[2] { + t.Errorf("Edge {%d->%d (%d)} not found", edge[0], edge[1], edge[2]) + } + } + }) + } +} + +func TestUndirectedGraph(t *testing.T) { + + for _, test := range graphTestCases { + t.Run(fmt.Sprint(test.name), func(t *testing.T) { + // Initializing graph, adding edges + graph := New(test.vertices) + for _, edge := range test.edges { + graph.AddWeightedEdge(edge[0], edge[1], edge[2]) + } + + if graph.vertices != test.vertices { + t.Errorf("Number of vertices, Expected: %d, Computed: %d", test.vertices, graph.vertices) + } + edgeCount := 0 + for _, e := range graph.edges { + edgeCount += len(e) + } + if edgeCount != len(test.edges)*2 { + t.Errorf("Number of edges, Expected: %d, Computed: %d", len(test.edges)*2, edgeCount) + } + for _, edge := range test.edges { + if val, found := graph.edges[edge[0]][edge[1]]; !found || val != edge[2] { + t.Errorf("Edge {%d->%d (%d)} not found", edge[0], edge[1], edge[2]) + } + } + }) + } +} diff --git a/graph/kahn.go b/graph/kahn.go new file mode 100644 index 000000000..6f9d44d71 --- /dev/null +++ b/graph/kahn.go @@ -0,0 +1,66 @@ +// Kahn's algorithm computes a topological ordering of a directed acyclic graph (DAG). +// Time Complexity: O(V + E) +// Space Complexity: O(V + E) +// Reference: https://en.wikipedia.org/wiki/Topological_sorting#Kahn's_algorithm +// see graph.go, topological.go, kahn_test.go + +package graph + +// Kahn's algorithm computes a topological ordering of a directed acyclic graph (DAG). +// `n` is the number of vertices, +// `dependencies` is a list of directed edges, where each pair [a, b] represents +// a directed edge from a to b (i.e. b depends on a). +// Vertices are assumed to be labelled 0, 1, ..., n-1. +// If the graph is not a DAG, the function returns nil. +func Kahn(n int, dependencies [][]int) []int { + g := Graph{vertices: n, Directed: true} + // track the in-degree (number of incoming edges) of each vertex + inDegree := make([]int, n) + + // populate g with edges, increase the in-degree counts accordingly + for _, d := range dependencies { + // make sure we don't add the same edge twice + if _, ok := g.edges[d[0]][d[1]]; !ok { + g.AddEdge(d[0], d[1]) + inDegree[d[1]]++ + } + } + + // queue holds all vertices with in-degree 0 + // these vertices have no dependency and thus can be ordered first + queue := make([]int, 0, n) + + for i := 0; i < n; i++ { + if inDegree[i] == 0 { + queue = append(queue, i) + } + } + + // order holds a valid topological order + order := make([]int, 0, n) + + // process the dependency-free vertices + // every time we process a vertex, we "remove" it from the graph + for len(queue) > 0 { + // pop the first vertex from the queue + vtx := queue[0] + queue = queue[1:] + // add the vertex to the topological order + order = append(order, vtx) + // "remove" all the edges coming out of this vertex + // every time we remove an edge, the corresponding in-degree reduces by 1 + // if all dependencies on a vertex is removed, enqueue the vertex + for neighbour := range g.edges[vtx] { + inDegree[neighbour]-- + if inDegree[neighbour] == 0 { + queue = append(queue, neighbour) + } + } + } + + // if the graph is a DAG, order should contain all the certices + if len(order) != n { + return nil + } + return order +} diff --git a/graph/kahn_test.go b/graph/kahn_test.go new file mode 100644 index 000000000..71536b4f6 --- /dev/null +++ b/graph/kahn_test.go @@ -0,0 +1,115 @@ +package graph + +import ( + "testing" +) + +func TestKahn(t *testing.T) { + testCases := []struct { + name string + n int + dependencies [][]int + wantNil bool + }{ + { + "linear graph", + 3, + [][]int{{0, 1}, {1, 2}}, + false, + }, + { + "diamond graph", + 4, + [][]int{{0, 1}, {0, 2}, {1, 3}, {2, 3}}, + false, + }, + { + "star graph", + 5, + [][]int{{0, 1}, {0, 2}, {0, 3}, {0, 4}}, + false, + }, + { + "disconnected graph", + 5, + [][]int{{0, 1}, {0, 2}, {3, 4}}, + false, + }, + { + "cycle graph 1", + 4, + [][]int{{0, 1}, {1, 2}, {2, 3}, {3, 0}}, + true, + }, + { + "cycle graph 2", + 4, + [][]int{{0, 1}, {1, 2}, {2, 0}, {2, 3}}, + true, + }, + { + "single node graph", + 1, + [][]int{}, + false, + }, + { + "empty graph", + 0, + [][]int{}, + false, + }, + { + "redundant dependencies", + 4, + [][]int{{0, 1}, {1, 2}, {1, 2}, {2, 3}}, + false, + }, + { + "island vertex", + 4, + [][]int{{0, 1}, {0, 2}}, + false, + }, + { + "more complicated graph", + 14, + [][]int{{1, 9}, {2, 0}, {3, 2}, {4, 5}, {4, 6}, {4, 7}, {6, 7}, + {7, 8}, {9, 4}, {10, 0}, {10, 1}, {10, 12}, {11, 13}, + {12, 0}, {12, 11}, {13, 5}}, + false, + }, + } + + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := Kahn(tc.n, tc.dependencies) + if tc.wantNil { + if actual != nil { + t.Errorf("Kahn(%d, %v) = %v; want nil", tc.n, tc.dependencies, actual) + } + } else { + if actual == nil { + t.Errorf("Kahn(%d, %v) = nil; want valid order", tc.n, tc.dependencies) + } else { + seen := make([]bool, tc.n) + positions := make([]int, tc.n) + for i, v := range actual { + seen[v] = true + positions[v] = i + } + for i, v := range seen { + if !v { + t.Errorf("missing vertex %v", i) + } + } + for _, d := range tc.dependencies { + if positions[d[0]] > positions[d[1]] { + t.Errorf("dependency %v not satisfied", d) + } + } + } + } + }) + } +} diff --git a/graph/kosaraju.go b/graph/kosaraju.go new file mode 100644 index 000000000..d36949e5f --- /dev/null +++ b/graph/kosaraju.go @@ -0,0 +1,92 @@ +// kosaraju.go +// description: Implementation of Kosaraju's algorithm to find Strongly Connected Components (SCCs) in a directed graph. +// details: The algorithm consists of three steps: +// 1. Perform DFS and fill the stack with vertices in the order of their finish times. +// 2. Create a transposed graph by reversing all edges. +// 3. Perform DFS on the transposed graph in the order defined by the stack to find SCCs. +// time: O(V + E), where V is the number of vertices and E is the number of edges in the graph. +// space: O(V), where V is the number of vertices in the graph. +// ref link: https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm +// author: mapcrafter2048 + +package graph + +// Kosaraju returns a list of Strongly Connected Components (SCCs). +func (g *Graph) Kosaraju() [][]int { + stack := []int{} + visited := make([]bool, g.vertices) + + // Step 1: Perform DFS and fill stack based on finish times. + for i := 0; i < g.vertices; i++ { + if !visited[i] { + g.fillOrder(i, visited, &stack) + } + } + + // Step 2: Create a transposed graph. + transposed := g.transpose() + + // Step 3: Perform DFS on the transposed graph in the order defined by the stack. + visited = make([]bool, g.vertices) + var sccs [][]int + + for len(stack) > 0 { + // Pop vertex from stack + v := stack[len(stack)-1] + stack = stack[:len(stack)-1] + + // Perform DFS if not already visited. + if !visited[v] { + scc := []int{} + transposed.dfs(v, visited, &scc) + sccs = append(sccs, scc) + } + } + + return sccs +} + +// Helper function to fill the stack with vertices in the order of their finish times. +func (g *Graph) fillOrder(v int, visited []bool, stack *[]int) { + visited[v] = true + + for neighbor := range g.edges[v] { + if !visited[neighbor] { + g.fillOrder(neighbor, visited, stack) + } + } + + // Push the current vertex to the stack after exploring all neighbors. + *stack = append(*stack, v) +} + +// Helper function to create a transposed (reversed) graph. +func (g *Graph) transpose() *Graph { + transposed := &Graph{ + vertices: g.vertices, + edges: make(map[int]map[int]int), + } + + for v, neighbors := range g.edges { + for neighbor := range neighbors { + if transposed.edges[neighbor] == nil { + transposed.edges[neighbor] = make(map[int]int) + } + transposed.edges[neighbor][v] = 1 // Add the reversed edge + } + } + + return transposed +} + +// Helper DFS function used in the transposed graph to collect SCCs. +func (g *Graph) dfs(v int, visited []bool, scc *[]int) { + visited[v] = true + *scc = append(*scc, v) + + for neighbor := range g.edges[v] { + if !visited[neighbor] { + g.dfs(neighbor, visited, scc) + } + } +} diff --git a/graph/kosaraju_test.go b/graph/kosaraju_test.go new file mode 100644 index 000000000..360b72a3e --- /dev/null +++ b/graph/kosaraju_test.go @@ -0,0 +1,106 @@ +package graph + +import ( + "reflect" + "sort" + "testing" +) + +func TestKosaraju(t *testing.T) { + tests := []struct { + name string + vertices int + edges map[int][]int + expected [][]int + }{ + { + name: "Single SCC", + vertices: 5, + edges: map[int][]int{ + 0: {1}, + 1: {2}, + 2: {0, 3}, + 3: {4}, + 4: {}, + }, + expected: [][]int{{4}, {3}, {0, 2, 1}}, + }, + { + name: "Multiple SCCs", + vertices: 8, + edges: map[int][]int{ + 0: {1}, + 1: {2}, + 2: {0, 3}, + 3: {4}, + 4: {5}, + 5: {3, 6}, + 6: {7}, + 7: {6}, + }, + expected: [][]int{{6, 7}, {3, 4, 5}, {0, 2, 1}}, + }, + { + name: "Disconnected graph", + vertices: 4, + edges: map[int][]int{ + 0: {1}, + 1: {}, + 2: {3}, + 3: {}, + }, + expected: [][]int{{1}, {0}, {3}, {2}}, + }, + { + name: "No edges", + vertices: 3, + edges: map[int][]int{ + 0: {}, + 1: {}, + 2: {}, + }, + expected: [][]int{{0}, {1}, {2}}, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + // Initializing graph + graph := &Graph{ + vertices: tt.vertices, + edges: make(map[int]map[int]int), + } + for v, neighbors := range tt.edges { + graph.edges[v] = make(map[int]int) + for _, neighbor := range neighbors { + graph.edges[v][neighbor] = 1 + } + } + + // Running Kosaraju's algorithm to get the SCCs + result := graph.Kosaraju() + + // Sort the expected and result SCCs to ensure order doesn't matter + sortSlices(tt.expected) + sortSlices(result) + + // Compare the sorted SCCs + if !reflect.DeepEqual(result, tt.expected) { + t.Errorf("expected %v, got %v", tt.expected, result) + } + }) + } +} + +// Utility function to sort the slices and their contents +func sortSlices(s [][]int) { + for _, inner := range s { + sort.Ints(inner) + } + sort.Slice(s, func(i, j int) bool { + if len(s[i]) == 0 || len(s[j]) == 0 { + return len(s[i]) < len(s[j]) + } + return s[i][0] < s[j][0] + }) +} diff --git a/graph/kruskal.go b/graph/kruskal.go new file mode 100644 index 000000000..1b0328da3 --- /dev/null +++ b/graph/kruskal.go @@ -0,0 +1,51 @@ +// KRUSKAL'S ALGORITHM +// Reference: Kruskal's Algorithm: https://www.scaler.com/topics/data-structures/kruskal-algorithm/ +// Reference: Union Find Algorithm: https://www.scaler.com/topics/data-structures/disjoint-set/ +// Author: Author: Mugdha Behere[https://github.com/MugdhaBehere] +// Worst Case Time Complexity: O(E log E), where E is the number of edges. +// Worst Case Space Complexity: O(V + E), where V is the number of vertices and E is the number of edges. +// see kruskal.go, kruskal_test.go + +package graph + +import ( + "sort" +) + +type Vertex int + +type Edge struct { + Start Vertex + End Vertex + Weight int +} + +func KruskalMST(n int, edges []Edge) ([]Edge, int) { + // Initialize variables to store the minimum spanning tree and its total cost + var mst []Edge + var cost int + + // Create a new UnionFind data structure with 'n' nodes + u := NewUnionFind(n) + + // Sort the edges in non-decreasing order based on their weights + sort.SliceStable(edges, func(i, j int) bool { + return edges[i].Weight < edges[j].Weight + }) + + // Iterate through the sorted edges + for _, edge := range edges { + // Check if adding the current edge forms a cycle or not + if u.Find(int(edge.Start)) != u.Find(int(edge.End)) { + // Add the edge to the minimum spanning tree + mst = append(mst, edge) + // Add the weight of the edge to the total cost + cost += edge.Weight + // Merge the sets containing the start and end vertices of the current edge + u.Union(int(edge.Start), int(edge.End)) + } + } + + // Return the minimum spanning tree and its total cost + return mst, cost +} diff --git a/graph/kruskal_test.go b/graph/kruskal_test.go new file mode 100644 index 000000000..09ed6949d --- /dev/null +++ b/graph/kruskal_test.go @@ -0,0 +1,85 @@ +package graph + +import ( + "fmt" + "testing" +) + +func TestKruskalMST(t *testing.T) { + // Define test cases with inputs, expected outputs, and sample graphs + var testCases = []struct { + n int + graph []Edge + cost int + }{ + // Test Case 1 + { + n: 5, + graph: []Edge{ + {Start: 0, End: 1, Weight: 4}, + {Start: 0, End: 2, Weight: 13}, + {Start: 0, End: 3, Weight: 7}, + {Start: 0, End: 4, Weight: 7}, + {Start: 1, End: 2, Weight: 9}, + {Start: 1, End: 3, Weight: 3}, + {Start: 1, End: 4, Weight: 7}, + {Start: 2, End: 3, Weight: 10}, + {Start: 2, End: 4, Weight: 14}, + {Start: 3, End: 4, Weight: 4}, + }, + cost: 20, + }, + // Test Case 2 + { + n: 3, + graph: []Edge{ + {Start: 0, End: 1, Weight: 12}, + {Start: 0, End: 2, Weight: 18}, + {Start: 1, End: 2, Weight: 6}, + }, + cost: 18, + }, + // Test Case 3 + { + n: 4, + graph: []Edge{ + {Start: 0, End: 1, Weight: 2}, + {Start: 0, End: 2, Weight: 1}, + {Start: 0, End: 3, Weight: 2}, + {Start: 1, End: 2, Weight: 1}, + {Start: 1, End: 3, Weight: 2}, + {Start: 2, End: 3, Weight: 3}, + }, + cost: 4, + }, + // Test Case 4 + { + n: 2, + graph: []Edge{ + {Start: 0, End: 1, Weight: 4000000}, + }, + cost: 4000000, + }, + // Test Case 5 + { + n: 1, + graph: []Edge{ + {Start: 0, End: 0, Weight: 0}, + }, + cost: 0, + }, + } + + // Iterate through the test cases and run the tests + for i, testCase := range testCases { + t.Run(fmt.Sprintf("Test Case %d", i), func(t *testing.T) { + // Execute KruskalMST for the current test case + _, computed := KruskalMST(testCase.n, testCase.graph) + + // Compare the computed result with the expected result + if computed != testCase.cost { + t.Errorf("Test Case %d, Expected: %d, Computed: %d", i, testCase.cost, computed) + } + }) + } +} diff --git a/graph/lowestcommonancestor.go b/graph/lowestcommonancestor.go new file mode 100644 index 000000000..891bac50d --- /dev/null +++ b/graph/lowestcommonancestor.go @@ -0,0 +1,123 @@ +// lowestcommonancestor.go +// description: Implementation of Lowest common ancestor (LCA) algorithm. +// detail: +// Let `T` be a tree. The LCA of `u` and `v` in T is the shared ancestor of `u` and `v` +// that is located farthest from the root. +// time complexity: O(n log n) where n is the number of vertices in the tree +// space complexity: O(n log n) where n is the number of vertices in the tree +// references: [cp-algorithms](https://cp-algorithms.com/graph/lca_binary_lifting.html) +// author(s) [Dat](https://github.com/datbeohbbh) +// see lowestcommonancestor_test.go for a test implementation. + +package graph + +type TreeEdge struct { + from int + to int +} + +type ITree interface { + dfs(int, int) + addEdge(int, int) + GetDepth(int) int + GetDad(int) int + GetLCA(int, int) int +} + +type Tree struct { + numbersVertex int + root int + MAXLOG int + depth []int + dad []int + jump [][]int + edges [][]int +} + +func (tree *Tree) addEdge(u, v int) { + tree.edges[u] = append(tree.edges[u], v) + tree.edges[v] = append(tree.edges[v], u) +} + +func (tree *Tree) dfs(u, par int) { + tree.jump[0][u] = par + tree.dad[u] = par + for _, v := range tree.edges[u] { + if v != par { + tree.depth[v] = tree.depth[u] + 1 + tree.dfs(v, u) + } + } +} + +func (tree *Tree) GetDepth(u int) int { + return tree.depth[u] +} + +func (tree *Tree) GetDad(u int) int { + return tree.dad[u] +} + +func (tree *Tree) GetLCA(u, v int) int { + if tree.GetDepth(u) < tree.GetDepth(v) { + u, v = v, u + } + + for j := tree.MAXLOG - 1; j >= 0; j-- { + if tree.GetDepth(tree.jump[j][u]) >= tree.GetDepth(v) { + u = tree.jump[j][u] + } + } + + if u == v { + return u + } + + for j := tree.MAXLOG - 1; j >= 0; j-- { + if tree.jump[j][u] != tree.jump[j][v] { + u = tree.jump[j][u] + v = tree.jump[j][v] + } + } + + return tree.jump[0][u] +} + +func NewTree(numbersVertex, root int, edges []TreeEdge) (tree *Tree) { + tree = new(Tree) + tree.numbersVertex, tree.root, tree.MAXLOG = numbersVertex, root, 0 + tree.depth = make([]int, numbersVertex) + tree.dad = make([]int, numbersVertex) + + for (1 << tree.MAXLOG) <= numbersVertex { + (tree.MAXLOG) += 1 + } + (tree.MAXLOG) += 1 + + tree.jump = make([][]int, tree.MAXLOG) + for j := 0; j < tree.MAXLOG; j++ { + tree.jump[j] = make([]int, numbersVertex) + } + + tree.edges = make([][]int, numbersVertex) + for _, e := range edges { + tree.addEdge(e.from, e.to) + } + + return tree +} + +// For each node, we will precompute its ancestor above him, its ancestor two nodes above, its ancestor four nodes above, etc. +// Let's call `jump[j][u]` is the `2^j`-th ancestor above the node `u` with `u` in range `[0, numbersVertex)`, `j` in range `[0,MAXLOG)`. +// These information allow us to jump from any node to any ancestor above it in `O(MAXLOG)` time. +func LowestCommonAncestor(tree *Tree) { + // call dfs to compute depth from the root to each node and the parent of each node. + tree.dfs(tree.root, tree.root) + + // compute jump[j][u] + for j := 1; j < tree.MAXLOG; j++ { + for u := 0; u < tree.numbersVertex; u++ { + tree.jump[j][u] = tree.jump[j-1][tree.jump[j-1][u]] + } + } +} diff --git a/graph/lowestcommonancestor_test.go b/graph/lowestcommonancestor_test.go new file mode 100644 index 000000000..ab55219fb --- /dev/null +++ b/graph/lowestcommonancestor_test.go @@ -0,0 +1,250 @@ +package graph + +import ( + "math/rand" + "testing" + "time" +) + +type Query struct { + u int + v int + expected int +} + +func TestLCA(t *testing.T) { + testSuites := []struct { + numbersVertex int + root int + edges []TreeEdge + queries []Query + }{ + { + numbersVertex: 2, + root: 0, + edges: []TreeEdge{ + { + from: 0, + to: 1, + }, + }, + queries: []Query{ + { + u: 0, + v: 0, + expected: 0, + }, + { + u: 0, + v: 1, + expected: 0, + }, + { + u: 1, + v: 1, + expected: 1, + }, + }, + }, { + numbersVertex: 1, + root: 0, + edges: []TreeEdge{}, + queries: []Query{ + { + u: 0, + v: 0, + expected: 0, + }, + }, + }, { + numbersVertex: 9, + root: 7, + edges: []TreeEdge{ + { + from: 0, + to: 1, + }, + { + from: 0, + to: 2, + }, + { + from: 2, + to: 3, + }, + { + from: 2, + to: 4, + }, + { + from: 2, + to: 6, + }, + { + from: 3, + to: 5, + }, + { + from: 6, + to: 7, + }, + { + from: 6, + to: 8, + }, + }, + queries: []Query{ + { + u: 1, + v: 0, + expected: 0, + }, + { + u: 8, + v: 2, + expected: 6, + }, + { + u: 1, + v: 5, + expected: 2, + }, + { + u: 4, + v: 7, + expected: 7, + }, + { + u: 0, + v: 8, + expected: 6, + }, + }, + }, + } + // Test #2: + // 7 + // / + // 6 + // / \ + // 2 8 + // / | \ + // 0 3 4 + // / | + // 1 5 + for idx, test := range testSuites { + tree := NewTree(test.numbersVertex, test.root, test.edges) + LowestCommonAncestor(tree) + + for qi, query := range test.queries { + actual := tree.GetLCA(query.u, query.v) + expected := query.expected + if actual != expected { + t.Errorf("\nTest #%d:\nQuery #%d: u = %d, v = %d\nExpected %d, but actual %d", idx, qi, query.u, query.v, expected, actual) + } + } + } +} + +func generateTree() *Tree { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + + const MAXVERTEX int = 2000 + var numbersVertex int = rnd.Intn(MAXVERTEX) + 1 + var root int = rnd.Intn(numbersVertex) + var edges []TreeEdge + + var fullGraph []TreeEdge + for u := 0; u < numbersVertex; u++ { + for v := 0; v < numbersVertex; v++ { + fullGraph = append(fullGraph, TreeEdge{ + from: u, + to: v, + }) + } + } + rnd.Shuffle(len(fullGraph), func(i, j int) { + fullGraph[i], fullGraph[j] = fullGraph[j], fullGraph[i] + }) + + par := make([]int, numbersVertex) + for u := 0; u < numbersVertex; u++ { + par[u] = u + } + + var findp func(int) int + findp = func(u int) int { + if u == par[u] { + return u + } else { + par[u] = findp(par[u]) + return par[u] + } + } + + join := func(u, v int) bool { + u, v = findp(u), findp(v) + if u == v { + return false + } + par[v] = u + return true + } + + for _, e := range fullGraph { + if join(e.from, e.to) == true { + edges = append(edges, e) + } + } + + return NewTree(numbersVertex, root, edges) +} + +func generateQuery(tree *Tree) []Query { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + const MAXQUERY = 50 + var queries []Query + + bruteforceLCA := func(u, v int) int { + for u != v { + if tree.GetDepth(u) > tree.GetDepth(v) { + u = tree.GetDad(u) + } else { + v = tree.GetDad(v) + } + } + return u + } + + for q := 1; q <= MAXQUERY; q++ { + u := rnd.Intn(tree.numbersVertex) + v := rnd.Intn(tree.numbersVertex) + queries = append(queries, Query{ + u: u, + v: v, + expected: bruteforceLCA(u, v), + }) + } + + return queries +} + +// Test with the tree with up to 2000 vertices. +func TestLCAWithLargeTree(t *testing.T) { + const MAXTEST int = 20 + + for test := 1; test <= MAXTEST; test++ { + tree := generateTree() + LowestCommonAncestor(tree) + + queries := generateQuery(tree) + + for qi, query := range queries { + actual := tree.GetLCA(query.u, query.v) + expected := query.expected + if actual != expected { + t.Errorf("\nTest #%d:\nQuery #%d: u = %d, v = %d\nExpected %d, but actual %d", test, qi, query.u, query.v, expected, actual) + } + } + } +} diff --git a/graph/prim.go b/graph/prim.go new file mode 100644 index 000000000..d99dcd6e1 --- /dev/null +++ b/graph/prim.go @@ -0,0 +1,58 @@ +// The Prim's algorithm computes the minimum spanning tree for a weighted undirected graph +// Worst Case Time Complexity: O(E log V) using Binary heap, where V is the number of vertices and E is the number of edges +// Space Complexity: O(V + E) +// Implementation is based on the book 'Introduction to Algorithms' (CLRS) + +package graph + +import ( + "container/heap" +) + +type minEdge []Edge + +func (h minEdge) Len() int { return len(h) } +func (h minEdge) Less(i, j int) bool { return h[i].Weight < h[j].Weight } +func (h minEdge) Swap(i, j int) { h[i], h[j] = h[j], h[i] } + +func (h *minEdge) Push(x interface{}) { + *h = append(*h, x.(Edge)) +} + +func (h *minEdge) Pop() interface{} { + old := *h + n := len(old) + x := old[n-1] + *h = old[0 : n-1] + return x +} + +func (g *Graph) PrimMST(start Vertex) ([]Edge, int) { + var mst []Edge + marked := make([]bool, g.vertices) + h := &minEdge{} + // Pushing neighbors of the start node to the binary heap + for neighbor, weight := range g.edges[int(start)] { + heap.Push(h, Edge{start, Vertex(neighbor), weight}) + } + marked[start] = true + cost := 0 + for h.Len() > 0 { + e := heap.Pop(h).(Edge) + end := int(e.End) + // To avoid cycles + if marked[end] { + continue + } + marked[end] = true + cost += e.Weight + mst = append(mst, e) + // Check for neighbors of the newly added edge's End vertex + for neighbor, weight := range g.edges[end] { + if !marked[neighbor] { + heap.Push(h, Edge{e.End, Vertex(neighbor), weight}) + } + } + } + return mst, cost +} diff --git a/graph/prim_test.go b/graph/prim_test.go new file mode 100644 index 000000000..8a3d42c12 --- /dev/null +++ b/graph/prim_test.go @@ -0,0 +1,143 @@ +package graph + +import ( + "fmt" + "reflect" + "testing" +) + +func TestPrimMST(t *testing.T) { + + var testCases = []struct { + edges []Edge + vertices int + start int + cost int + mst []Edge + }{ + { + edges: []Edge{ + {Start: 0, End: 1, Weight: 4}, + {Start: 0, End: 2, Weight: 13}, + {Start: 0, End: 3, Weight: 7}, + {Start: 0, End: 4, Weight: 7}, + {Start: 1, End: 2, Weight: 9}, + {Start: 1, End: 3, Weight: 3}, + {Start: 1, End: 4, Weight: 7}, + {Start: 2, End: 3, Weight: 10}, + {Start: 2, End: 4, Weight: 14}, + {Start: 3, End: 4, Weight: 4}, + }, + vertices: 5, + start: 0, + cost: 20, + mst: []Edge{ + {Start: 0, End: 1, Weight: 4}, + {Start: 1, End: 3, Weight: 3}, + {Start: 3, End: 4, Weight: 4}, + {Start: 1, End: 2, Weight: 9}, + }, + }, + { + edges: []Edge{ + {Start: 0, End: 1, Weight: 4}, + {Start: 0, End: 7, Weight: 8}, + {Start: 1, End: 2, Weight: 8}, + {Start: 1, End: 7, Weight: 11}, + {Start: 2, End: 3, Weight: 7}, + {Start: 2, End: 5, Weight: 4}, + {Start: 2, End: 8, Weight: 2}, + {Start: 3, End: 4, Weight: 9}, + {Start: 3, End: 5, Weight: 14}, + {Start: 4, End: 5, Weight: 10}, + {Start: 5, End: 6, Weight: 2}, + {Start: 6, End: 7, Weight: 1}, + {Start: 6, End: 8, Weight: 6}, + {Start: 7, End: 8, Weight: 7}, + }, + vertices: 9, + start: 3, + cost: 37, + mst: []Edge{ + {Start: 3, End: 2, Weight: 7}, + {Start: 2, End: 8, Weight: 2}, + {Start: 2, End: 5, Weight: 4}, + {Start: 5, End: 6, Weight: 2}, + {Start: 6, End: 7, Weight: 1}, + {Start: 2, End: 1, Weight: 8}, + {Start: 1, End: 0, Weight: 4}, + {Start: 3, End: 4, Weight: 9}, + }, + }, + { + edges: []Edge{ + {Start: 0, End: 1, Weight: 2}, + {Start: 0, End: 3, Weight: 6}, + {Start: 1, End: 2, Weight: 3}, + {Start: 1, End: 3, Weight: 8}, + {Start: 1, End: 4, Weight: 5}, + {Start: 2, End: 4, Weight: 7}, + {Start: 3, End: 4, Weight: 9}, + }, + vertices: 5, + start: 2, + cost: 16, + mst: []Edge{ + {Start: 2, End: 1, Weight: 3}, + {Start: 1, End: 0, Weight: 2}, + {Start: 1, End: 4, Weight: 5}, + {Start: 0, End: 3, Weight: 6}, + }, + }, + { + edges: []Edge{ + {Start: 0, End: 0, Weight: 0}, + }, + vertices: 1, + start: 0, + cost: 0, + mst: nil, + }, + { + edges: []Edge{ + {Start: 0, End: 1, Weight: 1}, + {Start: 0, End: 2, Weight: 6}, + {Start: 0, End: 3, Weight: 5}, + {Start: 1, End: 2, Weight: 2}, + {Start: 1, End: 4, Weight: 4}, + {Start: 2, End: 4, Weight: 9}, + }, + vertices: 5, + start: 4, + cost: 12, + mst: []Edge{ + {Start: 4, End: 1, Weight: 4}, + {Start: 1, End: 0, Weight: 1}, + {Start: 1, End: 2, Weight: 2}, + {Start: 0, End: 3, Weight: 5}, + }, + }, + } + + for i, testCase := range testCases { + t.Run(fmt.Sprintf("Test Case %d", i), func(t *testing.T) { + // Initializing graph, adding edges + graph := New(testCase.vertices) + graph.Directed = false + for _, edge := range testCase.edges { + graph.AddWeightedEdge(int(edge.Start), int(edge.End), edge.Weight) + } + + computedMST, computedCost := graph.PrimMST(Vertex(testCase.start)) + + // Compare the computed result with the expected result + if computedCost != testCase.cost { + t.Errorf("Test Case %d, Expected Cost: %d, Computed: %d", i, testCase.cost, computedCost) + } + + if !reflect.DeepEqual(testCase.mst, computedMST) { + t.Errorf("Test Case %d, Expected MST: %v, Computed: %v", i, testCase.mst, computedMST) + } + }) + } +} diff --git a/graph/topological.go b/graph/topological.go new file mode 100644 index 000000000..8cd1856e0 --- /dev/null +++ b/graph/topological.go @@ -0,0 +1,42 @@ +// topological.go +// description: Topological sort +// details: Topological sorting for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge u v, vertex u comes before v in the ordering. Topological Sorting for a graph is not possible if the graph is not a DAG. +// time complexity: O(V+E) where V is the number of vertices and E is the number of edges in the graph +// space complexity: O(V) where V is the number of vertices in the graph +// reference: https://en.wikipedia.org/wiki/Topological_sorting + +package graph + +// Topological assumes that graph given is valid and that its +// possible to get a topological ordering. +// constraints are array of []int{a, b}, representing +// an edge going from a to b +func Topological(N int, constraints [][]int) []int { + dependencies := make([]int, N) + nodes := make([]int, N) + for i := range nodes { + nodes[i] = i + } + edges := make([][]bool, N) + for i := range edges { + edges[i] = make([]bool, N) + } + + for _, c := range constraints { + a := c[0] + b := c[1] + dependencies[b]++ + edges[a][b] = true + } + + var answer []int + for s := 0; s < N; s++ { + // Only start walking from top level nodes + if dependencies[s] == 0 { + route, _ := DepthFirstSearchHelper(s, N, nodes, edges, true) + answer = append(answer, route...) + } + } + + return answer +} diff --git a/graph/topological_test.go b/graph/topological_test.go new file mode 100644 index 000000000..2a914e0ae --- /dev/null +++ b/graph/topological_test.go @@ -0,0 +1,59 @@ +package graph + +import ( + "testing" +) + +var testCases = []struct { + name string + N int + constraints [][]int +}{ + { + "basic test", 2, + [][]int{{1, 0}}, + }, + { + "double path", 7, + [][]int{ + {0, 1}, {1, 3}, {3, 5}, + {0, 2}, {2, 4}, {4, 6}}, + }, + { + "star shape", 7, + [][]int{ + {0, 1}, {0, 3}, {0, 5}, + {0, 2}, {0, 4}, {0, 6}}, + }, + { + "tree shape", 7, + [][]int{ + {0, 1}, {1, 3}, {1, 5}, + {0, 2}, {2, 4}, {2, 6}}, + }, +} + +func TestTopological(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := Topological(tc.N, tc.constraints) + + visited := make([]bool, tc.N) + positions := make([]int, tc.N) + for i := 0; i < tc.N; i++ { + positions[actual[i]] = i + visited[actual[i]] = true + } + for _, v := range visited { + if !v { + t.Errorf("nodes not all visited, %v", visited) + } + } + for _, c := range tc.constraints { + if positions[c[0]] > positions[c[1]] { + t.Errorf("%v dun satisfy %v", actual, c) + } + } + }) + } +} diff --git a/graph/unionfind.go b/graph/unionfind.go new file mode 100644 index 000000000..42714ab39 --- /dev/null +++ b/graph/unionfind.go @@ -0,0 +1,62 @@ +// Union Find Algorithm or Dynamic Connectivity algorithm, often implemented with the help +//of the union find data structure, +// is used to efficiently maintain connected components in a graph that undergoes dynamic changes, +// such as edges being added or removed over time +// Worst Case Time Complexity: The time complexity of find operation is nearly constant or +//O(α(n)), where α(n) is the inverse Ackermann function +// practically, this is a very slowly growing function making the time complexity for find +//operation nearly constant. +// The time complexity of the union operation is also nearly constant or O(α(n)) +// Worst Case Space Complexity: O(n), where n is the number of nodes or element in the structure +// Reference: https://www.scaler.com/topics/data-structures/disjoint-set/ +// https://en.wikipedia.org/wiki/Disjoint-set_data_structure +// Author: Mugdha Behere[https://github.com/MugdhaBehere] +// see: unionfind.go, unionfind_test.go + +package graph + +// Defining the union-find data structure +type UnionFind struct { + parent []int + rank []int +} + +// Initialise a new union find data structure with s nodes +func NewUnionFind(s int) UnionFind { + parent := make([]int, s) + rank := make([]int, s) + for i := 0; i < s; i++ { + parent[i] = i + rank[i] = 1 + } + return UnionFind{parent, rank} +} + +// Find finds the root of the set to which the given element belongs. +// It performs path compression to make future Find operations faster. +func (u *UnionFind) Find(q int) int { + if q != u.parent[q] { + u.parent[q] = u.Find(u.parent[q]) + } + return u.parent[q] +} + +// Union merges the sets, if not already merged, to which the given elements belong. +// It performs union by rank to keep the tree as flat as possible. +func (u *UnionFind) Union(p, q int) { + rootP := u.Find(p) + rootQ := u.Find(q) + + if rootP == rootQ { + return + } + + if u.rank[rootP] < u.rank[rootQ] { + u.parent[rootP] = rootQ + } else if u.rank[rootP] > u.rank[rootQ] { + u.parent[rootQ] = rootP + } else { + u.parent[rootQ] = rootP + u.rank[rootP]++ + } +} diff --git a/graph/unionfind_test.go b/graph/unionfind_test.go new file mode 100644 index 000000000..35eea59d4 --- /dev/null +++ b/graph/unionfind_test.go @@ -0,0 +1,41 @@ +package graph + +import ( + "testing" +) + +func TestUnionFind(t *testing.T) { + u := NewUnionFind(10) // Creating a Union-Find data structure with 10 elements + + //union operations + u.Union(0, 1) + u.Union(2, 3) + u.Union(4, 5) + u.Union(6, 7) + + // Testing the parent of specific elements + t.Run("Test Find", func(t *testing.T) { + if u.Find(0) != u.Find(1) || u.Find(2) != u.Find(3) || u.Find(4) != u.Find(5) || u.Find(6) != u.Find(7) { + t.Error("Union operation not functioning correctly") + } + }) + + u.Union(1, 5) // Additional union operation + u.Union(3, 7) // Additional union operation + + // Testing the parent of specific elements after more union operations + t.Run("Test Find after Union", func(t *testing.T) { + if u.Find(0) != u.Find(5) || u.Find(1) != u.Find(4) || u.Find(2) != u.Find(7) || u.Find(3) != u.Find(6) { + t.Error("Union operation not functioning correctly") + } + }) + + u.Union(3, 7) // Repeated union operation + + // Testing that repeated union operations are idempotent + t.Run("Test Find after repeated Union", func(t *testing.T) { + if u.Find(2) != u.Find(6) || u.Find(2) != u.Find(7) || u.Find(3) != u.Find(6) || u.Find(3) != u.Find(7) { + t.Error("Union operation not functioning correctly") + } + }) +} diff --git a/hashing/doc.go b/hashing/doc.go new file mode 100644 index 000000000..1e4425334 --- /dev/null +++ b/hashing/doc.go @@ -0,0 +1,2 @@ +// Package hashing containing different implementation of certain hashing +package hashing diff --git a/hashing/hashing_test.go b/hashing/hashing_test.go new file mode 100644 index 000000000..9067f8411 --- /dev/null +++ b/hashing/hashing_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package hashing diff --git a/hashing/md5/md5.go b/hashing/md5/md5.go new file mode 100644 index 000000000..5fad61ef4 --- /dev/null +++ b/hashing/md5/md5.go @@ -0,0 +1,118 @@ +// md5.go +// description: The MD5 hashing function as defined in RFC 1321. +// author: Simon Waldherr +// ref: https://datatracker.ietf.org/doc/html/rfc1321 +// see md5_test.go for testing + +package md5 + +import ( + "encoding/binary" +) + +// Constants for MD5 +var ( + s = [64]uint32{ + 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, + 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20, + 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, + 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, + } + + K = [64]uint32{ + 0xd76aa478, 0xe8c7b756, 0x242070db, 0xc1bdceee, + 0xf57c0faf, 0x4787c62a, 0xa8304613, 0xfd469501, + 0x698098d8, 0x8b44f7af, 0xffff5bb1, 0x895cd7be, + 0x6b901122, 0xfd987193, 0xa679438e, 0x49b40821, + 0xf61e2562, 0xc040b340, 0x265e5a51, 0xe9b6c7aa, + 0xd62f105d, 0x02441453, 0xd8a1e681, 0xe7d3fbc8, + 0x21e1cde6, 0xc33707d6, 0xf4d50d87, 0x455a14ed, + 0xa9e3e905, 0xfcefa3f8, 0x676f02d9, 0x8d2a4c8a, + 0xfffa3942, 0x8771f681, 0x6d9d6122, 0xfde5380c, + 0xa4beea44, 0x4bdecfa9, 0xf6bb4b60, 0xbebfbc70, + 0x289b7ec6, 0xeaa127fa, 0xd4ef3085, 0x04881d05, + 0xd9d4d039, 0xe6db99e5, 0x1fa27cf8, 0xc4ac5665, + 0xf4292244, 0x432aff97, 0xab9423a7, 0xfc93a039, + 0x655b59c3, 0x8f0ccc92, 0xffeff47d, 0x85845dd1, + 0x6fa87e4f, 0xfe2ce6e0, 0xa3014314, 0x4e0811a1, + 0xf7537e82, 0xbd3af235, 0x2ad7d2bb, 0xeb86d391, + } +) + +// leftRotate rotates x left by n bits +func leftRotate(x, n uint32) uint32 { + return (x << n) | (x >> (32 - n)) +} + +// pad pads the input message so that its length is congruent to 448 modulo 512 +func pad(message []byte) []byte { + originalLength := len(message) * 8 + message = append(message, 0x80) + for (len(message)*8)%512 != 448 { + message = append(message, 0x00) + } + + lengthBytes := make([]byte, 8) + binary.LittleEndian.PutUint64(lengthBytes, uint64(originalLength)) + message = append(message, lengthBytes...) + + return message +} + +// Hash computes the MD5 hash of the input message +func Hash(message []byte) [16]byte { + message = pad(message) + + // Initialize MD5 state variables + a0, b0, c0, d0 := uint32(0x67452301), uint32(0xefcdab89), uint32(0x98badcfe), uint32(0x10325476) + + // Process the message in successive 512-bit chunks + for i := 0; i < len(message); i += 64 { + chunk := message[i : i+64] + var M [16]uint32 + for j := 0; j < 16; j++ { + M[j] = binary.LittleEndian.Uint32(chunk[j*4 : (j+1)*4]) + } + + // Initialize hash value for this chunk + A, B, C, D := a0, b0, c0, d0 + + // Main loop + for i := 0; i < 64; i++ { + var F, g uint32 + if i < 16 { + F = (B & C) | ((^B) & D) + g = uint32(i) + } else if i < 32 { + F = (D & B) | ((^D) & C) + g = uint32((5*i + 1) % 16) + } else if i < 48 { + F = B ^ C ^ D + g = uint32((3*i + 5) % 16) + } else { + F = C ^ (B | (^D)) + g = uint32((7 * i) % 16) + } + F = F + A + K[i] + M[g] + A = D + D = C + C = B + B = B + leftRotate(F, s[i]) + } + + // Add this chunk's hash to result so far + a0 += A + b0 += B + c0 += C + d0 += D + } + + // Produce the final hash value (digest) + var digest [16]byte + binary.LittleEndian.PutUint32(digest[0:4], a0) + binary.LittleEndian.PutUint32(digest[4:8], b0) + binary.LittleEndian.PutUint32(digest[8:12], c0) + binary.LittleEndian.PutUint32(digest[12:16], d0) + + return digest +} diff --git a/hashing/md5/md5_test.go b/hashing/md5/md5_test.go new file mode 100644 index 000000000..b013c0bb3 --- /dev/null +++ b/hashing/md5/md5_test.go @@ -0,0 +1,42 @@ +// md5_test.go +// description: Tests for the MD5 hashing function as defined in RFC 1321. +// author: Simon Waldherr + +package md5 + +import ( + "encoding/hex" + "testing" +) + +// Helper function to convert hash output to hex string for comparison +func toHexString(hash [16]byte) string { + return hex.EncodeToString(hash[:]) +} + +// Test vectors for MD5 (from RFC 1321 and other known sources) +var tests = []struct { + input string + expected string +}{ + {"", "d41d8cd98f00b204e9800998ecf8427e"}, + {"a", "0cc175b9c0f1b6a831c399e269772661"}, + {"abc", "900150983cd24fb0d6963f7d28e17f72"}, + {"message digest", "f96b697d7cb7938d525a2f31aaf161d0"}, + {"abcdefghijklmnopqrstuvwxyz", "c3fcd3d76192e4007dfb496cca67e13b"}, + {"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789", "d174ab98d277d9f5a5611c2c9f419d9f"}, + {"12345678901234567890123456789012345678901234567890123456789012345678901234567890", "57edf4a22be3c955ac49da2e2107b67a"}, +} + +// TestHash verifies that the Hash function produces the correct MD5 hash values +func TestHash(t *testing.T) { + for _, tt := range tests { + t.Run(tt.input, func(t *testing.T) { + result := Hash([]byte(tt.input)) + resultHex := toHexString(result) + if resultHex != tt.expected { + t.Errorf("MD5(%q) = %s; want %s", tt.input, resultHex, tt.expected) + } + }) + } +} diff --git a/hashing/sha1/sha1.go b/hashing/sha1/sha1.go new file mode 100644 index 000000000..ba30fe615 --- /dev/null +++ b/hashing/sha1/sha1.go @@ -0,0 +1,110 @@ +// sha1.go +// description: The SHA-1 hashing function as defined in RFC 3174. +// author: Simon Waldherr +// ref: https://datatracker.ietf.org/doc/html/rfc3174 +// see sha1_test.go for testing + +package sha1 + +import ( + "encoding/binary" // Used for interacting with uint at the byte level +) + +// Constants for SHA-1 +const ( + h0 uint32 = 0x67452301 + h1 uint32 = 0xEFCDAB89 + h2 uint32 = 0x98BADCFE + h3 uint32 = 0x10325476 + h4 uint32 = 0xC3D2E1F0 +) + +// pad pads the input message so that its length is congruent to 448 modulo 512 +func pad(message []byte) []byte { + originalLength := len(message) * 8 + message = append(message, 0x80) + for (len(message)*8)%512 != 448 { + message = append(message, 0x00) + } + + lengthBytes := make([]byte, 8) + binary.BigEndian.PutUint64(lengthBytes, uint64(originalLength)) + message = append(message, lengthBytes...) + + return message +} + +// leftRotate rotates x left by n bits +func leftRotate(x, n uint32) uint32 { + return (x << n) | (x >> (32 - n)) +} + +// Hash computes the SHA-1 hash of the input message +func Hash(message []byte) [20]byte { + message = pad(message) + + // Initialize variables + a, b, c, d, e := h0, h1, h2, h3, h4 + + // Process the message in successive 512-bit chunks + for i := 0; i < len(message); i += 64 { + var w [80]uint32 + chunk := message[i : i+64] + + // Break chunk into sixteen 32-bit big-endian words + for j := 0; j < 16; j++ { + w[j] = binary.BigEndian.Uint32(chunk[j*4 : (j+1)*4]) + } + + // Extend the sixteen 32-bit words into eighty 32-bit words + for j := 16; j < 80; j++ { + w[j] = leftRotate(w[j-3]^w[j-8]^w[j-14]^w[j-16], 1) + } + + // Initialize hash value for this chunk + A, B, C, D, E := a, b, c, d, e + + // Main loop + for j := 0; j < 80; j++ { + var f, k uint32 + switch { + case j < 20: + f = (B & C) | ((^B) & D) + k = 0x5A827999 + case j < 40: + f = B ^ C ^ D + k = 0x6ED9EBA1 + case j < 60: + f = (B & C) | (B & D) | (C & D) + k = 0x8F1BBCDC + default: + f = B ^ C ^ D + k = 0xCA62C1D6 + } + + temp := leftRotate(A, 5) + f + E + k + w[j] + E = D + D = C + C = leftRotate(B, 30) + B = A + A = temp + } + + // Add this chunk's hash to result so far + a += A + b += B + c += C + d += D + e += E + } + + // Produce the final hash value (digest) + var digest [20]byte + binary.BigEndian.PutUint32(digest[0:4], a) + binary.BigEndian.PutUint32(digest[4:8], b) + binary.BigEndian.PutUint32(digest[8:12], c) + binary.BigEndian.PutUint32(digest[12:16], d) + binary.BigEndian.PutUint32(digest[16:20], e) + + return digest +} diff --git a/hashing/sha1/sha1_test.go b/hashing/sha1/sha1_test.go new file mode 100644 index 000000000..f7d1d2079 --- /dev/null +++ b/hashing/sha1/sha1_test.go @@ -0,0 +1,42 @@ +// sha1_test.go +// description: Tests for the SHA-1 hashing function as defined in RFC 3174. +// author: Simon Waldherr + +package sha1 + +import ( + "encoding/hex" + "testing" +) + +// Helper function to convert hash output to hex string for comparison +func toHexString(hash [20]byte) string { + return hex.EncodeToString(hash[:]) +} + +// Test vectors for SHA-1 (from RFC 3174 and other known sources) +var tests = []struct { + input string + expected string +}{ + {"", "da39a3ee5e6b4b0d3255bfef95601890afd80709"}, + {"a", "86f7e437faa5a7fce15d1ddcb9eaeaea377667b8"}, + {"abc", "a9993e364706816aba3e25717850c26c9cd0d89d"}, + {"message digest", "c12252ceda8be8994d5fa0290a47231c1d16aae3"}, + {"abcdefghijklmnopqrstuvwxyz", "32d10c7b8cf96570ca04ce37f2a19d84240d3a89"}, + {"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789", "761c457bf73b14d27e9e9265c46f4b4dda11f940"}, + {"1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890", "fecfd28bbc9345891a66d7c1b8ff46e60192d284"}, +} + +// TestHash verifies that the Hash function produces the correct SHA-1 hash values +func TestHash(t *testing.T) { + for _, tt := range tests { + t.Run(tt.input, func(t *testing.T) { + result := Hash([]byte(tt.input)) + resultHex := toHexString(result) + if resultHex != tt.expected { + t.Errorf("SHA-1(%q) = %s; want %s", tt.input, resultHex, tt.expected) + } + }) + } +} diff --git a/hashing/sha256/sha256.go b/hashing/sha256/sha256.go new file mode 100644 index 000000000..0dd38a557 --- /dev/null +++ b/hashing/sha256/sha256.go @@ -0,0 +1,114 @@ +// sha256.go +// description: The sha256 cryptographic hash function as defined in the RFC6234 standard. +// time complexity: O(n) +// space complexity: O(n) +// author: [Paul Leydier] (https://github.com/paul-leydier) +// ref: https://datatracker.ietf.org/doc/html/rfc6234 +// ref: https://en.wikipedia.org/wiki/SHA-2 +// see sha256_test.go + +package sha256 + +import ( + "encoding/binary" // Used for interacting with uint at the byte level + "math/bits" // Used for bits rotation operations +) + +var K = [64]uint32{ + 0x428a2f98, 0x71374491, 0xb5c0fbcf, 0xe9b5dba5, 0x3956c25b, 0x59f111f1, 0x923f82a4, 0xab1c5ed5, + 0xd807aa98, 0x12835b01, 0x243185be, 0x550c7dc3, 0x72be5d74, 0x80deb1fe, 0x9bdc06a7, 0xc19bf174, + 0xe49b69c1, 0xefbe4786, 0x0fc19dc6, 0x240ca1cc, 0x2de92c6f, 0x4a7484aa, 0x5cb0a9dc, 0x76f988da, + 0x983e5152, 0xa831c66d, 0xb00327c8, 0xbf597fc7, 0xc6e00bf3, 0xd5a79147, 0x06ca6351, 0x14292967, + 0x27b70a85, 0x2e1b2138, 0x4d2c6dfc, 0x53380d13, 0x650a7354, 0x766a0abb, 0x81c2c92e, 0x92722c85, + 0xa2bfe8a1, 0xa81a664b, 0xc24b8b70, 0xc76c51a3, 0xd192e819, 0xd6990624, 0xf40e3585, 0x106aa070, + 0x19a4c116, 0x1e376c08, 0x2748774c, 0x34b0bcb5, 0x391c0cb3, 0x4ed8aa4a, 0x5b9cca4f, 0x682e6ff3, + 0x748f82ee, 0x78a5636f, 0x84c87814, 0x8cc70208, 0x90befffa, 0xa4506ceb, 0xbef9a3f7, 0xc67178f2, +} + +const chunkSize = 64 + +// pad returns a padded version of the input message, such as the padded message's length is a multiple +// of 512 bits. +// The padding methodology is as follows: +// A "1" bit is appended at the end of the input message, followed by m "0" bits such as the length is +// 64 bits short of a 512 bits multiple. The remaining 64 bits are filled with the initial length of the +// message, represented as a 64-bits unsigned integer. +// For more details, see: https://datatracker.ietf.org/doc/html/rfc6234#section-4.1 +func pad(message []byte) []byte { + L := make([]byte, 8) + binary.BigEndian.PutUint64(L, uint64(len(message)*8)) + message = append(message, 0x80) // "1" bit followed by 7 "0" bits + for (len(message)+8)%64 != 0 { + message = append(message, 0x00) // 8 "0" bits + } + message = append(message, L...) + + return message +} + +// Hash hashes the input message using the sha256 hashing function, and return a 32 byte array. +// The implementation follows the RGC6234 standard, which is documented +// at https://datatracker.ietf.org/doc/html/rfc6234 +func Hash(message []byte) [32]byte { + message = pad(message) + + // Initialize round constants + h0, h1, h2, h3, h4, h5, h6, h7 := uint32(0x6a09e667), uint32(0xbb67ae85), uint32(0x3c6ef372), uint32(0xa54ff53a), + uint32(0x510e527f), uint32(0x9b05688c), uint32(0x1f83d9ab), uint32(0x5be0cd19) + + // Iterate through 512-bit chunks + for chunkStart := 0; chunkStart < len(message); chunkStart += chunkSize { + // Message schedule + var w [64]uint32 + for i := 0; i*4 < chunkSize; i++ { + w[i] = binary.BigEndian.Uint32(message[chunkStart+i*4 : chunkStart+(i+1)*4]) + } + + // Extend the 16 bytes chunk to the whole 64 bytes message schedule + for i := 16; i < 64; i++ { + s0 := bits.RotateLeft32(w[i-15], -7) ^ bits.RotateLeft32(w[i-15], -18) ^ (w[i-15] >> 3) + s1 := bits.RotateLeft32(w[i-2], -17) ^ bits.RotateLeft32(w[i-2], -19) ^ (w[i-2] >> 10) + w[i] = w[i-16] + s0 + w[i-7] + s1 + } + + // Actual hashing loop + a, b, c, d, e, f, g, h := h0, h1, h2, h3, h4, h5, h6, h7 + for i := 0; i < 64; i++ { + S1 := bits.RotateLeft32(e, -6) ^ bits.RotateLeft32(e, -11) ^ bits.RotateLeft32(e, -25) + ch := (e & f) ^ ((^e) & g) + tmp1 := h + S1 + ch + K[i] + w[i] + S0 := bits.RotateLeft32(a, -2) ^ bits.RotateLeft32(a, -13) ^ bits.RotateLeft32(a, -22) + maj := (a & b) ^ (a & c) ^ (b & c) + tmp2 := S0 + maj + h = g + g = f + f = e + e = d + tmp1 + d = c + c = b + b = a + a = tmp1 + tmp2 + } + h0 += a + h1 += b + h2 += c + h3 += d + h4 += e + h5 += f + h6 += g + h7 += h + } + + // Export digest + digest := [32]byte{} + binary.BigEndian.PutUint32(digest[:4], h0) + binary.BigEndian.PutUint32(digest[4:8], h1) + binary.BigEndian.PutUint32(digest[8:12], h2) + binary.BigEndian.PutUint32(digest[12:16], h3) + binary.BigEndian.PutUint32(digest[16:20], h4) + binary.BigEndian.PutUint32(digest[20:24], h5) + binary.BigEndian.PutUint32(digest[24:28], h6) + binary.BigEndian.PutUint32(digest[28:], h7) + + return digest +} diff --git a/hashing/sha256/sha256_test.go b/hashing/sha256/sha256_test.go new file mode 100644 index 000000000..7e87a71ef --- /dev/null +++ b/hashing/sha256/sha256_test.go @@ -0,0 +1,48 @@ +package sha256 + +import ( + "encoding/hex" + "testing" +) + +func TestHash(t *testing.T) { + testCases := []struct { + in string + expected string + }{ + {"hello world", "b94d27b9934d3e08a52e52d7da7dabfac484efe37a5380ee9088f7ace2efcde9"}, + {"", "e3b0c44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855"}, + {"a", "ca978112ca1bbdcafac231b39a23dc4da786eff8147c4e72b9807785afee48bb"}, + {"The quick brown fox jumps over the lazy dog", "d7a8fbb307d7809469ca9abcb0082e4f8d5651e46d3cdb762d02d0bf37c9e592"}, + {"The quick brown fox jumps over the lazy dog.", "ef537f25c895bfa782526529a9b63d97aa631564d5d789c2b765448c8635fb6c"}, + {"Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.", "2d8c2f6d978ca21712b5f6de36c9d31fa8e96a4fa5d8ff8b0188dfb9e7c171bb"}, + } + for _, tc := range testCases { + res := Hash([]byte(tc.in)) + result := hex.EncodeToString(res[:]) + if result != tc.expected { + t.Fatalf("Hash(%s) = %s, expected %s", tc.in, result, tc.expected) + } + } +} + +func BenchmarkHash(b *testing.B) { + testCases := []struct { + name string + in string + }{ + {"hello world", "hello world"}, + {"empty", ""}, + {"a", "a"}, + {"The quick brown fox jumps over the lazy dog", "The quick brown fox jumps over the lazy dog"}, + {"The quick brown fox jumps over the lazy dog.", "The quick brown fox jumps over the lazy dog."}, + {"Lorem ipsum", "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum."}, + } + for _, testCase := range testCases { + b.Run(testCase.name, func(b *testing.B) { + for i := 0; i < b.N; i++ { + Hash([]byte(testCase.in)) + } + }) + } +} diff --git a/math/abs.go b/math/abs.go new file mode 100644 index 000000000..7d0b3e6ac --- /dev/null +++ b/math/abs.go @@ -0,0 +1,16 @@ +// abs.go +// description: Absolute value +// details: +// In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. [Absolute value](https://en.wikipedia.org/wiki/Average#Arithmetic_mean) +// author(s) [red_byte](https://github.com/i-redbyte) +// see abs_test.go + +package math + +// Abs returns absolute value +func Abs(n int) int { + if n < 0 { + return -n + } + return n +} diff --git a/math/abs_test.go b/math/abs_test.go new file mode 100644 index 000000000..cd166f91d --- /dev/null +++ b/math/abs_test.go @@ -0,0 +1,61 @@ +package math + +import ( + "github.com/TheAlgorithms/Go/math/binary" + "math" + "testing" +) + +func TestAbs(t *testing.T) { + tests := getTests() + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := Abs(test.n); got != test.want { + t.Errorf("Abs() = %v, want %v", got, test.want) + } + }) + } +} + +func getTests() []struct { + name string + n int + want int +} { + tests := []struct { + name string + n int + want int + }{ + {"-1 = |1| ", -1, 1}, + {"-255 = |255| ", -255, 255}, + {"0 = |0| ", 0, 0}, + {"5 = |5| ", 5, 5}, + {"-5 = |5| ", -5, 5}, + {"-98368972 = |98368972| ", -98368972, 98368972}, + } + return tests +} + +func BenchmarkSimpleAbs(b *testing.B) { + for i := 0; i < b.N; i++ { + Abs(-1024) + } +} +func BenchmarkBinaryAbs32(b *testing.B) { + for i := 0; i < b.N; i++ { + binary.Abs(32, -1024) + } +} + +func BenchmarkBinaryAbs64(b *testing.B) { + for i := 0; i < b.N; i++ { + binary.Abs(64, -1024) + } +} + +func BenchmarkStdLibAbs(b *testing.B) { + for i := 0; i < b.N; i++ { + math.Abs(-1024) + } +} diff --git a/math/aliquot_test.go b/math/aliquot_test.go new file mode 100644 index 000000000..efeda425c --- /dev/null +++ b/math/aliquot_test.go @@ -0,0 +1,40 @@ +// aliquotsum_test.go +// description: Returns s(n) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see aliquotsum.go + +package math_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math" +) + +func TestAliquotSum(t *testing.T) { + var tests = []struct { + name string + n int + expectedValue int + expectedError error + }{ + {"n = 10", 10, 8, nil}, + {"n = 11", 11, 1, nil}, + {"n = 1", 1, 0, nil}, + {"n = -1", -1, 0, math.ErrPosArgsOnly}, + {"n = 0", 0, 0, math.ErrNonZeroArgsOnly}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + result, err := math.AliquotSum(test.n) + if result != test.expectedValue || test.expectedError != err { + t.Errorf("expected error: %s, got: %s; expected value: %v, got: %v", test.expectedError, err, test.expectedValue, result) + } + }) + } +} +func BenchmarkAliquotSum(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = math.AliquotSum(65536) + } +} diff --git a/math/aliquotsum.go b/math/aliquotsum.go new file mode 100644 index 000000000..cc6bd326a --- /dev/null +++ b/math/aliquotsum.go @@ -0,0 +1,31 @@ +// aliquotsum.go +// description: Returns s(n) +// details: +// the aliquot sum s(n) of a positive integer n +// is the sum of all proper divisors of n, +// that is, all divisors of n other than n itself +// wikipedia: https://en.wikipedia.org/wiki/Aliquot_sum +// time complexity: O(n) +// space complexity: O(1) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see aliquotsum_test.go + +package math + +// This function returns s(n) for given number +func AliquotSum(n int) (int, error) { + switch { + case n < 0: + return 0, ErrPosArgsOnly + case n == 0: + return 0, ErrNonZeroArgsOnly + default: + var sum int + for i := 1; i <= n/2; i++ { + if n%i == 0 { + sum += i + } + } + return sum, nil + } +} diff --git a/math/armstrong/isarmstrong.go b/math/armstrong/isarmstrong.go new file mode 100644 index 000000000..851b9612a --- /dev/null +++ b/math/armstrong/isarmstrong.go @@ -0,0 +1,34 @@ +// isarmstrong.go +// description: Checks if the given number is armstrong number or not +// details: An Armstrong number is a n-digit number that is equal to the sum of each of its digits taken to the nth power. +// time complexity: O(log(n)) +// space complexity: O(1) +// ref: https://mathlair.allfunandgames.ca/armstrong.php +// author: Kavitha J + +package armstrong + +import ( + "math" + "strconv" +) + +func IsArmstrong(number int) bool { + var rightMost int + var sum int = 0 + var tempNum int = number + + // to get the number of digits in the number + length := float64(len(strconv.Itoa(number))) + + // get the right most digit and break the loop once all digits are iterated + for tempNum > 0 { + rightMost = tempNum % 10 + sum += int(math.Pow(float64(rightMost), length)) + + // update the input digit minus the processed rightMost + tempNum /= 10 + } + + return number == sum +} diff --git a/math/armstrong/isarmstrong_test.go b/math/armstrong/isarmstrong_test.go new file mode 100644 index 000000000..bab9601c8 --- /dev/null +++ b/math/armstrong/isarmstrong_test.go @@ -0,0 +1,53 @@ +// isarmstrong_test.go + +package armstrong + +import "testing" + +var testCases = []struct { + name string // test description + input int // user input + expected bool // expected return +}{ + { + "negative number: Not an armstrong number", + -140, + false, + }, + { + "positive number: Not an armstrong number", + 23, + false, + }, + { + "smallest armstrong number", + 0, + true, + }, + { + "smallest armstrong number with more than one digit", + 153, + true, + }, + { + "random armstrong number", + 407, + true, + }, + { + "random armstrong number", + 9474, + true, + }, +} + +func TestIsArmstrong(t *testing.T) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + funcResult := IsArmstrong(test.input) + if test.expected != funcResult { + t.Errorf("Expected answer '%t' for the number '%d' but answer given was %t", test.expected, test.input, funcResult) + } + }) + } +} diff --git a/math/binary/abs.go b/math/binary/abs.go new file mode 100644 index 000000000..5c95fa5e8 --- /dev/null +++ b/math/binary/abs.go @@ -0,0 +1,18 @@ +// abs.go +// description: returns absolute value using binary operation +// time complexity: O(1) +// space complexity: O(1) + +package binary + +// Abs returns absolute value using binary operation +// Principle of operation: +// 1) Get the mask by right shift by the base +// 2) Base is the size of an integer variable in bits, for example, for int32 it will be 32, for int64 it will be 64 +// 3) For negative numbers, above step sets mask as 1 1 1 1 1 1 1 1 and 0 0 0 0 0 0 0 0 for positive numbers. +// 4) Add the mask to the given number. +// 5) XOR of mask + n and mask gives the absolute value. +func Abs(base, n int) int { + m := n >> (base - 1) + return (n + m) ^ m +} diff --git a/math/binary/abs_test.go b/math/binary/abs_test.go new file mode 100644 index 000000000..20500ec5a --- /dev/null +++ b/math/binary/abs_test.go @@ -0,0 +1,37 @@ +package binary + +import "testing" + +func TestAbs(t *testing.T) { + tests := getAbsTests() + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := Abs(test.base, test.n); got != test.want { + t.Errorf("Abs() = %v, want %v", got, test.want) + } + }) + } +} + +func getAbsTests() []struct { + name string + base int + n int + want int +} { + tests := []struct { + name string + base int + n int + want int + }{ + {"-1 = |1| ", 32, -1, 1}, + {"-255 = |255| ", 32, -255, 255}, + {"0 = |0| ", 64, 0, 0}, + {"5 = |5| ", 16, 5, 5}, + {"-5 = |5| ", 32, -5, 5}, + {"-98368972 = |98368972| ", 64, -98368972, 98368972}, + {"-110298368972 = |110298368972| ", 64, -98368972, 98368972}, + } + return tests +} diff --git a/math/binary/arithmeticmean.go b/math/binary/arithmeticmean.go new file mode 100644 index 000000000..f7812b6be --- /dev/null +++ b/math/binary/arithmeticmean.go @@ -0,0 +1,21 @@ +// arithmeticmean.go +// description: Arithmetic mean +// details: +// The most common type of average is the arithmetic mean. If n numbers are given, each number denoted by ai (where i = 1,2, ..., n), the arithmetic mean is the sum of the as divided by n or - [Arithmetic mean](https://en.wikipedia.org/wiki/Average#Arithmetic_mean) +// time complexity: O(1) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see arithmeticmean_test.go + +// Package binary describes algorithms that use binary operations for different calculations. +package binary + +// MeanUsingAndXor This function finds arithmetic mean using "AND" and "XOR" operations +func MeanUsingAndXor(a int, b int) int { + return ((a ^ b) >> 1) + (a & b) +} + +// MeanUsingRightShift This function finds arithmetic mean using right shift +func MeanUsingRightShift(a int, b int) int { + return (a + b) >> 1 +} diff --git a/math/binary/arithmeticmean_test.go b/math/binary/arithmeticmean_test.go new file mode 100644 index 000000000..fe030e859 --- /dev/null +++ b/math/binary/arithmeticmean_test.go @@ -0,0 +1,65 @@ +// arithmeticmean_test.go +// description: Test for Arithmetic mean +// author(s) [red_byte](https://github.com/i-redbyte) +// see arithmeticmean.go + +package binary + +import "testing" + +func TestMeanUsingAndXor(t *testing.T) { + tests := getTests() + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := MeanUsingAndXor(tv.a, tv.b) + if result != tv.result { + t.Errorf("Wrong result! Expected:%d, returned:%d ", tv.result, result) + } + }) + } + +} + +func TestMeanUsingRightShift(t *testing.T) { + tests := getTests() + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := MeanUsingRightShift(tv.a, tv.b) + if result != tv.result { + t.Errorf("Wrong result! Expected:%d, returned:%d ", tv.result, result) + } + }) + } + +} +func getTests() []struct { + name string + a int + b int + result int +} { + var tests = []struct { + name string + a int + b int + result int + }{ + {"Average of 2 and 4", 2, 4, 3}, + {"Average of 5 and 5", 5, 5, 5}, + {"Average of 1000 and 1002", 1000, 1002, 1001}, + {"Average of 80 and 40", 80, 40, 60}, + {"Average of 7 and 4", 7, 4, 5}, + } + return tests +} +func BenchmarkMeanUsingAndXor(b *testing.B) { + for i := 0; i < b.N; i++ { + MeanUsingAndXor(222, 888) + } +} + +func BenchmarkMeanUsingRightShift(b *testing.B) { + for i := 0; i < b.N; i++ { + MeanUsingRightShift(222, 888) + } +} diff --git a/math/binary/bitcounter.go b/math/binary/bitcounter.go new file mode 100644 index 000000000..baf8dcd7b --- /dev/null +++ b/math/binary/bitcounter.go @@ -0,0 +1,22 @@ +// bitcounter.go +// description: Counts the number of set bits in a number +// details: +// For unsigned integer number N, return the number of bits set to 1 - [Bit numbering](https://en.wikipedia.org/wiki/Bit_numbering) +// time complexity: O(log(n)) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see bitcounter_test.go + +package binary + +// BitCounter - The function returns the number of set bits for an unsigned integer number +func BitCounter(n uint) int { + counter := 0 + for n != 0 { + if n&1 == 1 { + counter++ + } + n >>= 1 + } + return counter +} diff --git a/math/binary/bitcounter_test.go b/math/binary/bitcounter_test.go new file mode 100644 index 000000000..f5d61ec3f --- /dev/null +++ b/math/binary/bitcounter_test.go @@ -0,0 +1,33 @@ +// bitcounter_test.go +// description: Test for counts the number of set bits in a number +// author(s) [red_byte](https://github.com/i-redbyte) +// see bitcounter.go + +package binary + +import "testing" + +func TestBitCounter(t *testing.T) { + tests := []struct { + name string + number uint + want int + }{ + {"Number of bits in a number 0", 0, 0}, + {"Number of bits in a number 1", 1, 1}, + {"Number of bits in a number 255", 255, 8}, + {"Number of bits in a number 7", 7, 3}, + {"Number of bits in a number 8", 8, 1}, + {"Number of bits in a number 9223372036854775807", 9223372036854775807, 63}, + {"Number of bits in a number 2147483647", 2147483647, 31}, + {"Number of bits in a number 15", 15, 4}, + {"Number of bits in a number 16", 16, 1}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := BitCounter(test.number); got != test.want { + t.Errorf("BitCounter() = %v, want %v", got, test.want) + } + }) + } +} diff --git a/math/binary/checkisnumberpoweroftwo.go b/math/binary/checkisnumberpoweroftwo.go new file mode 100644 index 000000000..d836396f5 --- /dev/null +++ b/math/binary/checkisnumberpoweroftwo.go @@ -0,0 +1,37 @@ +// checkisnumberpoweroftwo.go +// description: Is the number a power of two +// details: +// Checks if a number is a power of two- [Power of two](https://en.wikipedia.org/wiki/Power_of_two) +// time complexity: O(1) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see checkisnumberpoweroftwo_test.go + +package binary + +// IsPowerOfTwo This function uses the fact that powers of 2 are represented +// like 10...0 in binary, and numbers one less than the power of 2 +// are represented like 11...1. +// Therefore, using the and function: +// +// 10...0 +// & 01...1 +// 00...0 -> 0 +// +// This is also true for 0, which is not a power of 2, for which we +// have to add and extra condition. +func IsPowerOfTwo(x int) bool { + return x > 0 && (x&(x-1)) == 0 +} + +// IsPowerOfTwoLeftShift This function takes advantage of the fact that left shifting a number +// by 1 is equivalent to multiplying by 2. For example, binary 00000001 when shifted by 3 becomes 00001000, +// which in decimal system is 8 or = 2 * 2 * 2 +func IsPowerOfTwoLeftShift(number uint) bool { + for p := uint(1); p <= number; p = p << 1 { + if number == p { + return true + } + } + return false +} diff --git a/math/binary/checkisnumberpoweroftwo_test.go b/math/binary/checkisnumberpoweroftwo_test.go new file mode 100644 index 000000000..83c0b0083 --- /dev/null +++ b/math/binary/checkisnumberpoweroftwo_test.go @@ -0,0 +1,93 @@ +// checkisnumberpoweroftwo_test.go +// description: Test for Is the number a power of two +// author(s) [red_byte](https://github.com/i-redbyte) +// see checkisnumberpoweroftwo.go + +package binary + +import ( + math2 "github.com/TheAlgorithms/Go/math" + "math" + "testing" +) + +func getTestsForPowerOfTwo() []struct { + name string + a int + missing bool +} { + var tests = []struct { + name string + a int + missing bool + }{ + {"Is 64 a power of 2? - YES", 64, true}, + {"Is 1 a power of 2? - YES", 1, true}, + {"Is 2 a power of 2? - YES", 2, true}, + {"Is 5 a power of 2? - NO", 5, false}, + {"Is 1023 a power of 2? - NO", 1023, false}, + {"Is 1024 a power of 2? - YES", 1024, true}, + {"Is 0 a power of 2? - NO", 0, false}, + {"Is 9223372036854775807 a power of 2? - NO", math.MaxInt64, false}, + {"Is 9223372036854775806 a power of 2? - NO", math.MaxInt64, false}, + {"Is 4611686018427387904 a power of 2? - YES", 4611686018427387904, true}, + } + return tests +} + +func TestIsPowerOfTwo(t *testing.T) { + tests := getTestsForPowerOfTwo() + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := IsPowerOfTwo(tv.a) + t.Log(tv.a, " ", result) + if result != tv.missing { + t.Errorf("Wrong result! Expected:%v, returned:%v ", tv.missing, result) + } + }) + } +} + +func TestIsPowerOfTwoLeftShift(t *testing.T) { + tests := getTestsForPowerOfTwo() + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := IsPowerOfTwoLeftShift(uint(tv.a)) + t.Log(tv.a, " ", result) + if result != tv.missing { + t.Errorf("Wrong result! Expected:%v, returned:%v ", tv.missing, result) + } + }) + } +} + +func TestIsPowOfTwoUseLog(t *testing.T) { + tests := getTestsForPowerOfTwo() + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := math2.IsPowOfTwoUseLog(float64(tv.a)) + t.Log(tv.a, " ", result) + if result != tv.missing { + t.Errorf("Wrong result! Expected:%v, returned:%v ", tv.missing, result) + } + }) + } +} + +func BenchmarkIsPowerOfTwoBinaryMethod(b *testing.B) { + for i := 0; i < b.N; i++ { + IsPowerOfTwo(1024) + } +} + +func BenchmarkIsPowerOfTwoUseCycleAndLeftShift(b *testing.B) { + for i := 0; i < b.N; i++ { + IsPowerOfTwoLeftShift(1024) + } +} + +func BenchmarkIsPowerOfTwoUseLog(b *testing.B) { + for i := 0; i < b.N; i++ { + math2.IsPowOfTwoUseLog(1024) + } +} diff --git a/math/binary/fast_inverse_sqrt.go b/math/binary/fast_inverse_sqrt.go new file mode 100644 index 000000000..c8689b451 --- /dev/null +++ b/math/binary/fast_inverse_sqrt.go @@ -0,0 +1,31 @@ +// Calculating the inverse square root +// time complexity: O(1) +// space complexity: O(1) +// [See more](https://en.wikipedia.org/wiki/Fast_inverse_square_root) + +package binary + +import ( + "math" +) + +// FastInverseSqrt assumes that argument is always positive, +// and it does not deal with negative numbers. +// The "magic" number 0x5f3759df is hex for 1597463007 in decimals. +// The math.Float32bits is alias to *(*uint32)(unsafe.Pointer(&f)) +// and math.Float32frombits is to *(*float32)(unsafe.Pointer(&b)). +func FastInverseSqrt(number float32) float32 { + var i uint32 + var y, x2 float32 + const threehalfs float32 = 1.5 + + x2 = number * float32(0.5) + y = number + i = math.Float32bits(y) // evil floating point bit level hacking + i = 0x5f3759df - (i >> 1) // magic number and bitshift hacking + y = math.Float32frombits(i) + + y = y * (threehalfs - (x2 * y * y)) // 1st iteration of Newton's method + y = y * (threehalfs - (x2 * y * y)) // 2nd iteration, this can be removed + return y +} diff --git a/math/binary/logarithm.go b/math/binary/logarithm.go new file mode 100644 index 000000000..3d73ac428 --- /dev/null +++ b/math/binary/logarithm.go @@ -0,0 +1,20 @@ +// author(s) [red_byte](https://github.com/i-redbyte) +// time complexity: O(1) +// space complexity: O(1) +// see logarithm_test.go + +package binary + +// LogBase2 Finding the exponent of n = 2**x using bitwise operations (logarithm in base 2 of n) [See more](https://en.wikipedia.org/wiki/Logarithm) +func LogBase2(n uint32) uint32 { + base := [5]uint32{0x2, 0xC, 0xF0, 0xFF00, 0xFFFF0000} + exponents := [5]uint32{1, 2, 4, 8, 16} + var result uint32 + for i := 4; i >= 0; i-- { + if n&base[i] != 0 { + n >>= exponents[i] + result |= exponents[i] + } + } + return result +} diff --git a/math/binary/logarithm_test.go b/math/binary/logarithm_test.go new file mode 100644 index 000000000..8aaaabe72 --- /dev/null +++ b/math/binary/logarithm_test.go @@ -0,0 +1,48 @@ +// logarithm_test.go +// description: Test for finding the exponent of n = 2**x using bitwise operations (logarithm in base 2 of n) +// author(s) [red_byte](https://github.com/i-redbyte) +// see logarithm.go + +package binary + +import ( + "math" + "testing" +) + +func TestLogBase2(t *testing.T) { + tests := []struct { + name string + n uint32 + want uint32 + }{ + {"log2(1) = 0", 1, 0}, + {"log2(2) = 1", 2, 1}, + {"log2(4) = 2", 4, 2}, + {"log2(8) = 3", 8, 3}, + {"log2(16) = 4", 16, 4}, + {"log2(32) = 5", 32, 5}, + {"log2(64) = 6", 64, 6}, + {"log2(128) = 7", 128, 7}, + {"log2(256) = 8", 256, 8}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := LogBase2(test.n); got != test.want { + t.Errorf("LogBase2() = %v, want %v", got, test.want) + } + }) + } +} + +func BenchmarkBitwiseLogBase2(b *testing.B) { + for i := 0; i < b.N; i++ { + LogBase2(1024) + } +} + +func BenchmarkMathPAckageLogBase2(b *testing.B) { + for i := 0; i < b.N; i++ { + math.Log2(1024) + } +} diff --git a/math/binary/rbc.go b/math/binary/rbc.go new file mode 100644 index 000000000..b6ef45f68 --- /dev/null +++ b/math/binary/rbc.go @@ -0,0 +1,20 @@ +// rbc.go +// description: Reflected binary code (RBC) +// details: +// The reflected binary code (RBC), also known just as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). - [RBC](https://en.wikipedia.org/wiki/Gray_code) +// time complexity: O(n) +// space complexity: O(n) +// author(s) [red_byte](https://github.com/i-redbyte) +// see rbc_test.go + +package binary + +// SequenceGrayCode The function generates an "Gray code" sequence of length n +func SequenceGrayCode(n uint) []uint { + result := make([]uint, 0) + var i uint + for i = 0; i < 1<>1)) + } + return result +} diff --git a/math/binary/rbc_test.go b/math/binary/rbc_test.go new file mode 100644 index 000000000..60b6ff448 --- /dev/null +++ b/math/binary/rbc_test.go @@ -0,0 +1,37 @@ +// rbc_test.go +// description: Test for Reflected binary code +// author(s) [red_byte](https://github.com/i-redbyte) +// see rbc.go + +package binary + +import ( + "reflect" + "testing" +) + +func TestSequenceGrayCode(t *testing.T) { + tests := []struct { + name string + n uint + want []uint + }{ + {"Sequence of values for 1", 1, []uint{0, 1}}, + {"Sequence of values for 2", 2, []uint{0, 1, 3, 2}}, + {"Sequence of values for 6", 6, []uint{0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32}}, + {"Sequence of values for 8", 8, []uint{0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, 11, 9, 8, 24, 25, 27, 26, 30, 31, 29, 28, 20, 21, 23, 22, 18, 19, 17, 16, 48, 49, 51, 50, 54, 55, 53, 52, 60, 61, 63, 62, 58, 59, 57, 56, 40, 41, 43, 42, 46, 47, 45, 44, 36, 37, 39, 38, 34, 35, 33, 32, 96, 97, 99, 98, 102, 103, 101, 100, 108, 109, 111, 110, 106, 107, 105, 104, 120, 121, 123, 122, 126, 127, 125, 124, 116, 117, 119, 118, 114, 115, 113, 112, 80, 81, 83, 82, 86, 87, 85, 84, 92, 93, 95, 94, 90, 91, 89, 88, 72, 73, 75, 74, 78, 79, 77, 76, 68, 69, 71, 70, 66, 67, 65, 64, 192, 193, 195, 194, 198, 199, 197, 196, 204, 205, 207, 206, 202, 203, 201, 200, 216, 217, 219, 218, 222, 223, 221, 220, 212, 213, 215, 214, 210, 211, 209, 208, 240, 241, 243, 242, 246, 247, 245, 244, 252, 253, 255, 254, 250, 251, 249, 248, 232, 233, 235, 234, 238, 239, 237, 236, 228, 229, 231, 230, 226, 227, 225, 224, 160, 161, 163, 162, 166, 167, 165, 164, 172, 173, 175, 174, 170, 171, 169, 168, 184, 185, 187, 186, 190, 191, 189, 188, 180, 181, 183, 182, 178, 179, 177, 176, 144, 145, 147, 146, 150, 151, 149, 148, 156, 157, 159, 158, 154, 155, 153, 152, 136, 137, 139, 138, 142, 143, 141, 140, 132, 133, 135, 134, 130, 131, 129, 128}}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := SequenceGrayCode(test.n); !reflect.DeepEqual(got, test.want) { + t.Errorf("SequenceGrayCode() = %v, want %v", got, test.want) + } + }) + } +} + +func BenchmarkSequenceGrayCode(b *testing.B) { + for i := 0; i < b.N; i++ { + SequenceGrayCode(6) + } +} diff --git a/math/binary/reversebits.go b/math/binary/reversebits.go new file mode 100644 index 000000000..751fbcfd5 --- /dev/null +++ b/math/binary/reversebits.go @@ -0,0 +1,25 @@ +// reversebits.go +// description: Reverse bits +// details: +// Reverse the bits of an integer number +// time complexity: O(log(n)) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see reversebits_test.go + +package binary + +// ReverseBits This function initialized the result by 0 (all bits 0) and process the given number starting +// from its least significant bit. If the current bit is 1, set the corresponding most significant bit in the result +// and finally move on to the next bit in the input number. +// Repeat this till all its bits are processed. +func ReverseBits(number uint) uint { + result := uint(0) + intSize := 31 + for number != 0 { + result += (number & 1) << intSize + number = number >> 1 + intSize -= 1 + } + return result +} diff --git a/math/binary/reversebits_test.go b/math/binary/reversebits_test.go new file mode 100644 index 000000000..c53d3600a --- /dev/null +++ b/math/binary/reversebits_test.go @@ -0,0 +1,37 @@ +// reversebits_test.go +// description: Reverse bits +// author(s) [red_byte](https://github.com/i-redbyte) +// see reversebits.go + +package binary + +import "testing" + +func TestReverseBits(t *testing.T) { + var tests = []struct { + name string + number uint + result uint + }{ + {"43261596 (00000010100101000001111010011100) to 964176192 (00111001011110000010100101000000)", 43261596, 964176192}, + {"3758096384 (11100000000000000000000000000000) to 7 (00000000000000000000000000000111)", 3758096384, 7}, + {"7 (00000000000000000000000000000111) to 3758096384 (11100000000000000000000000000000)", 7, 3758096384}, + {"2684354560 (10100000000000000000000000000000) to 5 (00000000000000000000000000000101)", 2684354560, 5}, + {"2684354561 (10100000000000000000000000000001) to 5 (10000000000000000000000000000101)", 2684354561, 2147483653}, + } + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := ReverseBits(tv.number) + t.Log(result) + if result != tv.result { + t.Errorf("Wrong result! Expected:%d, returned:%d ", tv.result, result) + } + }) + } +} + +func BenchmarkReverseBits(b *testing.B) { + for i := 0; i < b.N; i++ { + ReverseBits(2684354560) + } +} diff --git a/math/binary/sqrt.go b/math/binary/sqrt.go new file mode 100644 index 000000000..8c967bf91 --- /dev/null +++ b/math/binary/sqrt.go @@ -0,0 +1,12 @@ +// sqrt.go +// description: Square root calculation +// details: +// Calculating the square root using binary operations and a magic number 0x5f3759df [See more](https://en.wikipedia.org/wiki/Fast_inverse_square_root) +// author(s) [red_byte](https://github.com/i-redbyte) +// time complexity: O(1) +// space complexity: O(1) +// see sqrt_test.go + +package binary + +func Sqrt(n float32) float32 { return 1 / FastInverseSqrt(n) } diff --git a/math/binary/sqrt_test.go b/math/binary/sqrt_test.go new file mode 100644 index 000000000..fe31aefac --- /dev/null +++ b/math/binary/sqrt_test.go @@ -0,0 +1,50 @@ +// sqrt_test.go +// description: Test for square root calculation +// author(s) [red_byte](https://github.com/i-redbyte) +// see sqrt.go + +package binary + +import ( + "math" + "testing" +) + +const epsilon = 0.001 + +func TestSquareRootCalculation(t *testing.T) { + tests := []struct { + name string + number float32 + want float64 + }{ + {"sqrt(1)", 1, 1}, + {"sqrt(9)", 9, 3}, + {"sqrt(25)", 25, 5}, + {"sqrt(121)", 121, 11}, + {"sqrt(10000)", 10000, 100}, + {"sqrt(169)", 169, 13}, + {"sqrt(0)", 0, 0}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + got := Sqrt(test.number) + delta := math.Abs(test.want - float64(got)) + if delta > epsilon { + t.Errorf("Sqrt() = %v, want %v delta %v", got, test.want, delta) + } + }) + } +} + +func BenchmarkSquareRootCalculation(b *testing.B) { + for i := 0; i < b.N; i++ { + Sqrt(225) + } +} + +func BenchmarkMathSqrt(b *testing.B) { + for i := 0; i < b.N; i++ { + math.Sqrt(225) + } +} diff --git a/math/binary/xorsearch.go b/math/binary/xorsearch.go new file mode 100644 index 000000000..9e914da83 --- /dev/null +++ b/math/binary/xorsearch.go @@ -0,0 +1,20 @@ +// xorsearch.go +// description: Find a missing number in a sequence +// details: +// Given an array A containing n distinct numbers in the range [0, n], return the only number in the range that is missing from the array. - [xor](https://en.wikipedia.org/wiki/Exclusive_or) +// time complexity: O(n) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see xorsearch_test.go + +package binary + +// XorSearchMissingNumber This function finds a missing number in a sequence +func XorSearchMissingNumber(a []int) int { + n := len(a) + result := len(a) + for i := 0; i < n; i++ { + result ^= i ^ a[i] + } + return result +} diff --git a/math/binary/xorsearch_test.go b/math/binary/xorsearch_test.go new file mode 100644 index 000000000..2168a49f6 --- /dev/null +++ b/math/binary/xorsearch_test.go @@ -0,0 +1,39 @@ +// xorsearch_test.go +// description: Test for Find a missing number in a sequence +// author(s) [red_byte](https://github.com/i-redbyte) +// see xorsearch.go + +package binary + +import ( + "testing" +) + +func TestXorSearchMissingNumber(t *testing.T) { + var tests = []struct { + name string + a []int + missing int + }{ + {"[3, 0, 1]/2", []int{3, 0, 1}, 2}, + {"[0, 1, 3, 4, 5, 6, 7]/2", []int{0, 1, 3, 4, 5, 6, 7}, 2}, + {"[0, 2, 3, 4, 5, 6, 7, 8, 9]/1", []int{0, 2, 3, 4, 5, 6, 7, 8, 9}, 1}, + {"[0, 10, 9, 7, 2, 1, 4, 3, 5, 6]/8", []int{0, 10, 9, 7, 2, 1, 4, 3, 5, 6}, 8}, + } + + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := XorSearchMissingNumber(tv.a) + if result != tv.missing { + t.Errorf("Wrong result! Expected:%d, returned:%d ", tv.missing, result) + } + }) + } + +} + +func BenchmarkTestXorSearchMissingNumber(b *testing.B) { + for i := 0; i < b.N; i++ { + XorSearchMissingNumber([]int{0, 10, 9, 7, 2, 1, 4, 3, 5, 6}) + } +} diff --git a/math/binomialcoefficient.go b/math/binomialcoefficient.go new file mode 100644 index 000000000..614f4b7db --- /dev/null +++ b/math/binomialcoefficient.go @@ -0,0 +1,35 @@ +// binomialcoefficient.go +// description: Returns C(n, k) +// details: +// a binomial coefficient C(n,k) gives number ways +// in which k objects can be chosen from n objects. +// wikipedia: https://en.wikipedia.org/wiki/Binomial_coefficient +// time complexity: O(k) or O(n-k) whichever is smaller (O(n) in worst case) +// space complexity: O(1) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see binomialcoefficient_test.go + +package math + +import ( + "errors" +) + +var ErrPosArgsOnly error = errors.New("arguments must be positive") + +// C is Binomial Coefficient function +// This function returns C(n, k) for given n and k +func Combinations(n int, k int) (int, error) { + if n < 0 || k < 0 { + return -1, ErrPosArgsOnly + } + if k > (n - k) { + k = n - k + } + res := 1 + for i := 0; i < k; i++ { + res *= (n - i) + res /= (i + 1) + } + return res, nil +} diff --git a/math/binomialcoefficient_test.go b/math/binomialcoefficient_test.go new file mode 100644 index 000000000..20b9c4373 --- /dev/null +++ b/math/binomialcoefficient_test.go @@ -0,0 +1,42 @@ +// binomialcoefficient_test.go +// description: Returns C(n, k) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see binomialcoefficient.go + +package math_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math" +) + +func TestCombinations(t *testing.T) { + var tests = []struct { + name string + n int + k int + expectedValue int + expectedError error + }{ + {"n = 5, k = 2", 5, 2, 10, nil}, + {"n = 7, k = 4", 7, 4, 35, nil}, + {"n = 0, k = 0", 0, 0, 1, nil}, + {"n = -1, k = 1", -1, 1, -1, math.ErrPosArgsOnly}, + {"n = 1, k = -1", 1, -1, -1, math.ErrPosArgsOnly}, + {"n = -1, k = -1", -1, -1, -1, math.ErrPosArgsOnly}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + result, err := math.Combinations(test.n, test.k) + if result != test.expectedValue || test.expectedError != err { + t.Errorf("expected error: %s, got: %s; expected value: %v, got: %v", test.expectedError, err, test.expectedValue, result) + } + }) + } +} +func BenchmarkCombinations(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = math.Combinations(65536, 65536) + } +} diff --git a/math/catalan/catalannumber.go b/math/catalan/catalannumber.go new file mode 100644 index 000000000..5f81cb9f4 --- /dev/null +++ b/math/catalan/catalannumber.go @@ -0,0 +1,28 @@ +// catalannumber.go +// description: Returns the Catalan number +// details: +// In combinatorial mathematics, the Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. - [Catalan number](https://en.wikipedia.org/wiki/Catalan_number) +// time complexity: O(n) +// space complexity: O(1) +// The input is the number of the Catalan number n, at the output we get the value of the number +// author(s) [red_byte](https://github.com/i-redbyte) +// see catalannumber_test.go + +package catalan + +import ( + f "github.com/TheAlgorithms/Go/math/factorial" +) + +func factorial(n int) int { + result, error := f.Iterative(n) + if error != nil { + panic(error) + } + return result +} + +// CatalanNumber This function returns the `nth` Catalan number +func CatalanNumber(n int) int { + return factorial(n*2) / (factorial(n) * factorial(n+1)) +} diff --git a/math/catalan/catalannumber_test.go b/math/catalan/catalannumber_test.go new file mode 100644 index 000000000..6d7896d35 --- /dev/null +++ b/math/catalan/catalannumber_test.go @@ -0,0 +1,37 @@ +// catalannumber_test.go +// description: Test for returns the Catalan number +// author(s) [red_byte](https://github.com/i-redbyte) +// see catalannumber.go + +package catalan + +import "testing" + +func TestCatalanNumber(t *testing.T) { + tests := []struct { + name string + n int + want int + }{ + {"zero Catalan number ", 0, 1}, + {"second Catalan number ", 2, 2}, + {"third Catalan number ", 3, 5}, + {"fourth Catalan number ", 4, 14}, + {"fifth Catalan number ", 5, 42}, + {"sixth Catalan number ", 6, 132}, + {"tenth Catalan number ", 10, 16796}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := CatalanNumber(test.n); got != test.want { + t.Errorf("CatalanNumber() = %v, want %v", got, test.want) + } + }) + } +} + +func BenchmarkCatalanNumber(b *testing.B) { + for i := 0; i < b.N; i++ { + CatalanNumber(10) + } +} diff --git a/math/checkisnumberpoweroftwo.go b/math/checkisnumberpoweroftwo.go new file mode 100644 index 000000000..48f0fe84a --- /dev/null +++ b/math/checkisnumberpoweroftwo.go @@ -0,0 +1,16 @@ +package math + +import ( + "math" +) + +// IsPowOfTwoUseLog This function checks if a number is a power of two using the logarithm. +// The limiting degree can be from 0 to 63. +// See alternatives in the binary package. +func IsPowOfTwoUseLog(number float64) bool { + if number == 0 || math.Round(number) == math.MaxInt64 { + return false + } + log := math.Log2(number) + return log == math.Round(log) +} diff --git a/math/checkisnumberpoweroftwo_test.go b/math/checkisnumberpoweroftwo_test.go new file mode 100644 index 000000000..834b99d83 --- /dev/null +++ b/math/checkisnumberpoweroftwo_test.go @@ -0,0 +1,54 @@ +// checkisnumberpoweroftwo_test.go +// description: Test for Is the number a power of two +// author(s) [red_byte](https://github.com/i-redbyte) +// see checkisnumberpoweroftwo.go + +package math + +import ( + "math" + "testing" +) + +func getTestsForPowerOfTwo() []struct { + name string + a int + missing bool +} { + var tests = []struct { + name string + a int + missing bool + }{ + {"Is 64 a power of 2? - YES", 64, true}, + {"Is 1 a power of 2? - YES", 1, true}, + {"Is 2 a power of 2? - YES", 2, true}, + {"Is 5 a power of 2? - NO", 5, false}, + {"Is 1023 a power of 2? - NO", 1023, false}, + {"Is 1024 a power of 2? - YES", 1024, true}, + {"Is 0 a power of 2? - NO", 0, false}, + {"Is 9223372036854775807 a power of 2? - NO", math.MaxInt64, false}, + {"Is 9223372036854775806 a power of 2? - NO", math.MaxInt64, false}, + {"Is 4611686018427387904 a power of 2? - YES", 4611686018427387904, true}, + } + return tests +} + +func TestIsPowOfTwoUseLog(t *testing.T) { + tests := getTestsForPowerOfTwo() + for _, tv := range tests { + t.Run(tv.name, func(t *testing.T) { + result := IsPowOfTwoUseLog(float64(tv.a)) + t.Log(tv.a, " ", result) + if result != tv.missing { + t.Errorf("Wrong result! Expected:%v, returned:%v ", tv.missing, result) + } + }) + } +} + +func BenchmarkIsPowerOfTwoUseLog(b *testing.B) { + for i := 0; i < b.N; i++ { + IsPowOfTwoUseLog(1024) + } +} diff --git a/math/cos.go b/math/cos.go new file mode 100644 index 000000000..369cd588c --- /dev/null +++ b/math/cos.go @@ -0,0 +1,17 @@ +// author(s) [red_byte](https://github.com/i-redbyte) +// see cos_test.go + +package math + +import "math" + +// Cos returns the cosine of the radian argument x. [See more](https://en.wikipedia.org/wiki/Sine_and_cosine) +// [Based on the idea of Bhaskara approximation of cos(x)](https://math.stackexchange.com/questions/3886552/bhaskara-approximation-of-cosx) +func Cos(x float64) float64 { + tp := 1.0 / (2.0 * math.Pi) + x *= tp + x -= 0.25 + math.Floor(x+0.25) + x *= 16.0 * (math.Abs(x) - 0.5) + x += 0.225 * x * (math.Abs(x) - 1.0) //Extra precision + return x +} diff --git a/math/cos_test.go b/math/cos_test.go new file mode 100644 index 000000000..16110c855 --- /dev/null +++ b/math/cos_test.go @@ -0,0 +1,46 @@ +package math_test + +import ( + algmath "github.com/TheAlgorithms/Go/math" + stdmath "math" + "testing" +) + +const epsilon = 0.001 + +func TestCos(t *testing.T) { + tests := []struct { + name string + n float64 + want float64 + }{ + {"cos(0)", 0, 1}, + {"cos(90)", 90, -0.447}, + {"cos(180)", 180, -0.598}, + {"cos(1)", 1, 0.540}, + {"cos(π)", stdmath.Pi, -1}, + {"cos(π/2)", stdmath.Pi / 2, 0}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + got := algmath.Cos(test.n) + if stdmath.Abs(got-test.want) >= epsilon { + t.Errorf("Cos() = %v, want %v", got, test.want) + t.Errorf("MATH Cos() = %v", stdmath.Cos(test.n)) + } + }) + } +} + +func BenchmarkCos(b *testing.B) { + for i := 0; i < b.N; i++ { + algmath.Cos(180) + } +} + +// BenchmarkMathCos is slower because the standard library `math.Cos` calculates a more accurate value. +func BenchmarkMathCos(b *testing.B) { + for i := 0; i < b.N; i++ { + stdmath.Cos(180) + } +} diff --git a/math/doc.go b/math/doc.go new file mode 100644 index 000000000..d44df9e6d --- /dev/null +++ b/math/doc.go @@ -0,0 +1,2 @@ +// Package math is a package that contains mathematical algorithms and its different implementations. +package math diff --git a/math/eulertotient.go b/math/eulertotient.go new file mode 100644 index 000000000..6e0d5d23b --- /dev/null +++ b/math/eulertotient.go @@ -0,0 +1,23 @@ +package math + +// Phi is the Euler totient function. +// This function computes the number of numbers less then n that are coprime with n. +func Phi(n int64) int64 { + result := n + for i := int64(2); i*i <= n; i += 1 { + if n%i == 0 { + for { + if n%i != 0 { + break + } + n /= i + } + result -= result / i + } + } + + if n > 1 { + result -= result / n + } + return result +} diff --git a/math/eulertotient_test.go b/math/eulertotient_test.go new file mode 100644 index 000000000..5a7d7e21b --- /dev/null +++ b/math/eulertotient_test.go @@ -0,0 +1,44 @@ +package math + +import ( + "testing" +) + +func getTestsForPhi() []struct { + n int64 + expected int64 +} { + var tests = []struct { + n int64 + expected int64 + }{ + {4, 2}, + {5, 4}, + {7, 6}, + {10, 4}, + {999, 648}, + {1000, 400}, + {1000000, 400000}, + {999999, 466560}, + {999999999999878, 473684210526240}, + } + return tests +} + +func TestPhi(t *testing.T) { + + tests := getTestsForPhi() + for _, test := range tests { + result := Phi(test.n) + t.Log(test.n, " ", result) + if result != test.expected { + t.Errorf("Wrong result! Expected:%v, returned:%v ", test.expected, result) + } + } +} + +func BenchmarkPhi(b *testing.B) { + for i := 0; i < b.N; i++ { + Phi(65536) + } +} diff --git a/math/factorial/factorial.go b/math/factorial/factorial.go new file mode 100644 index 000000000..6703e6c75 --- /dev/null +++ b/math/factorial/factorial.go @@ -0,0 +1,69 @@ +// factorial.go +// description: Calculating factorial +// details: +// The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n - [Factorial](https://en.wikipedia.org/wiki/Factorial) +// time complexity: O(n) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see factorial_test.go + +// Package factorial describes algorithms Factorials calculations. +package factorial + +import ( + "errors" +) + +var ErrNegativeArgument = errors.New("input argument must be non-negative integer") + +// Iterative returns the iteratively brute forced factorial of n +func Iterative(n int) (int, error) { + if n < 0 { + return 0, ErrNegativeArgument + } + result := 1 + for i := 2; i <= n; i++ { + result *= i + } + return result, nil +} + +// Recursive This function recursively computes the factorial of a number +func Recursive(n int) (int, error) { + if n < 0 { + return 0, ErrNegativeArgument + } + if n <= 1 { + return 1, nil + } + prev, _ := Recursive(n - 1) + return n * prev, nil +} + +// UsingTree This function finds the factorial of a number using a binary tree +func UsingTree(n int) (int, error) { + if n < 0 { + return 0, ErrNegativeArgument + } + if n == 0 { + return 1, nil + } + if n == 1 || n == 2 { + return n, nil + } + return prodTree(2, n), nil +} + +func prodTree(l int, r int) int { + if l > r { + return 1 + } + if l == r { + return l + } + if r-l == 1 { + return l * r + } + m := (l + r) / 2 + return prodTree(l, m) * prodTree(m+1, r) +} diff --git a/math/factorial/factorial_test.go b/math/factorial/factorial_test.go new file mode 100644 index 000000000..1d3ed727d --- /dev/null +++ b/math/factorial/factorial_test.go @@ -0,0 +1,69 @@ +// factorial_test.go +// description: Test for calculating factorial +// see factorial.go + +package factorial + +import "testing" +import "fmt" + +type factorialFun func(int) (int, error) + +var implementations = map[string]factorialFun{ + "Iterative": Iterative, + "Recursive": Recursive, + "UsingTree": UsingTree, +} + +var testCases = []struct { + n int + expected int +}{ + {0, 1}, + {1, 1}, + {2, 2}, + {3, 6}, + {4, 24}, + {5, 120}, + {6, 720}, + {7, 5040}, + {8, 40320}, + {9, 362880}, + {10, 3628800}, + {11, 39916800}, + {12, 479001600}, +} + +func TestFactorial(t *testing.T) { + for implName, implFunction := range implementations { + t.Run(implName+" errors for negative input", func(t *testing.T) { + _, error := implFunction(-1) + if error != ErrNegativeArgument { + t.Errorf("No error captured for negative input") + } + }) + for _, tc := range testCases { + t.Run(fmt.Sprintf("%s with input %d", implName, tc.n), func(t *testing.T) { + actual, err := implFunction(tc.n) + if err != nil { + t.Errorf("unexpected error captured") + } + if actual != tc.expected { + t.Errorf("Expected: %d, got: %d", tc.expected, actual) + } + }) + } + } +} + +func BenchmarkFactorial(b *testing.B) { + for _, input := range []int{5, 10, 15} { + for implName, implFunction := range implementations { + b.Run(fmt.Sprintf("%s_%d", implName, input), func(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = implFunction(input) + } + }) + } + } +} diff --git a/math/fibonacci/fibonacci.go b/math/fibonacci/fibonacci.go new file mode 100644 index 000000000..c2fd1b2e2 --- /dev/null +++ b/math/fibonacci/fibonacci.go @@ -0,0 +1,59 @@ +// fibonacci.go +// description: Get the nth Fibonacci Number +// details: +// In mathematics, the Fibonacci numbers, commonly denoted Fn, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. [Fibonacci number](https://en.wikipedia.org/wiki/Fibonacci_number) +// time complexity: O(log n) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see fibonacci_test.go + +package fibonacci + +import ( + "math" +) + +// Matrix This function calculates the n-th fibonacci number using the matrix method. [See](https://en.wikipedia.org/wiki/Fibonacci_number#Matrix_form) +func Matrix(n uint) uint { + a, b := 1, 1 + c, rc, tc := 1, 0, 0 + d, rd := 0, 1 + + for n != 0 { + if n&1 == 1 { + tc = rc + rc = rc*a + rd*c + rd = tc*b + rd*d + } + + ta := a + tb := b + tc = c + a = a*a + b*c + b = ta*b + b*d + c = c*ta + d*c + d = tc*tb + d*d + + n >>= 1 + } + return uint(rc) +} + +// Formula This function calculates the n-th fibonacci number using the [formula](https://en.wikipedia.org/wiki/Fibonacci_number#Relation_to_the_golden_ratio) +// Attention! Tests for large values fall due to rounding error of floating point numbers, works well, only on small numbers +func Formula(n uint) uint { + sqrt5 := math.Sqrt(5) + phi := (sqrt5 + 1) / 2 + powPhi := math.Pow(phi, float64(n)) + return uint(powPhi/sqrt5 + 0.5) +} + +// Recursive calculates the n-th fibonacci number recursively by adding the previous two Fibonacci numbers. +// This algorithm is extremely slow for bigger numbers, but provides a simpler implementation. +func Recursive(n uint) uint { + if n <= 1 { + return n + } + + return Recursive(n-1) + Recursive(n-2) +} diff --git a/math/fibonacci/fibonacci_test.go b/math/fibonacci/fibonacci_test.go new file mode 100644 index 000000000..bfdbed0bc --- /dev/null +++ b/math/fibonacci/fibonacci_test.go @@ -0,0 +1,96 @@ +package fibonacci + +import ( + "github.com/TheAlgorithms/Go/dynamic" + "testing" +) + +func getTests() []struct { + name string + n uint + want uint +} { + tests := []struct { + name string + n uint + want uint + }{ + {"Fibonacci 0-th number == 0", 0, 0}, + {"Fibonacci 1-th number == 1", 1, 1}, + {"Fibonacci 2-th number == 1", 2, 1}, + {"Fibonacci 3-th number == 2", 3, 2}, + {"Fibonacci 4-th number == 3", 4, 3}, + {"Fibonacci 5-th number == 5", 5, 5}, + {"Fibonacci 6-th number == 8", 6, 8}, + {"Fibonacci 7-th number == 13", 7, 13}, + {"Fibonacci 8-th number == 21", 8, 21}, + {"Fibonacci 9-th number == 34", 9, 34}, + {"Fibonacci 10-th number == 55", 10, 55}, + {"Fibonacci 90-th number == 2880067194370816120", 90, 2880067194370816120}, + } + return tests +} + +func TestMatrix(t *testing.T) { + tests := getTests() + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := Matrix(test.n); got != test.want { + t.Errorf("Return value = %v, want %v", got, test.want) + } + }) + } +} + +func TestNthFibonacci(t *testing.T) { + tests := getTests() + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := dynamic.NthFibonacci(test.n); got != test.want { + t.Errorf("Return value = %v, want %v", got, test.want) + } + }) + } +} + +func TestFormula(t *testing.T) { + tests := getTests() + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := Formula(test.n); test.n <= 10 && got != test.want { + t.Errorf("Return value = %v, want %v", got, test.want) + } + }) + } +} + +func TestRecursive(t *testing.T) { + tests := getTests() + for _, test := range tests { + if test.n <= 10 { + t.Run(test.name, func(t *testing.T) { + if got := Recursive(test.n); got != test.want { + t.Errorf("Return value = %v, want %v", got, test.want) + } + }) + } + } +} + +func BenchmarkNthFibonacci(b *testing.B) { + for i := 0; i < b.N; i++ { + dynamic.NthFibonacci(90) + } +} + +func BenchmarkMatrix(b *testing.B) { + for i := 0; i < b.N; i++ { + Matrix(90) + } +} + +func BenchmarkFormula(b *testing.B) { + for i := 0; i < b.N; i++ { + Formula(90) + } +} diff --git a/math/gcd/extended.go b/math/gcd/extended.go new file mode 100644 index 000000000..229630141 --- /dev/null +++ b/math/gcd/extended.go @@ -0,0 +1,20 @@ +// extended.go +// description: Implementation of Extended GCD Algorithm +// details: +// A simple implementation of Extended GCD algorithm, that returns GCD, a and b +// which solves ax + by = gcd(a, b) +// time complexity: O(log(min(a, b))) where a and b are the two numbers +// space complexity: O(log(min(a, b))) where a and b are the two numbers +// author(s) [Taj](https://github.com/tjgurwara99) +// see extended_test.go + +package gcd + +// Extended simple extended gcd +func Extended(a, b int64) (int64, int64, int64) { + if a == 0 { + return b, 0, 1 + } + gcd, xPrime, yPrime := Extended(b%a, a) + return gcd, yPrime - (b/a)*xPrime, xPrime +} diff --git a/math/gcd/extended_test.go b/math/gcd/extended_test.go new file mode 100644 index 000000000..b87e927ae --- /dev/null +++ b/math/gcd/extended_test.go @@ -0,0 +1,29 @@ +// extended_test.go +// description: Test for Extended GCD algorithm in extended.go +// author(s) [Taj](https://github.com/tjgurwara99) +// see extended.go + +package gcd + +import "testing" + +func TestExtended(t *testing.T) { + var testCasesExtended = []struct { + name string + a int64 + b int64 + gcd int64 + x int64 + y int64 + }{ + {"gcd of 30 and 50", 30, 50, 10, 2, -1}, + } + for _, tc := range testCasesExtended { + t.Run(tc.name, func(t *testing.T) { + gcd, x, y := Extended(tc.a, tc.b) + if gcd != tc.gcd && x != tc.x && y != tc.y { + t.Fatalf("Expected values:\n\tGCD: Expected %v Returned %v,\n\tx: Expected %v Returned %v\n\ty: Expected %v Returned %v", tc.gcd, gcd, tc.x, x, tc.y, y) + } + }) + } +} diff --git a/math/gcd/extendedgcd.go b/math/gcd/extendedgcd.go new file mode 100644 index 000000000..0f5a750dc --- /dev/null +++ b/math/gcd/extendedgcd.go @@ -0,0 +1,17 @@ +// extendedgcd.go +// description: Implementation of Extended GCD Algorithm +// time complexity: O(log(min(a, b))) where a and b are the two numbers +// space complexity: O(log(min(a, b))) where a and b are the two numbers + +package gcd + +// ExtendedRecursive finds and returns gcd(a, b), x, y satisfying a*x + b*y = gcd(a, b). +func ExtendedRecursive(a, b int64) (int64, int64, int64) { + if b > 0 { + d, y, x := ExtendedRecursive(b, a%b) + y -= (a / b) * x + return d, x, y + } + + return a, 1, 0 +} diff --git a/math/gcd/extendedgcd_test.go b/math/gcd/extendedgcd_test.go new file mode 100644 index 000000000..f8fc2b820 --- /dev/null +++ b/math/gcd/extendedgcd_test.go @@ -0,0 +1,56 @@ +package gcd + +import "testing" + +type testExtendedFunction func(int64, int64) (int64, int64, int64) + +func TemplateTestExtendedGCD(t *testing.T, f testExtendedFunction) { + var testCasesExtended = []struct { + name string + a int64 + b int64 + gcd int64 + x int64 + y int64 + }{ + {"gcd of 10 and 0", 10, 0, 10, 1, 0}, + {"gcd of 98 and 56", 98, 56, 14, -1, 2}, + {"gcd of 0 and 10", 0, 10, 10, 0, 1}, + } + for _, tc := range testCasesExtended { + t.Run(tc.name, func(t *testing.T) { + actualGcd, actualX, actualY := f(tc.a, tc.b) + if actualGcd != tc.gcd { + t.Errorf("Expected GCD of %d and %d to be: %v, but got: %d", tc.a, tc.b, tc.gcd, actualGcd) + } + if actualX != tc.x { + t.Errorf("Expected x satisfying %d * x + %d * y = gcd to be: %v, but got: %d", tc.a, tc.b, tc.x, actualX) + } + if actualY != tc.y { + t.Errorf("Expected y satisfying %d * x + %d * y = gcd to be: %v, but got: %d", tc.a, tc.b, tc.y, actualY) + } + }) + } +} + +func TestExtendedGCDRecursive(t *testing.T) { + TemplateTestExtendedGCD(t, ExtendedRecursive) +} + +func TestExtendedGCDIterative(t *testing.T) { + TemplateTestExtendedGCD(t, ExtendedIterative) +} + +func TemplateBenchmarkExtendedGCD(b *testing.B, f testExtendedFunction) { + for i := 0; i < b.N; i++ { + f(98, 56) + } +} + +func BenchmarkExtendedGCDRecursive(b *testing.B) { + TemplateBenchmarkExtendedGCD(b, ExtendedRecursive) +} + +func BenchmarkExtendedGCDIterative(b *testing.B) { + TemplateBenchmarkExtendedGCD(b, ExtendedIterative) +} diff --git a/math/gcd/extendedgcditerative.go b/math/gcd/extendedgcditerative.go new file mode 100644 index 000000000..1c8e8ad72 --- /dev/null +++ b/math/gcd/extendedgcditerative.go @@ -0,0 +1,13 @@ +package gcd + +// ExtendedIterative finds and returns gcd(a, b), x, y satisfying a*x + b*y = gcd(a, b). +func ExtendedIterative(a, b int64) (int64, int64, int64) { + var u, y, v, x int64 = 1, 1, 0, 0 + for a > 0 { + var q int64 = b / a + x, u = u, x-q*u + y, v = v, y-q*v + b, a = a, b-q*a + } + return b, x, y +} diff --git a/math/gcd/gcd.go b/math/gcd/gcd.go new file mode 100644 index 000000000..2045d0901 --- /dev/null +++ b/math/gcd/gcd.go @@ -0,0 +1,12 @@ +// time complexity: O(log(min(a, b))) where a and b are the two numbers +// space complexity: O(1) + +package gcd + +// Recursive finds and returns the greatest common divisor of a given integer. +func Recursive(a, b int64) int64 { + if b == 0 { + return a + } + return Recursive(b, a%b) +} diff --git a/math/gcd/gcd_test.go b/math/gcd/gcd_test.go new file mode 100644 index 000000000..78b5b3155 --- /dev/null +++ b/math/gcd/gcd_test.go @@ -0,0 +1,49 @@ +package gcd + +import "testing" + +type testFunction func(int64, int64) int64 + +var testCases = []struct { + name string + a int64 + b int64 + output int64 +}{ + {"gcd of 10 and 0", 10, 0, 10}, + {"gcd of 98 and 56", 98, 56, 14}, + {"gcd of 0 and 10", 0, 10, 10}, +} + +func TemplateTestGCD(t *testing.T, f testFunction) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := f(tc.a, tc.b) + if actual != tc.output { + t.Errorf("Expected GCD of %d and %d to be: %v, but got: %d", tc.a, tc.b, tc.output, actual) + } + }) + } +} + +func TestGCDRecursive(t *testing.T) { + TemplateTestGCD(t, Recursive) +} + +func TestGCDIterative(t *testing.T) { + TemplateTestGCD(t, Iterative) +} + +func TemplateBenchmarkGCD(b *testing.B, f testFunction) { + for i := 0; i < b.N; i++ { + f(98, 56) + } +} + +func BenchmarkGCDRecursive(b *testing.B) { + TemplateBenchmarkGCD(b, Recursive) +} + +func BenchmarkGCDIterative(b *testing.B) { + TemplateBenchmarkGCD(b, Iterative) +} diff --git a/math/gcd/gcditerative.go b/math/gcd/gcditerative.go new file mode 100644 index 000000000..96c217cfa --- /dev/null +++ b/math/gcd/gcditerative.go @@ -0,0 +1,12 @@ +// time complexity: O(log(min(a, b))) where a and b are the two numbers +// space complexity: O(1) + +package gcd + +// Iterative Faster iterative version of GcdRecursive without holding up too much of the stack +func Iterative(a, b int64) int64 { + for b != 0 { + a, b = b, a%b + } + return a +} diff --git a/math/geometry/distance.go b/math/geometry/distance.go new file mode 100644 index 000000000..0baf64562 --- /dev/null +++ b/math/geometry/distance.go @@ -0,0 +1,38 @@ +// distance.go +// Find Euclidean distance between two points +// time complexity: O(n) where n is the number of dimensions +// space complexity: O(1) +// author(s) [Chetan Patil](https://github.com/Chetan07j) + +// Package geometry contains geometric algorithms +package geometry + +import ( + "errors" + "math" +) + +// EuclideanPoint defines a point with x and y coordinates. +type EuclideanPoint []float64 + +var ErrDimMismatch = errors.New("mismatched dimensions") + +// EuclideanDistance returns the Euclidean distance between points in +// any `n` dimensional Euclidean space. +func EuclideanDistance(p1 EuclideanPoint, p2 EuclideanPoint) (float64, error) { + n := len(p1) + + if len(p2) != n { + return -1, ErrDimMismatch + } + + var total float64 = 0 + + for i, x_i := range p1 { + // using Abs since the value could be negative but we require the magnitude + diff := math.Abs(x_i - p2[i]) + total += diff * diff + } + + return math.Sqrt(total), nil +} diff --git a/math/geometry/distance_test.go b/math/geometry/distance_test.go new file mode 100644 index 000000000..bea9ebba5 --- /dev/null +++ b/math/geometry/distance_test.go @@ -0,0 +1,80 @@ +package geometry_test + +import ( + "errors" + "testing" + + geometry "github.com/TheAlgorithms/Go/math/geometry" +) + +type args struct { + p1 geometry.EuclideanPoint + p2 geometry.EuclideanPoint +} + +func TestFindDistanceBetweenTwoPoints(t *testing.T) { + tests := []struct { + name string + args args + want float64 + wantErr bool + }{ + { + "(0,0) and (2,-2)", + args{ + geometry.EuclideanPoint{0, 0}, + geometry.EuclideanPoint{2, -2}, + }, + 2.8284271247461903, + false, + }, + { + "(-20,23) and (-15,68)", + args{ + geometry.EuclideanPoint{-20, 23}, + geometry.EuclideanPoint{-15, 68}, + }, + 45.27692569068709, + false, + }, + { + "(2,2) and (14,11)", + args{ + geometry.EuclideanPoint{2, 2}, + geometry.EuclideanPoint{14, 11}, + }, + 15, + false, + }, + { + "Return error for mismatched dimensions(2,2) and ()", + args{ + geometry.EuclideanPoint{2, 2}, + geometry.EuclideanPoint{}, + }, + -1, + true, + }, + } + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + got, err := geometry.EuclideanDistance(tt.args.p1, tt.args.p2) + if (err != nil) != tt.wantErr && errors.Is(err, geometry.ErrDimMismatch) { + t.Errorf("EuclideanDistance() error = %v, wantErr %v", err, tt.wantErr) + return + } + if got != tt.want { + t.Errorf("EuclideanDistance() = %v, want %v", got, tt.want) + } + }) + } +} + +func BenchmarkFindDistanceBetweenTwoPoints(b *testing.B) { + p1 := geometry.EuclideanPoint{0, 0} + p2 := geometry.EuclideanPoint{2, -2} + + for i := 0; i < b.N; i++ { + _, _ = geometry.EuclideanDistance(p1, p2) + } +} diff --git a/math/geometry/straightlines.go b/math/geometry/straightlines.go new file mode 100644 index 000000000..cf1951b07 --- /dev/null +++ b/math/geometry/straightlines.go @@ -0,0 +1,55 @@ +// Package geometry contains geometric algorithms +package geometry + +import ( + "math" +) + +// Point defines a point with x and y coordinates. +type Point struct { + X, Y float64 +} + +type Line struct { + P1, P2 Point +} + +// Distance calculates the shortest distance between two points. +func Distance(a, b *Point) float64 { + return math.Sqrt(math.Pow(a.X-b.X, 2) + math.Pow(a.Y-b.Y, 2)) +} + +// Section calculates the Point that divides a line in specific ratio. +// DO NOT specify the ratio in the form m:n, specify it as r, where r = m / n. +func Section(p1, p2 *Point, r float64) Point { + var point Point + point.X = (r*p2.X + p1.X) / (r + 1) + point.Y = (r*p2.Y + p1.Y) / (r + 1) + return point +} + +// Slope calculates the slope (gradient) of a line. +func Slope(l *Line) float64 { + return (l.P2.Y - l.P1.Y) / (l.P2.X - l.P1.X) +} + +// YIntercept calculates the Y-Intercept of a line from a specific Point. +func YIntercept(p *Point, slope float64) float64 { + return p.Y - (slope * p.X) +} + +// IsParallel checks if two lines are parallel or not. +func IsParallel(l1, l2 *Line) bool { + return Slope(l1) == Slope(l2) +} + +// IsPerpendicular checks if two lines are perpendicular or not. +func IsPerpendicular(l1, l2 *Line) bool { + return Slope(l1)*Slope(l2) == -1 +} + +// PointDistance calculates the distance of a given Point from a given line. +// The slice should contain the coefficiet of x, the coefficient of y and the constant in the respective order. +func PointDistance(p *Point, equation [3]float64) float64 { + return math.Abs(equation[0]*p.X+equation[1]*p.Y+equation[2]) / math.Sqrt(math.Pow(equation[0], 2)+math.Pow(equation[1], 2)) +} diff --git a/math/geometry/straightlines_test.go b/math/geometry/straightlines_test.go new file mode 100644 index 000000000..d71a78e5a --- /dev/null +++ b/math/geometry/straightlines_test.go @@ -0,0 +1,70 @@ +package geometry + +import ( + "testing" +) + +func TestDistance(t *testing.T) { + p1 := Point{0, 0} + p2 := Point{3, 4} + var wantedDistance float64 = 5 + var calculatedDistance float64 = Distance(&p1, &p2) + if calculatedDistance != wantedDistance { + t.Fatalf("Failed to calculate Distance.") + } +} + +func TestSection(t *testing.T) { + p1 := Point{1, 0} + p2 := Point{5, 0} + wantedPoint := Point{3, 0} + calculatedPoint := Section(&p1, &p2, 1) + if calculatedPoint != wantedPoint { + t.Fatalf("Failed to calculate Section.") + } +} + +func TestSlope(t *testing.T) { + line := Line{P1: Point{1, 2}, P2: Point{2, 4}} + var wantedSlope float64 = 2 + var calculatedSlope float64 = Slope(&line) + if calculatedSlope != wantedSlope { + t.Fatalf("Failed to calculate Slope.") + } +} + +func TestIntercept(t *testing.T) { + p := Point{0, 3} + var slope float64 = -5 + var wantedIntercept float64 = 3 + var calculatedIntercept float64 = YIntercept(&p, slope) + if calculatedIntercept != wantedIntercept { + t.Fatalf("Failed to calculate YIntercept.") + } +} + +func TestIsParallel(t *testing.T) { + l1 := Line{P1: Point{1, 2}, P2: Point{2, 4}} + l2 := Line{P1: Point{25, 50}, P2: Point{50, 100}} + if !IsParallel(&l1, &l2) { + t.Fatalf("Failed to check if Parallel.") + } +} + +func TestIsPerpendicular(t *testing.T) { + l1 := Line{P1: Point{1, 2}, P2: Point{2, 4}} + l2 := Line{P1: Point{2, 2}, P2: Point{4, 1}} + if !IsPerpendicular(&l1, &l2) { + t.Fatalf("Failed to check if Perpendicular.") + } +} + +func TestPointDistance(t *testing.T) { + p := Point{1, 1} + equation := [3]float64{4, 3, 1} + var wantedDistance float64 = 1.6 + var calculatedDistance float64 = PointDistance(&p, equation) + if calculatedDistance != wantedDistance { + t.Fatalf("Failed to calculate Point Distance.") + } +} diff --git a/math/isautomorphic.go b/math/isautomorphic.go new file mode 100644 index 000000000..855d224a1 --- /dev/null +++ b/math/isautomorphic.go @@ -0,0 +1,32 @@ +// isautomorphic.go +// description: Checks whether a whole number integer is Automorphic or not. If number < 0 then returns false. +// details: +// In mathematics, a number n is said to be a Automorphic number if the square of n ends in the same digits as n itself. +// ref: (https://en.wikipedia.org/wiki/Automorphic_number) +// time complexity: O(log10(N)) +// space complexity: O(1) +// author: [SilverDragonOfR](https://github.com/SilverDragonOfR) + +package math + +import ( + "github.com/TheAlgorithms/Go/constraints" +) + +func IsAutomorphic[T constraints.Integer](n T) bool { + // handling the negetive number case + if n < 0 { + return false + } + + n_sq := n * n + for n > 0 { + if (n % 10) != (n_sq % 10) { + return false + } + n /= 10 + n_sq /= 10 + } + + return true +} diff --git a/math/isautomorphic_test.go b/math/isautomorphic_test.go new file mode 100644 index 000000000..d8494b921 --- /dev/null +++ b/math/isautomorphic_test.go @@ -0,0 +1,58 @@ +package math + +import ( + "testing" +) + +var testCases = []struct { + name string + input int + expected bool +}{ + { + "negetive number: not Automorphic", + -1, + false, + }, + { + "negetive number: not Automorphic", + -146, + false, + }, + { + "0: is Automorphic", + 0, + true, + }, + { + "1: is Automorphic", + 1, + true, + }, + { + "7: not Automorphic", + 7, + false, + }, + { + "83: not Automorphic", + 83, + false, + }, + { + "376: is Automorphic", + 376, + true, + }, +} + +func TestIsAutomorphic(t *testing.T) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + funcResult := IsAutomorphic(test.input) + if test.expected != funcResult { + t.Errorf("Expected answer '%t' for the number '%d' but answer given was %t", test.expected, test.input, funcResult) + } + }) + } +} diff --git a/math/krishnamurthy.go b/math/krishnamurthy.go new file mode 100644 index 000000000..63bb6dbf6 --- /dev/null +++ b/math/krishnamurthy.go @@ -0,0 +1,34 @@ +// filename : krishnamurthy.go +// description: A program which contains the function that returns true if a given number is Krishnamurthy number or not. +// details: A number is a Krishnamurthy number if the sum of all the factorials of the digits is equal to the number. +// Ex: 1! = 1, 145 = 1! + 4! + 5! +// time complexity: O(log n) +// space complexity: O(1) +// author(s): [GooMonk](https://github.com/GooMonk) +// see krishnamurthy_test.go +package math + +import "github.com/TheAlgorithms/Go/constraints" + +// IsKrishnamurthyNumber returns if the provided number n is a Krishnamurthy number or not. +func IsKrishnamurthyNumber[T constraints.Integer](n T) bool { + if n <= 0 { + return false + } + + // Preprocessing: Using a slice to store the digit Factorials + digitFact := make([]T, 10) + digitFact[0] = 1 // 0! = 1 + + for i := 1; i < 10; i++ { + digitFact[i] = digitFact[i-1] * T(i) + } + + // Subtract the digit Facotorial from the number + nTemp := n + for n > 0 { + nTemp -= digitFact[n%10] + n /= 10 + } + return nTemp == 0 +} diff --git a/math/krishnamurthy_test.go b/math/krishnamurthy_test.go new file mode 100644 index 000000000..c4fc81895 --- /dev/null +++ b/math/krishnamurthy_test.go @@ -0,0 +1,51 @@ +package math + +import ( + "fmt" + "testing" +) + +func retCases() []struct { + input int64 + output bool + outputString string +} { + return []struct { + input int64 + output bool + outputString string + }{ + {-3112312321, false, "is not"}, + {0, false, "is not"}, + {1, true, "is"}, + {2, true, "is"}, + {109, false, "is not"}, + {145, true, "is"}, + {943, false, "is not"}, + {6327, false, "is not"}, + {40585, true, "is"}, + {9743821, false, "is not"}, + {3421488712, false, "is not"}, + } +} + +func TestIsKrishnamurthyNumber(t *testing.T) { + for _, test := range retCases() { + t.Run(fmt.Sprintf("%d %s a Krishnamurthy Number", test.input, test.outputString), func(t *testing.T) { + res := IsKrishnamurthyNumber(test.input) + if res != test.output { + t.Errorf("for input %d, expected: %t, found: %t", test.input, test.output, res) + } + }) + } +} + +func BenchmarkIsKrishnamurthyNumber(b *testing.B) { + for _, test := range retCases() { + b.Run(fmt.Sprintf("%d %s a Krishnamurthy Number", test.input, test.outputString), func(b *testing.B) { + for i := 0; i < b.N; i++ { + IsKrishnamurthyNumber(test.input) + } + }) + } +} diff --git a/math/kthnumber.go b/math/kthnumber.go new file mode 100644 index 000000000..802e2cf50 --- /dev/null +++ b/math/kthnumber.go @@ -0,0 +1,43 @@ +package math + +import ( + "github.com/TheAlgorithms/Go/search" + "github.com/TheAlgorithms/Go/sort" +) + +// FindKthMax returns the kth large element given an integer slice +// with nil `error` if found and returns -1 with `error` `search.ErrNotFound` +// if not found. NOTE: The `nums` slice gets mutated in the process. +func FindKthMax(nums []int, k int) (int, error) { + index := len(nums) - k + return kthNumber(nums, index) +} + +// FindKthMin returns kth small element given an integer slice +// with nil `error` if found and returns -1 with `error` `search.ErrNotFound` +// if not found. NOTE: The `nums` slice gets mutated in the process. +func FindKthMin(nums []int, k int) (int, error) { + index := k - 1 + return kthNumber(nums, index) +} + +// kthNumber use the selection algorithm (based on the partition method - the same one as used in quicksort). +func kthNumber(nums []int, k int) (int, error) { + if k < 0 || k >= len(nums) { + return -1, search.ErrNotFound + } + start := 0 + end := len(nums) - 1 + for start <= end { + pivot := sort.Partition(nums, start, end) + if k == pivot { + return nums[pivot], nil + } + if k > pivot { + start = pivot + 1 + continue + } + end = pivot - 1 + } + return -1, search.ErrNotFound +} diff --git a/math/kthnumber_test.go b/math/kthnumber_test.go new file mode 100644 index 000000000..558cf2240 --- /dev/null +++ b/math/kthnumber_test.go @@ -0,0 +1,104 @@ +package math + +import ( + "github.com/TheAlgorithms/Go/search" + "testing" +) + +func TestFindKthMax(t *testing.T) { + sortTests := []struct { + input []int + k int + expected int + err error + name string + }{ + { + input: []int{6, 7, 0, -1, 10, 70, 8, 22, 3, 9}, + k: 3, + expected: 10, + name: "3th largest number", + }, + { + input: []int{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, + k: 3, + expected: -1, + name: "3th largest number", + }, + { + input: []int{-1, -1, -1, -1, -1, -1}, + k: 7, + expected: -1, + err: search.ErrNotFound, + name: "This should be an error", + }, + { + input: []int{}, + k: 1, + expected: -1, + err: search.ErrNotFound, + name: "This should be an error", + }, + } + for _, test := range sortTests { + t.Run(test.name, func(t *testing.T) { + actual, err := FindKthMax(test.input, test.k) + if err != test.err { + t.Errorf("name:%v FindKthMax() = %v, want err: %v", test.name, err, test.err) + } + if actual != test.expected { + t.Errorf("test %s failed", test.name) + t.Errorf("actual %v expected %v", actual, test.expected) + } + }) + } +} + +func TestFindKthMin(t *testing.T) { + sortTests := []struct { + input []int + k int + expected int + err error + name string + }{ + { + input: []int{6, 7, 0, -1, 10, 70, 8, 22, 3, 9}, + k: 3, + expected: 3, + name: "3th smallest number", + }, + { + input: []int{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, + k: 3, + expected: -1, + name: "3th smallest number", + }, + { + input: []int{-1, -1, -1, -1, -1, -1}, + k: 7, + expected: -1, + err: search.ErrNotFound, + name: "This should be an error", + }, + { + input: []int{}, + k: 1, + expected: -1, + err: search.ErrNotFound, + name: "This should be an error", + }, + } + for _, test := range sortTests { + t.Run(test.name, func(t *testing.T) { + actual, err := FindKthMin(test.input, test.k) + if err != test.err { + t.Errorf("name:%v FindKthMin() = %v, want err: %v", test.name, err, test.err) + } + if actual != test.expected { + t.Errorf("test %s failed", test.name) + t.Errorf("actual %v expected %v", actual, test.expected) + } + }) + } +} diff --git a/math/lcm/lcm.go b/math/lcm/lcm.go new file mode 100644 index 000000000..e1de23e17 --- /dev/null +++ b/math/lcm/lcm.go @@ -0,0 +1,12 @@ +package lcm + +import ( + "math" + + "github.com/TheAlgorithms/Go/math/gcd" +) + +// Lcm returns the lcm of two numbers using the fact that lcm(a,b) * gcd(a,b) = | a * b | +func Lcm(a, b int64) int64 { + return int64(math.Abs(float64(a*b)) / float64(gcd.Iterative(a, b))) +} diff --git a/math/lcm/lcm_test.go b/math/lcm/lcm_test.go new file mode 100644 index 000000000..e685a6728 --- /dev/null +++ b/math/lcm/lcm_test.go @@ -0,0 +1,44 @@ +package lcm + +import "testing" + +func TestLcm(t *testing.T) { + testCases := []struct { + name string + a int64 + b int64 + output int64 + }{ + { + name: "LCM of 1 & 5", + a: 1, + b: 5, + output: 5, + }, { + name: "LCM of 2 & 5", + a: 2, + b: 5, + output: 10, + }, { + name: "LCM of 5 & 10", + a: 10, + b: 5, + output: 10, + }, { + name: "LCM of 5 & 5", + a: 5, + b: 5, + output: 5, + }, + } + + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual_output := Lcm(tc.a, tc.b) + if actual_output != tc.output { + t.Errorf("Expected LCM of %d and %d is %d, but got %d", tc.a, tc.b, tc.output, + actual_output) + } + }) + } +} diff --git a/math/lerp.go b/math/lerp.go new file mode 100644 index 000000000..1d2b59908 --- /dev/null +++ b/math/lerp.go @@ -0,0 +1,8 @@ +package math + +// Lerp or Linear interpolation +// This function will return new value in 't' percentage between 'v0' and 'v1' +func Lerp(v0, v1, t float64) float64 { + // see: https://en.wikipedia.org/wiki/Linear_interpolation + return (1-t)*v0 + t*v1 +} diff --git a/math/lerp_test.go b/math/lerp_test.go new file mode 100644 index 000000000..3a6ac25fd --- /dev/null +++ b/math/lerp_test.go @@ -0,0 +1,29 @@ +package math_test + +import ( + "testing" + + algmath "github.com/TheAlgorithms/Go/math" +) + +func TestLerp(t *testing.T) { + tests := []struct { + name string + testValues []float64 + answer float64 + }{ + {"Lerp(1,1,1)", []float64{1, 1, 1}, 1}, + {"Lerp(0,1,1)", []float64{0, 1, 1}, 1}, + {"Lerp(0,1,0.5)", []float64{0, 1, 0.5}, 0.5}, + {"Lerp(0,1,0.1)", []float64{0, 1, 0.1}, 0.1}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + got := algmath.Lerp(test.testValues[0], test.testValues[1], test.testValues[2]) + if got != test.answer { + t.Errorf("Lerp(%f,%f,%f) = %v, want %v", got, test.testValues[0], + test.testValues[1], test.testValues[2], test.answer) + } + }) + } +} diff --git a/math/liouville.go b/math/liouville.go new file mode 100644 index 000000000..55d2c95f4 --- /dev/null +++ b/math/liouville.go @@ -0,0 +1,37 @@ +// liouville.go +// description: Returns λ(n) +// details: +// For any positive integer n, define λ(n) as the sum of the primitive nth roots of unity. +// It has values in {−1, 1} depending on the factorization of n into prime factors: +// λ(n) = +1 if n is a positive integer with an even number of prime factors. +// λ(n) = −1 if n is a positive integer with an odd number of prime factors. +// wikipedia: https://en.wikipedia.org/wiki/Liouville_function +// time complexity: O(log n) +// space complexity: O(1) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see liouville_test.go + +package math + +import ( + "errors" + + "github.com/TheAlgorithms/Go/math/prime" +) + +var ErrNonZeroArgsOnly error = errors.New("arguments cannot be zero") + +// Lambda is the liouville function +// This function returns λ(n) for given number +func LiouvilleLambda(n int) (int, error) { + switch { + case n < 0: + return 0, ErrPosArgsOnly + case n == 0: + return 0, ErrNonZeroArgsOnly + case len(prime.Factorize(int64(n)))%2 == 0: + return 1, nil + default: + return -1, nil + } +} diff --git a/math/liouville_test.go b/math/liouville_test.go new file mode 100644 index 000000000..41d327c3e --- /dev/null +++ b/math/liouville_test.go @@ -0,0 +1,39 @@ +// liouville_test.go +// description: Returns λ(n) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see liouville.go + +package math_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math" +) + +func TestLiouvilleLambda(t *testing.T) { + var tests = []struct { + name string + n int + expectedValue int + expectedError error + }{ + {"n = 10", 10, 1, nil}, + {"n = 11", 11, -1, nil}, + {"n = -1", -1, 0, math.ErrPosArgsOnly}, + {"n = 0", 0, 0, math.ErrNonZeroArgsOnly}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + result, err := math.LiouvilleLambda(test.n) + if result != test.expectedValue || test.expectedError != err { + t.Errorf("expected error: %s, got: %s; expected value: %v, got: %v", test.expectedError, err, test.expectedValue, result) + } + }) + } +} +func BenchmarkLiouvilleLambda(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = math.LiouvilleLambda(65536) + } +} diff --git a/math/math_test.go b/math/math_test.go new file mode 100644 index 000000000..943c734ca --- /dev/null +++ b/math/math_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package math diff --git a/math/matrix/add.go b/math/matrix/add.go new file mode 100644 index 000000000..d5d79efdd --- /dev/null +++ b/math/matrix/add.go @@ -0,0 +1,69 @@ +// add.go +// description: Add two matrices +// time complexity: O(n^2) +// space complexity: O(n^2) + +package matrix + +import ( + "context" + "errors" + "sync" +) + +// Add adds two matrices. +func (m1 Matrix[T]) Add(m2 Matrix[T]) (Matrix[T], error) { + // Check if the matrices have the same dimensions. + if !m1.MatchDimensions(m2) { + return Matrix[T]{}, errors.New("matrices are not compatible for addition") + } + + // Create a new matrix to store the result. + var zeroVal T + result := New(m1.Rows(), m1.Columns(), zeroVal) + + ctx, cancel := context.WithCancel(context.Background()) + defer cancel() // Make sure it's called to release resources even if no errors + + var wg sync.WaitGroup + errCh := make(chan error, 1) + + for i := 0; i < m1.rows; i++ { + i := i // Capture the loop variable for the goroutine + wg.Add(1) + go func() { + defer wg.Done() + for j := 0; j < m1.columns; j++ { + select { + case <-ctx.Done(): + return // Context canceled; return without an error + default: + } + + sum := m1.elements[i][j] + m2.elements[i][j] + err := result.Set(i, j, sum) + if err != nil { + cancel() // Cancel the context on error + select { + case errCh <- err: + default: + } + return + } + } + }() + } + + // Wait for all goroutines to finish + go func() { + wg.Wait() + close(errCh) + }() + + // Check for any errors + if err := <-errCh; err != nil { + return Matrix[T]{}, err + } + + return result, nil +} diff --git a/math/matrix/add_test.go b/math/matrix/add_test.go new file mode 100644 index 000000000..f3543965c --- /dev/null +++ b/math/matrix/add_test.go @@ -0,0 +1,58 @@ +package matrix_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestAdd(t *testing.T) { + // Create two matrices with the same dimensions for addition + m1 := matrix.New(2, 2, 1) + m2 := matrix.New(2, 2, 2) + + // Test case 1: Valid matrix addition + addedMatrix, err := m1.Add(m2) + if err != nil { + t.Errorf("Add(m1, m2) returned an error: %v, expected no error", err) + } + expectedMatrix := matrix.New(2, 2, 3) + res := addedMatrix.CheckEqual(expectedMatrix) + if !res { + t.Errorf("Add(m1, m2) returned incorrect result:\n%v\nExpected:\n%v", addedMatrix, expectedMatrix) + } + + // Create two matrices with different dimensions for addition + m3 := matrix.New(2, 2, 1) + m4 := matrix.New(2, 3, 2) + + // Test case 2: Matrices with different dimensions + _, err2 := m3.Add(m4) + expectedError2 := fmt.Errorf("matrices are not compatible for addition") + if err2 == nil || err2.Error() != expectedError2.Error() { + t.Errorf("Add(m3, m4) returned error: %v, expected error: %v", err2, expectedError2) + } + +} + +func BenchmarkAddSmallMatrix(b *testing.B) { + m1 := matrix.New(10, 10, 0) // Create a 10x10 matrix with all zeros + m2 := matrix.New(10, 10, 1) // Create a 10x10 matrix with all ones + + for i := 0; i < b.N; i++ { + _, _ = m1.Add(m2) + } +} + +func BenchmarkAddLargeMatrix(b *testing.B) { + size := 1000 // Choose an appropriate size for your large matrix + m1 := MakeRandomMatrix[int](size, size) + m2 := MakeRandomMatrix[int](size, size) + + b.ResetTimer() // Reset the timer to exclude setup time + + for i := 0; i < b.N; i++ { + _, _ = m1.Add(m2) + } +} diff --git a/math/matrix/checkequal.go b/math/matrix/checkequal.go new file mode 100644 index 000000000..005c657af --- /dev/null +++ b/math/matrix/checkequal.go @@ -0,0 +1,35 @@ +package matrix + +// CheckEqual checks if the current matrix is equal to another matrix (m2). +// Two matrices are considered equal if they have the same dimensions and +// all their elements are equal. +// time complexity: O(n*m) where n and m are the dimensions of the matrix +// space complexity: O(1) + +func (m1 Matrix[T]) CheckEqual(m2 Matrix[T]) bool { + if !m1.MatchDimensions(m2) { + return false + } + + c := make(chan bool) + + for i := range m1.elements { + go func(i int) { + for j := range m1.elements[i] { + if m1.elements[i][j] != m2.elements[i][j] { + c <- false + return + } + } + c <- true + }(i) + } + + for range m1.elements { + if !<-c { + return false + } + } + + return true +} diff --git a/math/matrix/checkequal_test.go b/math/matrix/checkequal_test.go new file mode 100644 index 000000000..be93d82d7 --- /dev/null +++ b/math/matrix/checkequal_test.go @@ -0,0 +1,62 @@ +package matrix_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestCheckEqual(t *testing.T) { + // Create two matrices with the same dimensions and equal values + m1 := matrix.New(2, 2, 0) + m2 := matrix.New(2, 2, 0) + + // Test case 1: Matrices are equal + equal := m1.CheckEqual(m2) + + if !equal { + t.Errorf("CheckEqual(m1, m2) returned false, expected true (matrices are equal)") + } + + // Create two matrices with the same dimensions but different values + m3 := matrix.New(2, 2, 1) + m4 := matrix.New(2, 2, 0) + + // Test case 2: Matrices are not equal + equal2 := m3.CheckEqual(m4) + if equal2 { + t.Errorf("CheckEqual(m3, m4) returned true, expected false (matrices are not equal)") + } + + // Create two matrices with different dimensions + m5 := matrix.New(2, 2, 0) + m6 := matrix.New(2, 3, 0) + + // Test case 3: Matrices have different dimensions + equal3 := m5.CheckEqual(m6) + + if equal3 { + t.Errorf("CheckEqual(m5, m6) returned true, expected false (matrices are not equal)") + } +} + +func BenchmarkCheckEqualSmallMatrix(b *testing.B) { + m1 := matrix.New(10, 10, 0) // Create a 10x10 matrix with all zeros + m2 := matrix.New(10, 10, 0) // Create another 10x10 matrix with all zeros + + for i := 0; i < b.N; i++ { + _ = m1.CheckEqual(m2) + } +} + +func BenchmarkCheckEqualLargeMatrix(b *testing.B) { + size := 1000 // Choose an appropriate size for your large matrix + m1 := MakeRandomMatrix[int](size, size) + m2 := MakeRandomMatrix[int](size, size) + + b.ResetTimer() // Reset the timer to exclude setup time + + for i := 0; i < b.N; i++ { + _ = m1.CheckEqual(m2) + } +} diff --git a/math/matrix/copy.go b/math/matrix/copy.go new file mode 100644 index 000000000..11afb9237 --- /dev/null +++ b/math/matrix/copy.go @@ -0,0 +1,59 @@ +// copy.go +// description: Copy a matrix +// details: This function creates a new matrix with the same dimensions as the original matrix and copies all the elements from the original matrix to the new matrix. +// time complexity: O(n*m) where n and m are the dimensions of the matrix +// space complexity: O(n*m) where n and m are the dimensions of the matrix + +package matrix + +import "sync" + +func (m Matrix[T]) Copy() (Matrix[T], error) { + + rows := m.Rows() + columns := m.Columns() + if rows == 0 || columns == 0 { + return Matrix[T]{}, nil + } + zeroVal, err := m.Get(0, 0) // Get the zero value of the element type + if err != nil { + return Matrix[T]{}, err + } + copyMatrix := New(rows, columns, zeroVal) + var wg sync.WaitGroup + wg.Add(rows) + errChan := make(chan error, 1) + + for i := 0; i < rows; i++ { + go func(i int) { + defer wg.Done() + for j := 0; j < columns; j++ { + val, err := m.Get(i, j) + if err != nil { + select { + case errChan <- err: + default: + } + return + } + err = copyMatrix.Set(i, j, val) + if err != nil { + select { + case errChan <- err: + default: + } + return + } + } + }(i) + } + + wg.Wait() + close(errChan) + + if err, ok := <-errChan; ok { + return Matrix[T]{}, err + } + + return copyMatrix, nil +} diff --git a/math/matrix/copy_test.go b/math/matrix/copy_test.go new file mode 100644 index 000000000..027902843 --- /dev/null +++ b/math/matrix/copy_test.go @@ -0,0 +1,115 @@ +package matrix_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestMatrixCopy(t *testing.T) { + // Create a sample matrix + data := [][]int{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} + // Ensure that the copy is not the same as the original + matrix, err := matrix.NewFromElements(data) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + copyMatrix, err := matrix.Copy() + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + + // Ensure that the copy is not the same as the original + if &matrix == ©Matrix { + t.Errorf("Copy did not create a new matrix.") + } + + for i := 0; i < matrix.Rows(); i++ { + for j := 0; j < matrix.Columns(); j++ { + val1, err := matrix.Get(i, j) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + val2, err := copyMatrix.Get(i, j) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + if val1 != val2 { + t.Errorf("Copy did not correctly copy element (%d, %d).", i, j) + } + } + } + +} + +func TestMatrixCopyEmpty(t *testing.T) { + // Create an empty matrix + emptyMatrix := matrix.New(0, 0, 0) + + // Make a copy of the empty matrix + copyMatrix, err := emptyMatrix.Copy() + if err != nil { // as empty matrix + t.Fatalf("Failed to copy matrix: %v", err) + } + + // Ensure that the copy is not the same as the original by comparing their addresses + if &emptyMatrix == ©Matrix { + t.Errorf("Copy did not create a new matrix for an empty matrix.") + } + + // Check if the copy is also empty + if copyMatrix.Rows() != 0 || copyMatrix.Columns() != 0 { + t.Errorf("Copy of an empty matrix should also be empty.") + } +} + +func TestMatrixCopyWithDefaultValues(t *testing.T) { + // Create a matrix with default values (zeroes) + rows, columns := 3, 3 + defaultValue := 0 + defaultMatrix := matrix.New(rows, columns, defaultValue) + + // Make a copy of the matrix + copyMatrix, err := defaultMatrix.Copy() + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + + // Ensure that the copy is not the same as the original by comparing their addresses + if &defaultMatrix == ©Matrix { + t.Errorf("Copy did not create a new matrix for default values.") + } + + // Check if the copy has the same values as the original (all zeroes) + for i := 0; i < defaultMatrix.Rows(); i++ { + for j := 0; j < defaultMatrix.Columns(); j++ { + val1, err := defaultMatrix.Get(i, j) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + val2, err := copyMatrix.Get(i, j) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + if val1 != val2 || val1 != defaultValue || val2 != defaultValue { + t.Errorf("Copy did not preserve default values at row %d, column %d. Expected %v, got %v", i, j, defaultValue, val2) + } + } + } +} + +func BenchmarkCopyMatrix(b *testing.B) { + // Create a matrix for benchmarking + rows := 100 + columns := 100 + initialValue := 0 + matrix := matrix.New(rows, columns, initialValue) + + // Reset the benchmark timer + b.ResetTimer() + + // Run the benchmarks + for i := 0; i < b.N; i++ { + _, _ = matrix.Copy() + } +} diff --git a/math/matrix/determinant.go b/math/matrix/determinant.go new file mode 100644 index 000000000..371b1fa0a --- /dev/null +++ b/math/matrix/determinant.go @@ -0,0 +1,61 @@ +// determinant.go +// description: This method finds the determinant of a matrix. +// details: For a theoretical explanation as for what the determinant +// represents, see the [Wikipedia Article](https://en.wikipedia.org/wiki/Determinant) +// time complexity: O(n!) where n is the number of rows and columns in the matrix. +// space complexity: O(n^2) where n is the number of rows and columns in the matrix. +// author [Carter907](https://github.com/Carter907) +// see determinant_test.go + +package matrix + +import ( + "errors" +) + +// Calculates the determinant of the matrix. +// This method only works for square matrices (e.i. matrices with equal rows and columns). +func (mat Matrix[T]) Determinant() (T, error) { + + var determinant T = 0 + var elements = mat.elements + if mat.rows != mat.columns { + + return 0, errors.New("Matrix rows and columns must equal in order to find the determinant.") + } + + // Specify base cases for different sized matrices. + switch mat.rows { + case 1: + return elements[0][0], nil + case 2: + return elements[0][0]*elements[1][1] - elements[1][0]*elements[0][1], nil + default: + for i := 0; i < mat.rows; i++ { + + var initialValue T = 0 + minor := New(mat.rows-1, mat.columns-1, initialValue) + // Fill the contents of minor excluding the 0th row and the ith column. + for j, minor_i := 1, 0; j < mat.rows && minor_i < minor.rows; j, minor_i = j+1, minor_i+1 { + for k, minor_j := 0, 0; k < mat.rows && minor_j < minor.rows; k, minor_j = k+1, minor_j+1 { + if k != i { + minor.elements[minor_i][minor_j] = elements[j][k] + } else { + minor_j-- // Decrement the column of minor to account for skipping the ith column of the matrix. + } + } + } + + if i%2 == 0 { + minor_det, _ := minor.Determinant() + + determinant += elements[0][i] * minor_det + } else { + minor_det, _ := minor.Determinant() + + determinant += elements[0][i] * minor_det + } + } + return determinant, nil + } +} diff --git a/math/matrix/determinant_test.go b/math/matrix/determinant_test.go new file mode 100644 index 000000000..801058ff2 --- /dev/null +++ b/math/matrix/determinant_test.go @@ -0,0 +1,142 @@ +package matrix_test + +import ( + "errors" + "math" + "math/rand" + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +// Test different matrix contents +func TestMatrixDeterminant(t *testing.T) { + // Find Determinant of a 2 by 2 matrix. + matrix1, err := matrix.NewFromElements([][]int{ + {3, 8}, + {4, 6}, + }) + if err != nil { + t.Fatalf("Error creating 3 by 3 matrix: %v", err) + } + determinant, err := matrix1.Determinant() + if err != nil { + t.Fatalf("Error returned from 3 by 3 matrix: %v", err) + } + if determinant != -14 { + t.Fatalf("Determinant returned for a 3 by 3 matrix was %d; wanted -14", determinant) + } + + // Find Dertminant of a 1 by 1 matrix + expectedValue := rand.Intn(math.MaxInt) + matrix2, err := matrix.NewFromElements([][]int{ + {expectedValue}, + }) + if err != nil { + t.Fatalf("Error creating 1 by 1 matrix: %v", err) + } + determinant, err = matrix2.Determinant() + if err != nil { + t.Fatalf("Error returned from 1 by 1 matrix: %v", err) + } + if determinant != expectedValue { + t.Fatalf("Determinant returned for a 1 by 1 matrix was %d; wanted %d", determinant, expectedValue) + } + +} + +func TestEmptyMatrix(t *testing.T) { + emptyElements := [][]int{} + matrix, err := matrix.NewFromElements(emptyElements) + + if err != nil { + t.Fatalf("Error creating Matrix with empty elements: %v", err) + } + + determinant, err := matrix.Determinant() + + if err != nil { + t.Fatalf("Determinant returned an error for empty matrix: %v", err) + } + + // Check that 0 is returned from an empty matrix. + expectedValue := 0 + if determinant != expectedValue { + t.Errorf("Determinant returned from empty matrix was %d; wanted %d", determinant, expectedValue) + } + +} + +func TestNonSquareMatrix(t *testing.T) { + // Creating non-square matrix for testing. + initialValue := 0 + initialRows := 4 + initialCols := 2 + + nonSquareMatrix := matrix.New(initialRows, initialCols, initialValue) + + determinant, err := nonSquareMatrix.Determinant() + // Check if non square matrix returns an error. + if err == nil { + t.Fatalf("No error was returned for a non-square matrix") + } + + // Check if the correct error was returned. + expectedError := errors.New("Matrix rows and columns must equal in order to find the determinant.") + + if err.Error() != expectedError.Error() { + t.Errorf("Error returned from non-square matrix was \n\"%v\"; \nwanted \n\"%v\"", err, expectedError) + } + + // Check if the determinant of the non-square matrix is 0. + if determinant != 0 { + t.Errorf("Determinant of non-square matrix was not 0 but was %d", determinant) + } + +} + +// Test matrix returned from matrix.New +func TestDefaultMatrix(t *testing.T) { + initialValue := 0 + initialRows := 3 + initialCols := 3 + defaultMatrix := matrix.New(initialRows, initialCols, initialValue) + + determinant, err := defaultMatrix.Determinant() + + if err != nil { + t.Fatalf("Error finding the determinant of 3 by 3 default matrix: %v.", err) + } + expectedValue := 0 + if determinant != expectedValue { + t.Errorf("Determinant of the default matrix with an initial value 0 was %d; wanted %d.", initialValue, expectedValue) + } +} + +// Benchmark a 3 by 3 matrix for computational throughput +func BenchmarkSmallMatrixDeterminant(b *testing.B) { + // Create a 3 by 3 matrix for benchmarking + rows := 3 + columns := 3 + initialValue := 0 + matrix := matrix.New(rows, columns, initialValue) + + for i := 0; i < b.N; i++ { + _, _ = matrix.Determinant() + } +} + +// Benchmark a 10 by 10 matrix for computational throughput. +func BenchmarkMatrixDeterminant(b *testing.B) { + // Create a 10 by 10 matrix for benchmarking + rows := 10 + columns := 10 + initialValue := 0 + matrix := matrix.New(rows, columns, initialValue) + + b.ResetTimer() + + for i := 0; i < b.N; i++ { + _, _ = matrix.Determinant() + } +} diff --git a/math/matrix/isvalid.go b/math/matrix/isvalid.go new file mode 100644 index 000000000..afe8f5ed3 --- /dev/null +++ b/math/matrix/isvalid.go @@ -0,0 +1,17 @@ +package matrix + +import "github.com/TheAlgorithms/Go/constraints" + +// IsValid checks if the input matrix has consistent row lengths. +func IsValid[T constraints.Integer](elements [][]T) bool { + if len(elements) == 0 { + return true + } + columns := len(elements[0]) + for _, row := range elements { + if len(row) != columns { + return false + } + } + return true +} diff --git a/math/matrix/isvalid_test.go b/math/matrix/isvalid_test.go new file mode 100644 index 000000000..ea7dae338 --- /dev/null +++ b/math/matrix/isvalid_test.go @@ -0,0 +1,64 @@ +package matrix_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestIsValid(t *testing.T) { + // Test case 1: Valid matrix with consistent row lengths + validMatrix := [][]int{ + {1, 2, 3}, + {4, 5, 6}, + {7, 8, 9}, + } + result1 := matrix.IsValid(validMatrix) + if !result1 { + t.Errorf("IsValid(validMatrix) returned false, expected true (valid matrix)") + } + + // Test case 2: Valid matrix with empty rows (no inconsistency) + validMatrixEmptyRows := [][]int{ + {}, + {}, + {}, + } + result2 := matrix.IsValid(validMatrixEmptyRows) + if !result2 { + t.Errorf("IsValid(validMatrixEmptyRows) returned false, expected true (valid matrix with empty rows)") + } + + // Test case 3: Invalid matrix with inconsistent row lengths + invalidMatrix := [][]int{ + {1, 2, 3}, + {4, 5}, + {6, 7, 8}, + } + result3 := matrix.IsValid(invalidMatrix) + if result3 { + t.Errorf("IsValid(invalidMatrix) returned true, expected false (invalid matrix with inconsistent row lengths)") + } + +} + +func BenchmarkIsValid(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + elements := make([][]int, rows) + for i := range elements { + elements[i] = make([]int, columns) + for j := range elements[i] { + elements[i][j] = i*columns + j // Some arbitrary values + } + } + + // Reset the benchmark timer + b.ResetTimer() + + // Run the benchmark + for i := 0; i < b.N; i++ { + _ = matrix.IsValid(elements) + } +} diff --git a/math/matrix/matchdimensions.go b/math/matrix/matchdimensions.go new file mode 100644 index 000000000..982409191 --- /dev/null +++ b/math/matrix/matchdimensions.go @@ -0,0 +1,9 @@ +package matrix + +// MatchDimensions checks if two matrices have the same dimensions. +func (m Matrix[T]) MatchDimensions(m1 Matrix[T]) bool { + if m.rows == m1.rows && m.columns == m1.columns { + return true + } + return false +} diff --git a/math/matrix/matchdimensions_test.go b/math/matrix/matchdimensions_test.go new file mode 100644 index 000000000..645b4211f --- /dev/null +++ b/math/matrix/matchdimensions_test.go @@ -0,0 +1,40 @@ +package matrix_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestMatrixMatchDimensions(t *testing.T) { + // Create two matrices with the same dimensions + m1 := matrix.New(2, 3, 0) + m2 := matrix.New(2, 3, 0) + + // Test case 1: Same dimensions + if !m1.MatchDimensions(m2) { + t.Errorf("m1.MatchDimensions(m2) returned %t, expected 1 (same dimensions)", m1.MatchDimensions(m2)) + } + + // Create two matrices with different dimensions + m3 := matrix.New(2, 3, 0) + m4 := matrix.New(3, 2, 0) + + // Test case 2: Different dimensions + if m3.MatchDimensions(m4) { + t.Errorf("m3.MatchDimensions(m4) returned : %v, expected: %v", m3.MatchDimensions(m4), false) + } +} + +// BenchmarkMatchDimensions benchmarks the MatchDimensions method. +func BenchmarkMatchDimensions(b *testing.B) { + // Create sample matrices for benchmarking + rows := 100 + columns := 100 + m1 := matrix.New(rows, columns, 0) // Replace with appropriate values + m2 := matrix.New(rows, columns, 0) // Replace with appropriate values + + for i := 0; i < b.N; i++ { + _ = m1.MatchDimensions(m2) + } +} diff --git a/math/matrix/matrix.go b/math/matrix/matrix.go new file mode 100644 index 000000000..5a03e1e0b --- /dev/null +++ b/math/matrix/matrix.go @@ -0,0 +1,92 @@ +package matrix + +import ( + "errors" + "sync" + + "github.com/TheAlgorithms/Go/constraints" +) + +type Matrix[T constraints.Integer] struct { + elements [][]T + rows int + columns int +} + +// NewMatrix creates a new Matrix based on the provided arguments. +func New[T constraints.Integer](rows, columns int, initial T) Matrix[T] { + if rows < 0 || columns < 0 { + return Matrix[T]{} // Invalid dimensions, return an empty matrix + } + + // Initialize the matrix with the specified dimensions and fill it with the initial value. + elements := make([][]T, rows) + var wg sync.WaitGroup + wg.Add(rows) + + for i := range elements { + go func(i int) { + defer wg.Done() + elements[i] = make([]T, columns) + for j := range elements[i] { + elements[i][j] = initial + } + }(i) + } + + wg.Wait() + + return Matrix[T]{elements, rows, columns} +} + +// NewFromElements creates a new Matrix from the given elements. +func NewFromElements[T constraints.Integer](elements [][]T) (Matrix[T], error) { + if !IsValid(elements) { + return Matrix[T]{}, errors.New("rows have different numbers of columns") + } + rows := len(elements) + if rows == 0 { + return Matrix[T]{}, nil // Empty matrix + } + + columns := len(elements[0]) + matrix := Matrix[T]{ + elements: make([][]T, rows), + rows: rows, // Set the rows field + columns: columns, // Set the columns field + } + for i := range matrix.elements { + matrix.elements[i] = make([]T, columns) + copy(matrix.elements[i], elements[i]) + } + + return matrix, nil +} + +func (m Matrix[T]) Get(row, col int) (T, error) { + if row < 0 || row >= m.rows || col < 0 || col >= m.columns { + var zeroVal T + return zeroVal, errors.New("index out of range") + } + return m.elements[row][col], nil +} + +func (m Matrix[T]) Set(row, col int, val T) error { + if row < 0 || row >= m.rows || col < 0 || col >= m.columns { + return errors.New("index out of bounds") + } + + m.elements[row][col] = val + return nil +} + +func (m Matrix[T]) Rows() int { + return len(m.elements) +} + +func (m Matrix[T]) Columns() int { + if len(m.elements) == 0 { + return 0 + } + return len(m.elements[0]) +} diff --git a/math/matrix/matrix_test.go b/math/matrix/matrix_test.go new file mode 100644 index 000000000..b8c0f7c72 --- /dev/null +++ b/math/matrix/matrix_test.go @@ -0,0 +1,250 @@ +package matrix_test + +import ( + "errors" + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestNewMatrix(t *testing.T) { + + nullMatrix := matrix.New(0, 0, 0) + if nullMatrix.Rows() != 0 || nullMatrix.Columns() != 0 { + t.Errorf("matrix.New( 0, 0, 0) returned nil, expected a matrix") + } + // Test creating a matrix of integers + intMatrix := matrix.New(3, 4, 0) + if intMatrix.Rows() != 3 || intMatrix.Columns() != 4 { + t.Errorf("matrix.New( 3, 4, 0) returned nil, expected a matrix") + } + +} + +func TestNewFromElements(t *testing.T) { + // Test case 1: Valid matrix + validElements := [][]int{ + {1, 2, 3}, + {4, 5, 6}, + } + expectedm1 := matrix.New(2, 3, 0) + for i := 0; i < len(validElements); i++ { + for j := 0; j < len(validElements[0]); j++ { + err := expectedm1.Set(i, j, validElements[i][j]) + if err != nil { + t.Errorf("copyMatrix.Set error: %s", err.Error()) + } + } + } + + m1, err1 := matrix.NewFromElements(validElements) + if err1 != nil { + t.Errorf("NewFromElements(validElements) returned an error: %v", err1) + } + res := m1.CheckEqual(expectedm1) + if res != true { + t.Errorf("NewFromElements(validElements) returned %v, expected %v", m1, expectedm1) + } + + // Test case 2: Invalid matrix with different column counts + invalidElements := [][]int{ + {1, 2, 3}, + {4, 5}, + } + _, err2 := matrix.NewFromElements(invalidElements) + expectedError2 := errors.New("rows have different numbers of columns") + if err2 == nil || err2.Error() != expectedError2.Error() { + t.Errorf("NewFromElements(invalidElements) returned error: %v, expected error: %v", err2, expectedError2) + } + + // Test case 3: Empty matrix + emptyElements := [][]int{} + m3, err3 := matrix.NewFromElements(emptyElements) + if err3 != nil { + t.Errorf("NewFromElements(emptyElements) returned an error: %v", err3) + } + if m3.Rows() != 0 || m3.Columns() != 0 { + t.Errorf("NewFromElements(emptyElements) returned %v, expected nil", m3) + } +} + +func TestMatrixGet(t *testing.T) { + // Create a sample matrix for testing + matrix := matrix.New(3, 3, 0) + err := matrix.Set(1, 1, 42) // Set a specific value for testing + if err != nil { + t.Errorf("copyMatrix.Set error: %s", err.Error()) + } + // Test case 1: Valid Get + val1, err1 := matrix.Get(1, 1) + if err1 != nil { + t.Errorf("matrix.Get(1, 1) returned an error: %v, expected no error", err1) + } + if val1 != 42 { + t.Errorf("matrix.Get(1, 1) returned %v, expected 42", val1) + } + + // Test case 2: Get with invalid indices + _, err2 := matrix.Get(10, 10) + expectedError2 := errors.New("index out of range") + if err2 == nil || err2.Error() != expectedError2.Error() { + t.Errorf("matrix.Get(10, 10) returned error: %v, expected error: %v", err2, expectedError2) + } + // Test case 3: Get with invalid indices + _, err3 := matrix.Get(-1, -3) + expectedError3 := errors.New("index out of range") + if err3 == nil || err3.Error() != expectedError3.Error() { + t.Errorf("matrix.Get(10, 10) returned error: %v, expected error: %v", err3, expectedError3) + } +} + +func TestMatrixSet(t *testing.T) { + // Create a sample matrix for testing + matrix := matrix.New(3, 3, 0) + + // Test case 1: Valid Set + err1 := matrix.Set(1, 1, 42) + if err1 != nil { + t.Errorf("matrix.Set(1, 1, 42) returned an error: %v, expected no error", err1) + } + val1, err := matrix.Get(1, 1) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + if val1 != 42 { + t.Errorf("matrix.Set(1, 1, 42) did not set the value correctly, expected 42, got %v", val1) + } + + // Test case 2: Set with invalid indices + err2 := matrix.Set(10, 10, 100) + expectedError2 := errors.New("index out of bounds") + if err2 == nil || err2.Error() != expectedError2.Error() { + t.Errorf("matrix.Set(10, 10, 100) returned error: %v, expected error: %v", err2, expectedError2) + } + // Test case 3: Get with invalid indices + err3 := matrix.Set(-13, -1, 100) + expectedError3 := errors.New("index out of bounds") + if err3 == nil || err3.Error() != expectedError3.Error() { + t.Errorf("matrix.Get(10, 10) returned error: %v, expected error: %v", err3, expectedError3) + } +} + +func TestMatrixRows(t *testing.T) { + // Create a sample matrix + data := [][]int{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} + matrix, err := matrix.NewFromElements(data) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + // Check the number of rows + expectedRows := len(data) + rows := matrix.Rows() + if rows != expectedRows { + t.Errorf("Expected %d rows, but got %d", expectedRows, rows) + } +} + +func TestMatrixColumns(t *testing.T) { + // Create a sample matrix + data := [][]int{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} + matrix, err := matrix.NewFromElements(data) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + // Check the number of columns + expectedColumns := len(data[0]) + columns := matrix.Columns() + if columns != expectedColumns { + t.Errorf("Expected %d columns, but got %d", expectedColumns, columns) + } +} + +func TestMatrixEmptyRowsAndColumns(t *testing.T) { + // Create an empty matrix + emptyMatrix := matrix.New(0, 0, 0) + + // Check the number of rows and columns for an empty matrix + rows := emptyMatrix.Rows() + columns := emptyMatrix.Columns() + + if rows != 0 { + t.Errorf("Expected 0 rows for an empty matrix, but got %d", rows) + } + + if columns != 0 { + t.Errorf("Expected 0 columns for an empty matrix, but got %d", columns) + } +} + +// BenchmarkNew benchmarks the New function. +func BenchmarkNew(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = matrix.New(100, 100, 0) // Change the arguments to match your use case + } +} + +// BenchmarkNewFromElements benchmarks the NewFromElements function. +func BenchmarkNewFromElements(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + elements := make([][]int, rows) + for i := range elements { + elements[i] = make([]int, columns) + for j := range elements[i] { + elements[i][j] = i*columns + j // Some arbitrary values + } + } + + for i := 0; i < b.N; i++ { + _, _ = matrix.NewFromElements(elements) + } +} + +// BenchmarkGet benchmarks the Get method. +func BenchmarkGet(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + matrix := matrix.New(rows, columns, 0) + + for i := 0; i < b.N; i++ { + _, _ = matrix.Get(50, 50) // Change the row and column indices as needed + } +} + +// BenchmarkSet benchmarks the Set method. +func BenchmarkSet(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + matrix := matrix.New(rows, columns, 0) + + for i := 0; i < b.N; i++ { + _ = matrix.Set(50, 50, 42) // Change the row, column, and value as needed + } +} + +// BenchmarkRows benchmarks the Rows method. +func BenchmarkRows(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + matrix := matrix.New(rows, columns, 0) + + for i := 0; i < b.N; i++ { + _ = matrix.Rows() + } +} + +// BenchmarkColumns benchmarks the Columns method. +func BenchmarkColumns(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + matrix := matrix.New(rows, columns, 0) + + for i := 0; i < b.N; i++ { + _ = matrix.Columns() + } +} diff --git a/math/matrix/multiply.go b/math/matrix/multiply.go new file mode 100644 index 000000000..f59213da6 --- /dev/null +++ b/math/matrix/multiply.go @@ -0,0 +1,91 @@ +// multiply.go +// description: Implementation of matrix multiplication +// time complexity: O(n^3) where n is the number of rows in the first matrix +// space complexity: O(n^2) where n is the number of rows in the first matrix + +package matrix + +import ( + "context" + "errors" + "sync" +) + +// Multiply multiplies the current matrix (m1) with another matrix (m2) and returns the result as a new matrix. +func (m1 Matrix[T]) Multiply(m2 Matrix[T]) (Matrix[T], error) { + // Check if the matrices can be multiplied. + if m1.Columns() != m2.Rows() { + return Matrix[T]{}, errors.New("matrices cannot be multiplied: column count of the first matrix must match row count of the second matrix") + } + + // Create a new matrix to store the result. + var zeroVal T + result := New(m1.Rows(), m2.Columns(), zeroVal) + + ctx, cancel := context.WithCancel(context.Background()) + defer cancel() // Make sure it's called to release resources even if no errors + + var wg sync.WaitGroup + errCh := make(chan error, 1) + + for i := 0; i < m1.Rows(); i++ { + for j := 0; j < m2.Columns(); j++ { + i, j := i, j // Capture the loop variable for the goroutine + wg.Add(1) + go func() { + defer wg.Done() + // Compute the dot product of the row from the first matrix and the column from the second matrix. + dotProduct := zeroVal + for k := 0; k < m1.Columns(); k++ { + select { + case <-ctx.Done(): + return // Context canceled; return without an error + default: + } + + val1, err := m1.Get(i, k) + if err != nil { + cancel() + select { + case errCh <- err: + default: + } + return + } + val2, err := m2.Get(k, j) + if err != nil { + cancel() + select { + case errCh <- err: + default: + } + return + } + dotProduct += val1 * val2 + } + err := result.Set(i, j, dotProduct) + if err != nil { + cancel() + select { + case errCh <- err: + default: + } + return + } + }() + } + } + + // Wait for all goroutines to finish + go func() { + wg.Wait() + close(errCh) + }() + + // Check for any errors + if err := <-errCh; err != nil { + return Matrix[T]{}, err + } + + return result, nil +} diff --git a/math/matrix/multiply_test.go b/math/matrix/multiply_test.go new file mode 100644 index 000000000..1a1ca39a7 --- /dev/null +++ b/math/matrix/multiply_test.go @@ -0,0 +1,101 @@ +package matrix_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestMultiplyMatrix(t *testing.T) { + // Test case with compatible NULL matrices + t.Run("NULL Matrices", func(t *testing.T) { + mat1 := matrix.New(0, 0, 0) + mat2 := matrix.New(0, 0, 0) + + expected := matrix.New(0, 0, 0) + result, err := mat1.Multiply(mat2) + if err != nil { + t.Errorf("Expected no error, got %v", err) + } else if !result.CheckEqual(expected) { + t.Errorf("Result matrix does not match the expected result.") + } + + }) + // Test case with compatible matrices + t.Run("Compatible Matrices", func(t *testing.T) { + mat1 := [][]int{{1, 2, 3}, {4, 5, 6}} + mat2 := [][]int{{7, 8}, {9, 10}, {11, 12}} + m1, err := matrix.NewFromElements(mat1) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + m2, err := matrix.NewFromElements(mat2) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + exp := [][]int{{58, 64}, {139, 154}} + expected, err := matrix.NewFromElements(exp) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + result, err := m1.Multiply(m2) + if err != nil { + t.Errorf("Expected no error, got %v", err) + } else if !result.CheckEqual(expected) { + t.Errorf("Result matrix does not match the expected result.") + } + + }) + +} + +func TestMultiplyIncompatibleMatrix(t *testing.T) { + // Test case with incompatible matrices + t.Run("Incompatible Matrices", func(t *testing.T) { + mat1 := [][]int{{1, 2, 3}, {4, 5, 6}} + mat2 := [][]int{{7, 8}, {9, 10}} + m1, err := matrix.NewFromElements(mat1) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + m2, err := matrix.NewFromElements(mat2) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + + _, err = m1.Multiply(m2) + if err == nil { + t.Error("Expected an error, but got none") + } + }) + + t.Run("Incompatible Matrices", func(t *testing.T) { + mat1 := [][]int{{1, 2}} + mat2 := [][]int{{}} + m1, err := matrix.NewFromElements(mat1) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + m2, err := matrix.NewFromElements(mat2) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + _, err = m1.Multiply(m2) + + if err == nil { + t.Error("Expected an error, but got none") + } + }) +} + +func BenchmarkMatrixMultiply(b *testing.B) { + // Create sample matrices for benchmarking + rows := 10 + columns := 10 + m1 := matrix.New(rows, columns, 2) // Replace with appropriate values + m2 := matrix.New(rows, columns, 3) // Replace with appropriate values + + for i := 0; i < b.N; i++ { + _, _ = m1.Multiply(m2) + } +} diff --git a/math/matrix/strassenmatrixmultiply.go b/math/matrix/strassenmatrixmultiply.go new file mode 100644 index 000000000..9b5f01fdf --- /dev/null +++ b/math/matrix/strassenmatrixmultiply.go @@ -0,0 +1,229 @@ +// filename: strassenmatrixmultiply.go +// description: Implements matrix multiplication using the Strassen algorithm. +// details: +// This program takes two matrices as input and performs matrix multiplication +// using the Strassen algorithm, which is an optimized divide-and-conquer +// approach. It allows for efficient multiplication of large matrices. +// time complexity: O(n^2.81) +// space complexity: O(n^2) +// author(s): Mohit Raghav(https://github.com/mohit07raghav19) +// See strassenmatrixmultiply_test.go for test cases +package matrix + +// Perform matrix multiplication using Strassen's algorithm +func (A Matrix[T]) StrassenMatrixMultiply(B Matrix[T]) (Matrix[T], error) { + n := A.rows + // Check if matrices are 2x2 or smaller + if n == 1 { + a1, err := A.Get(0, 0) + if err != nil { + return Matrix[T]{}, err + } + b1, err := B.Get(0, 0) + if err != nil { + return Matrix[T]{}, err + } + result := New(1, 1, a1*b1) + return result, nil + } else { + // Calculate the size of submatrices + mid := n / 2 + + // Create submatrices + A11, err := A.SubMatrix(0, 0, mid, mid) + if err != nil { + return Matrix[T]{}, err + } + A12, err := A.SubMatrix(0, mid, mid, n-mid) + if err != nil { + return Matrix[T]{}, err + } + A21, err := A.SubMatrix(mid, 0, n-mid, mid) + if err != nil { + return Matrix[T]{}, err + } + A22, err := A.SubMatrix(mid, mid, n-mid, n-mid) + if err != nil { + return Matrix[T]{}, err + } + + B11, err := B.SubMatrix(0, 0, mid, mid) + if err != nil { + return Matrix[T]{}, err + } + B12, err := B.SubMatrix(0, mid, mid, n-mid) + if err != nil { + return Matrix[T]{}, err + } + B21, err := B.SubMatrix(mid, 0, n-mid, mid) + if err != nil { + return Matrix[T]{}, err + } + B22, err := B.SubMatrix(mid, mid, n-mid, n-mid) + if err != nil { + return Matrix[T]{}, err + } + + // Calculate result submatrices + A1, err := A11.Add(A22) + if err != nil { + return Matrix[T]{}, err + } + + A2, err := B11.Add(B22) + if err != nil { + return Matrix[T]{}, err + } + + A3, err := A21.Add(A22) + if err != nil { + return Matrix[T]{}, err + } + + A4, err := A11.Add(A12) + if err != nil { + return Matrix[T]{}, err + } + + A5, err := B11.Add(B12) + if err != nil { + return Matrix[T]{}, err + } + + A6, err := B21.Add(B22) + if err != nil { + return Matrix[T]{}, err + } + // + S1, err := B12.Subtract(B22) + if err != nil { + return Matrix[T]{}, err + } + S2, err := B21.Subtract(B11) + if err != nil { + return Matrix[T]{}, err + } + S3, err := A21.Subtract(A11) + if err != nil { + return Matrix[T]{}, err + } + S4, err := A12.Subtract(A22) + if err != nil { + return Matrix[T]{}, err + } + // Recursive steps + M1, err := A1.StrassenMatrixMultiply(A2) + if err != nil { + return Matrix[T]{}, err + } + M2, err := A3.StrassenMatrixMultiply(B11) + if err != nil { + return Matrix[T]{}, err + } + M3, err := A11.StrassenMatrixMultiply(S1) + if err != nil { + return Matrix[T]{}, err + } + M4, err := A22.StrassenMatrixMultiply(S2) + if err != nil { + return Matrix[T]{}, err + } + M5, err := A4.StrassenMatrixMultiply(B22) + if err != nil { + return Matrix[T]{}, err + } + M6, err := S3.StrassenMatrixMultiply(A5) + if err != nil { + return Matrix[T]{}, err + } + M7, err := S4.StrassenMatrixMultiply(A6) + + if err != nil { + return Matrix[T]{}, err + } // + A7, err := M1.Add(M4) + + if err != nil { + return Matrix[T]{}, err + } + A8, err := A7.Add(M7) + + if err != nil { + return Matrix[T]{}, err + } + A9, err := M1.Add(M3) + + if err != nil { + return Matrix[T]{}, err + } + A10, err := A9.Add(M6) + + if err != nil { + return Matrix[T]{}, err + } + // Calculate result submatrices + C11, err := A8.Subtract(M5) + if err != nil { + return Matrix[T]{}, err + } + C12, err := M3.Add(M5) + if err != nil { + return Matrix[T]{}, err + } + C21, err := M2.Add(M4) + if err != nil { + return Matrix[T]{}, err + } + C22, err := A10.Subtract(M2) + if err != nil { + return Matrix[T]{}, err + } + + // Combine subMatrices into the result matrix + var zeroVal T + C := New(n, n, zeroVal) + + for i := 0; i < mid; i++ { + for j := 0; j < mid; j++ { + val, err := C11.Get(i, j) + if err != nil { + return Matrix[T]{}, err + } + + err = C.Set(i, j, val) + if err != nil { + return Matrix[T]{}, err + } + + val, err = C12.Get(i, j) + if err != nil { + return Matrix[T]{}, err + } + + err1 := C.Set(i, j+mid, val) + if err1 != nil { + return Matrix[T]{}, err1 + } + val, err = C21.Get(i, j) + if err != nil { + return Matrix[T]{}, err + } + + err2 := C.Set(i+mid, j, val) + if err2 != nil { + return Matrix[T]{}, err2 + } + val, err = C22.Get(i, j) + if err != nil { + return Matrix[T]{}, err + } + + err3 := C.Set(i+mid, j+mid, val) + if err3 != nil { + return Matrix[T]{}, err3 + } + } + } + return C, nil + } +} diff --git a/math/matrix/strassenmatrixmultiply_test.go b/math/matrix/strassenmatrixmultiply_test.go new file mode 100644 index 000000000..b47b4c8fc --- /dev/null +++ b/math/matrix/strassenmatrixmultiply_test.go @@ -0,0 +1,131 @@ +package matrix_test + +import ( + "math/rand" + "testing" + "time" + + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestStrassenMatrixMultiply(t *testing.T) { + // Create two sample matrices + dataA := [][]int{{1, 2}, {4, 5}} + dataB := [][]int{{9, 8}, {6, 5}} + matrixA, err := matrix.NewFromElements(dataA) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + matrixB, err := matrix.NewFromElements(dataB) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + + // Perform matrix multiplication using Strassen's algorithm + resultMatrix, err := matrixA.StrassenMatrixMultiply(matrixB) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + + // Expected result + expectedData, err := matrixA.Multiply(matrixB) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + + // Check the dimensions of the result matrix + expectedRows := expectedData.Rows() + expectedColumns := expectedData.Columns() + rows := resultMatrix.Rows() + columns := resultMatrix.Columns() + + if rows != expectedRows { + t.Errorf("Expected %d rows in result matrix, but got %d", expectedRows, rows) + } + + if columns != expectedColumns { + t.Errorf("Expected %d columns in result matrix, but got %d", expectedColumns, columns) + } + + // Check the values in the result matrix + for i := 0; i < expectedRows; i++ { + for j := 0; j < expectedColumns; j++ { + val, err := resultMatrix.Get(i, j) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + expVal, err := expectedData.Get(i, j) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + if val != expVal { + t.Errorf("Expected value %d at (%d, %d) in result matrix, but got %d", expVal, i, j, val) + } + } + } +} +func TestMatrixMultiplication(t *testing.T) { + rand.New(rand.NewSource(time.Now().UnixNano())) + + // Generate random matrices for testing + size := 1 << (rand.Intn(8) + 1) // tests for matrix with n as power of 2 + matrixA := MakeRandomMatrix[int](size, size) + matrixB := MakeRandomMatrix[int](size, size) + + // Calculate the expected result using the standard multiplication + expected, err := matrixA.Multiply(matrixB) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + // Calculate the result using the Strassen algorithm + result, err := matrixA.StrassenMatrixMultiply(matrixB) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + + // Check if the result matches the expected result + for i := 0; i < size; i++ { + for j := 0; j < size; j++ { + val, err := result.Get(i, j) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + exp, err := expected.Get(i, j) + if err != nil { + t.Error("copyMatrix.Set error: " + err.Error()) + } + if val != exp { + t.Errorf("Mismatch at position (%d, %d). Expected %d, but got %d.", i, j, exp, val) + } + } + } +} + +func MakeRandomMatrix[T constraints.Integer](rows, columns int) matrix.Matrix[T] { + rand.New(rand.NewSource(time.Now().UnixNano())) + + matrixData := make([][]T, rows) + for i := 0; i < rows; i++ { + matrixData[i] = make([]T, columns) + for j := 0; j < columns; j++ { + matrixData[i][j] = T(rand.Intn(1000)) // Generate random integers between 0 and 1000 + } + } + + randomMatrix, _ := matrix.NewFromElements(matrixData) + return randomMatrix +} + +// BenchmarkStrassenMatrixMultiply benchmarks the StrassenMatrixMultiply function. +func BenchmarkStrassenMatrixMultiply(b *testing.B) { + // Create sample matrices for benchmarking + rows := 64 // it is large enough for multiplication + columns := 64 + m1 := matrix.New(rows, columns, 2) // Replace with appropriate values + m2 := matrix.New(rows, columns, 3) // Replace with appropriate values + + for i := 0; i < b.N; i++ { + _, _ = m1.StrassenMatrixMultiply(m2) + } +} diff --git a/math/matrix/string.go b/math/matrix/string.go new file mode 100644 index 000000000..b59fe8c6c --- /dev/null +++ b/math/matrix/string.go @@ -0,0 +1,15 @@ +package matrix + +import "fmt" + +// String implements the fmt.Stringer interface for Matrix. +func (m Matrix[T]) String() string { + var result string + for i := range m.elements { + for j := range m.elements[i] { + result += fmt.Sprintf("%v ", m.elements[i][j]) + } + result += "\n" + } + return result +} diff --git a/math/matrix/string_test.go b/math/matrix/string_test.go new file mode 100644 index 000000000..59ca24510 --- /dev/null +++ b/math/matrix/string_test.go @@ -0,0 +1,96 @@ +package matrix_test + +import ( + "bytes" + "fmt" + "io" + "os" + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestMatrixString(t *testing.T) { + // Create a sample matrix for testing + m1, err := matrix.NewFromElements([][]int{{1, 2}, {3, 4}}) + if err != nil { + t.Errorf("Error creating matrix: %v", err) + } + + // Redirect stdout to capture Stringed output + old := os.Stdout + r, w, err := os.Pipe() + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + os.Stdout = w + + // Call the String method + fmt.Print(m1) + + // Reset stdout + w.Close() + os.Stdout = old + + // Read the captured output + var buf bytes.Buffer + _, err = io.Copy(&buf, r) + if err != nil { + t.Errorf("Error copying output: %v", err) + } + capturedOutput := buf.String() + + // Define the expected output + expectedOutput := "1 2 \n3 4 \n" + + // Compare the captured output with the expected output + if capturedOutput != expectedOutput { + t.Errorf("Matrix.Print() produced incorrect output:\n%s\nExpected:\n%s", capturedOutput, expectedOutput) + } +} + +func TestNullMatrixString(t *testing.T) { + + m1 := matrix.New(0, 0, 0) + // Redirect stdout to capture Stringed output + old := os.Stdout + r, w, err := os.Pipe() + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + os.Stdout = w + + // Call the String method + fmt.Print(m1) + + // Reset stdout + w.Close() + os.Stdout = old + + // Read the captured output + var buf bytes.Buffer + _, err = io.Copy(&buf, r) + if err != nil { + t.Errorf("Error copying output: %v", err) + } + capturedOutput := buf.String() + + // Define the expected output + expectedOutput := "" + + // Compare the captured output with the expected output + if capturedOutput != expectedOutput { + t.Errorf("Matrix.Print() produced incorrect output:\n%s\nExpected:\n%s", capturedOutput, expectedOutput) + } +} + +func BenchmarkString(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + m := matrix.New(rows, columns, 0) // Replace with appropriate values + + for i := 0; i < b.N; i++ { + _ = m.String() + } +} diff --git a/math/matrix/submatrix.go b/math/matrix/submatrix.go new file mode 100644 index 000000000..4d636e2c0 --- /dev/null +++ b/math/matrix/submatrix.go @@ -0,0 +1,79 @@ +package matrix + +import ( + "context" + "errors" + "sync" +) + +// SubMatrix extracts a submatrix from the current matrix. +func (m Matrix[T]) SubMatrix(rowStart, colStart, numRows, numCols int) (Matrix[T], error) { + if rowStart < 0 || colStart < 0 || numRows < 0 || numCols < 0 { + return Matrix[T]{}, errors.New("negative dimensions are not allowed") + } + + if rowStart+numRows > m.rows || colStart+numCols > m.columns { + return Matrix[T]{}, errors.New("submatrix dimensions exceed matrix bounds") + } + + var zeroVal T + if numRows == 0 || numCols == 0 { + return New(numRows, numCols, zeroVal), nil // Return an empty matrix + } + + subMatrix := New(numRows, numCols, zeroVal) + + ctx, cancel := context.WithCancel(context.Background()) + defer cancel() // Make sure it's called to release resources even if no errors + + var wg sync.WaitGroup + errCh := make(chan error, 1) + + for i := 0; i < numRows; i++ { + i := i // Capture the loop variable for the goroutine + wg.Add(1) + go func() { + defer wg.Done() + for j := 0; j < numCols; j++ { + select { + case <-ctx.Done(): + return // Context canceled; return without an error + default: + } + + val, err := m.Get(rowStart+i, colStart+j) + if err != nil { + cancel() + select { + case errCh <- err: + default: + } + return + } + + err = subMatrix.Set(i, j, val) + if err != nil { + cancel() + select { + case errCh <- err: + default: + } + return + } + } + }() + } + + // Wait for all goroutines to finish + go func() { + wg.Wait() + close(errCh) + }() + + // Check for any errors + if err := <-errCh; err != nil { + return Matrix[T]{}, err + } + + return subMatrix, nil +} diff --git a/math/matrix/submatrix_test.go b/math/matrix/submatrix_test.go new file mode 100644 index 000000000..09452496d --- /dev/null +++ b/math/matrix/submatrix_test.go @@ -0,0 +1,88 @@ +package matrix_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestMatrixSubMatrix(t *testing.T) { + // Create a sample matrix + data := [][]int{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} + matrix, err := matrix.NewFromElements(data) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + // Extract a submatrix + subMatrix, err := matrix.SubMatrix(1, 1, 2, 2) + if err != nil { + t.Errorf("Error extracting submatrix: %v", err) + } + + // Check the dimensions of the submatrix + expectedRows := 2 + expectedColumns := 2 + rows := subMatrix.Rows() + columns := subMatrix.Columns() + + if rows != expectedRows { + t.Errorf("Expected %d rows in submatrix, but got %d", expectedRows, rows) + } + + if columns != expectedColumns { + t.Errorf("Expected %d columns in submatrix, but got %d", expectedColumns, columns) + } + + // Check the values in the submatrix + expectedData := [][]int{{5, 6}, {8, 9}} + for i := 0; i < expectedRows; i++ { + for j := 0; j < expectedColumns; j++ { + val, err := subMatrix.Get(i, j) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + if val != expectedData[i][j] { + t.Errorf("Expected value %d at (%d, %d) in submatrix, but got %d", expectedData[i][j], i, j, val) + } + } + } +} + +func TestMatrixInvalidSubMatrix(t *testing.T) { + // Create a sample matrix + data := [][]int{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}} + matrix, err := matrix.NewFromElements(data) + if err != nil { + t.Fatalf("Failed to copy matrix: %v", err) + } + // Attempt to extract an invalid submatrix + _, err = matrix.SubMatrix(1, 1, 3, 3) + + // Check if an error is returned + if err == nil { + t.Error("Expected an error for invalid submatrix dimensions, but got nil") + } + + // Check the error message + expectedErrorMessage := "submatrix dimensions exceed matrix bounds" + if err.Error() != expectedErrorMessage { + t.Errorf("Expected error message '%s', but got '%s'", expectedErrorMessage, err.Error()) + } +} + +// BenchmarkSubMatrix benchmarks the SubMatrix function. +func BenchmarkSubMatrix(b *testing.B) { + // Create a sample matrix for benchmarking + rows := 100 + columns := 100 + matrix := matrix.New(rows, columns, 2) // Replace with appropriate values + + rowStart := 10 + colStart := 10 + numRows := 20 + numCols := 20 + + for i := 0; i < b.N; i++ { + _, _ = matrix.SubMatrix(rowStart, colStart, numRows, numCols) + } +} diff --git a/math/matrix/subtract.go b/math/matrix/subtract.go new file mode 100644 index 000000000..761a7ed8c --- /dev/null +++ b/math/matrix/subtract.go @@ -0,0 +1,64 @@ +package matrix + +import ( + "context" + "errors" + "sync" +) + +// Subtract subtracts two matrices. +func (m1 Matrix[T]) Subtract(m2 Matrix[T]) (Matrix[T], error) { + // Check if the matrices have the same dimensions. + if !m1.MatchDimensions(m2) { + return Matrix[T]{}, errors.New("matrices are not compatible for subtraction") + } + + // Create a new matrix to store the result. + var zeroVal T + result := New(m1.Rows(), m1.Columns(), zeroVal) + + ctx, cancel := context.WithCancel(context.Background()) + defer cancel() // Make sure it's called to release resources even if no errors + + var wg sync.WaitGroup + errCh := make(chan error, 1) + + for i := 0; i < m1.rows; i++ { + i := i // Capture the loop variable for the goroutine + wg.Add(1) + go func() { + defer wg.Done() + for j := 0; j < m1.columns; j++ { + select { + case <-ctx.Done(): + return // Context canceled; return without an error + default: + } + + diff := m1.elements[i][j] - m2.elements[i][j] + err := result.Set(i, j, diff) + if err != nil { + cancel() // Cancel the context on error + select { + case errCh <- err: + default: + } + return + } + } + }() + } + + // Wait for all goroutines to finish + go func() { + wg.Wait() + close(errCh) + }() + + // Check for any errors + if err := <-errCh; err != nil { + return Matrix[T]{}, err + } + + return result, nil +} diff --git a/math/matrix/subtract_test.go b/math/matrix/subtract_test.go new file mode 100644 index 000000000..827d5c9e3 --- /dev/null +++ b/math/matrix/subtract_test.go @@ -0,0 +1,50 @@ +package matrix_test + +import ( + "fmt" + "testing" + + "github.com/TheAlgorithms/Go/math/matrix" +) + +func TestSubtract(t *testing.T) { + // Create two matrices with the same dimensions for Subtraction + m1 := matrix.New(2, 2, 1) + m2 := matrix.New(2, 2, 2) + + // Test case 1: Valid matrix Subtraction + subMatrix, err := m1.Subtract(m2) + if err != nil { + t.Errorf("Add(m1, m2) returned an error: %v, expected no error", err) + } + expectedMatrix := matrix.New(2, 2, -1) + res := subMatrix.CheckEqual(expectedMatrix) + if !res { + t.Errorf("Add(m1, m2) returned incorrect result:\n%v\nExpected:\n%v", subMatrix, expectedMatrix) + } + + // Create two matrices with different dimensions for Subtraction + m3 := matrix.New(2, 2, 1) + m4 := matrix.New(2, 3, 2) + + // Test case 2: Matrices with different dimensions + _, err2 := m3.Subtract(m4) + expectedError2 := fmt.Errorf("matrices are not compatible for subtraction") + if err2 == nil || err2.Error() != expectedError2.Error() { + t.Errorf("m3.Subtract(m4) returned error: %v, expected error: %v", err2, expectedError2) + } + +} + +// BenchmarkSubtract benchmarks the Subtract function. +func BenchmarkSubtract(b *testing.B) { + // Create sample matrices for benchmarking + rows := 100 + columns := 100 + m1 := matrix.New(rows, columns, 2) // Replace with appropriate values + m2 := matrix.New(rows, columns, 3) // Replace with appropriate values + + for i := 0; i < b.N; i++ { + _, _ = m1.Subtract(m2) + } +} diff --git a/math/max/bitwisemax.go b/math/max/bitwisemax.go new file mode 100644 index 000000000..a54f94654 --- /dev/null +++ b/math/max/bitwisemax.go @@ -0,0 +1,17 @@ +// bitwiseMax.go +// description: Gives max of two integers +// details: +// implementation of finding the maximum of two numbers using only binary operations without using conditions +// author(s) [red_byte](https://github.com/i-redbyte) +// time complexity: O(1) +// space complexity: O(1) +// see bitwiseMax_test.go + +package max + +// Bitwise computes using bitwise operator the maximum of all the integer input and returns it +func Bitwise(a int, b int, base int) int { + z := a - b + i := (z >> base) & 1 + return a - (i * z) +} diff --git a/math/max/bitwisemax_test.go b/math/max/bitwisemax_test.go new file mode 100644 index 000000000..c28bb1cf6 --- /dev/null +++ b/math/max/bitwisemax_test.go @@ -0,0 +1,77 @@ +// bitwiseMax_test.go +// description: Test for Bitwise +// author(s) [red_byte](https://github.com/i-redbyte) +// see bitwiseMax.go + +package max + +import "testing" + +func TestBitwiseMax(t *testing.T) { + base32 := 31 + + t.Run("Testing(32bit) a = 32 and m = 64: ", func(t *testing.T) { + max := Bitwise(32, 64, base32) + if max != 64 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + t.Run("Testing(32bit) a = 1024 and m = -9: ", func(t *testing.T) { + max := Bitwise(1024, -9, base32) + if max != 1024 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + t.Run("Testing(32bit) a = -6 and m = -6: ", func(t *testing.T) { + max := Bitwise(-6, -6, base32) + if max != -6 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + t.Run("Testing(32bit) a = -72 and m = -73: ", func(t *testing.T) { + max := Bitwise(-72, -73, base32) + if max != -72 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + base64 := 63 + t.Run("Testing(64bit) a = 32 and m = 9223372036854775807: ", func(t *testing.T) { + max := Bitwise(32, 9223372036854775807, base64) + if max != 9223372036854775807 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + t.Run("Testing(64bit) a = 1024 and m = -9223372036854770001: ", func(t *testing.T) { + max := Bitwise(1024, -9223372036854770001, base64) + if max != 1024 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + t.Run("Testing(64bit) a = -6 and m = -6: ", func(t *testing.T) { + max := Bitwise(-6, -6, base64) + if max != -6 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + t.Run("Testing(64bit) a = -4223372036854775809 and m = -4223372036854775808: ", func(t *testing.T) { + max := Bitwise(-4223372036854775809, -4223372036854775808, base64) + if max != -4223372036854775808 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) + + base8 := 7 + t.Run("Testing(8bit) a = 257 and m = 256: ", func(t *testing.T) { + max := Bitwise(8, 16, base8) + if max != 16 { + t.Fatalf("Error: Bitwise returned bad value") + } + }) +} diff --git a/math/max/max.go b/math/max/max.go new file mode 100644 index 000000000..d93aa5601 --- /dev/null +++ b/math/max/max.go @@ -0,0 +1,14 @@ +package max + +import "github.com/TheAlgorithms/Go/constraints" + +// Int is a function which returns the maximum of all the integers provided as arguments. +func Int[T constraints.Integer](values ...T) T { + max := values[0] + for _, value := range values { + if value > max { + max = value + } + } + return max +} diff --git a/math/max/max_test.go b/math/max/max_test.go new file mode 100644 index 000000000..1c289917f --- /dev/null +++ b/math/max/max_test.go @@ -0,0 +1,77 @@ +package max + +import "testing" + +func TestMax(t *testing.T) { + testCases := []struct { + name string + left int + right int + max int + }{ + { + name: "Left is max", + left: 10, + right: 9, + max: 10, + }, + { + name: "right is max", + left: 1, + right: 10, + max: 10, + }, + } + + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + returnedMax := Int(test.left, test.right) + if returnedMax != test.max { + t.Errorf("Failed test %s\n\tleft: %v, right: %v, max: %v but received: %v", + test.name, test.left, test.right, test.max, returnedMax) + } + }) + } +} + +func TestMaxOfThree(t *testing.T) { + testCases := []struct { + name string + left int + middle int + right int + max int + }{ + { + name: "right is max", + left: 1, + middle: 5, + right: 10, + max: 10, + }, + { + name: "left is max", + left: 10, + middle: 5, + right: 9, + max: 10, + }, + { + name: "left is max", + left: 10, + middle: 8, + right: 6, + max: 10, + }, + } + + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + actualMax := Int(test.left, test.middle, test.right) + if actualMax != test.max { + t.Errorf("Failed test %s\n\tleft: %v, middle: %v, right: %v, max: %v but received: %v", + test.name, test.left, test.middle, test.right, test.max, actualMax) + } + }) + } +} diff --git a/math/mean.go b/math/mean.go new file mode 100644 index 000000000..4bd0e40ed --- /dev/null +++ b/math/mean.go @@ -0,0 +1,21 @@ +package math + +import ( + "github.com/TheAlgorithms/Go/constraints" +) + +func Mean[T constraints.Number](values []T) float64 { + + if len(values) == 0 { + return 0 + } + + var summation float64 = 0 + + for _, singleValue := range values { + summation += float64(singleValue) + } + + return summation / float64(len(values)) + +} diff --git a/math/mean_test.go b/math/mean_test.go new file mode 100644 index 000000000..8f74511ef --- /dev/null +++ b/math/mean_test.go @@ -0,0 +1,52 @@ +package math_test + +import ( + "github.com/TheAlgorithms/Go/math" + "testing" +) + +func TestMean(t *testing.T) { + testCases := []struct { + name string + testValues []float64 + average float64 + }{ + { + name: "All 0s", + testValues: []float64{0, 0, 0, 0, 0}, + average: 0, + }, + { + name: "With integer values", + testValues: []float64{1, 2, 3, 4, 5}, + average: 3.0, + }, + { + name: "With negative values", + testValues: []float64{-1, 2, -3, 4, 5}, + average: 1.4, + }, + { + name: "With floating values", + testValues: []float64{1.1, 2.2, 3.3, 4.4, 5.5}, + average: 3.3, + }, + { + name: "With no values", + testValues: []float64{}, + average: 0, + }, + } + + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + returnedAverage := math.Mean(test.testValues) + if returnedAverage != test.average { + t.Errorf("\nFailed test: %s\ntestValues: %v\naverage: %v\nbut received: %v\n", + test.name, test.testValues, test.average, returnedAverage) + } + + }) + } + +} diff --git a/math/median.go b/math/median.go new file mode 100644 index 000000000..1b9dac834 --- /dev/null +++ b/math/median.go @@ -0,0 +1,30 @@ +// author(s) [jo3zeph](https://github.com/jo3zeph) +// description: Find the median from a set of values +// time complexity: O(n log n) +// space complexity: O(1) +// see median_test.go + +package math + +import ( + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/sort" +) + +func Median[T constraints.Number](values []T) float64 { + + sort.Bubble(values) + + l := len(values) + + switch { + case l == 0: + return 0 + + case l%2 == 0: + return float64((values[l/2-1] + values[l/2]) / 2) + + default: + return float64(values[l/2]) + } +} diff --git a/math/median_test.go b/math/median_test.go new file mode 100644 index 000000000..5210caec4 --- /dev/null +++ b/math/median_test.go @@ -0,0 +1,56 @@ +// author(s) [jo3zeph](https://github.com/jo3zeph) +// median_test.go +// see median.go + +package math_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math" +) + +func TestMedian(t *testing.T) { + testCases := []struct { + name string + testValues []float64 + answer float64 + }{ + + { + name: "Series of numbers in ascending order", + testValues: []float64{12, 14, 16, 18, 19}, + answer: 16, + }, + + { + name: "Series of numbers in random order", + testValues: []float64{21, 10, 22, 33, 11, 88}, + answer: 21.5, + }, + + { + name: "Series of decimals in random order", + testValues: []float64{11.2, 32.5, 2.5, 37.8, 21.8, 5.2}, + answer: 16.5, + }, + + { + testValues: []float64{}, + }, + } + + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + + returnedMedian := math.Median(test.testValues) + + t.Log(test.testValues, " ", returnedMedian) + + if returnedMedian != test.answer { + t.Errorf("Test failed. Median should have been %v but received %v", + test.answer, returnedMedian) + } + }) + } +} diff --git a/math/min/bitwisemin.go b/math/min/bitwisemin.go new file mode 100644 index 000000000..679d95840 --- /dev/null +++ b/math/min/bitwisemin.go @@ -0,0 +1,17 @@ +// bitwisemin.go +// description: Gives min of two integers +// details: +// implementation of finding the minimum of two numbers using only binary operations without using conditions +// author(s) [red_byte](https://github.com/i-redbyte) +// see bitwisemin_test.go + +package min + +// Bitwise This function returns the minimum integer using bit operations +func Bitwise(base int, value int, values ...int) int { + min := value + for _, val := range values { + min = min&((min-val)>>base) | val&(^(min-val)>>base) + } + return min +} diff --git a/math/min/min.go b/math/min/min.go new file mode 100644 index 000000000..3ef21272b --- /dev/null +++ b/math/min/min.go @@ -0,0 +1,14 @@ +package min + +import "github.com/TheAlgorithms/Go/constraints" + +// Int is a function which returns the minimum of all the integers provided as arguments. +func Int[T constraints.Integer](values ...T) T { + min := values[0] + for _, value := range values { + if value < min { + min = value + } + } + return min +} diff --git a/math/min/min_test.go b/math/min/min_test.go new file mode 100644 index 000000000..ec63ed0b8 --- /dev/null +++ b/math/min/min_test.go @@ -0,0 +1,62 @@ +package min + +import ( + "testing" +) + +func getTestCases() []struct { + name string + base int + numbers []int + min int +} { + var tests = []struct { + name string + base int + numbers []int + min int + }{ + {"Minimum of [128, 127], min = 117", 8, []int{128, 127}, 127}, + {"Minimum of [5], min = 5", 32, []int{5}, 5}, + {"Minimum of [-8, 32, 64, -1, 0], min = -8", 64, []int{-8, 32, 64, -1, 0}, -8}, + {"Minimum of [1, 2, 3, 4, 5], min = 1", 32, []int{1, 2, 3, 4, 5}, 1}, + {"Minimum of [1024, 512, 256, 333, 777], min = 256", 64, []int{1024, 512, 256, 333, 777}, 256}, + {"Minimum of [-9223372036854770001, -9223372036854770000, 256, 333, 777], min = 256", 64, []int{-9223372036854770001, -9223372036854770000, 256, 333, 777}, -9223372036854770001}, + } + return tests +} + +func TestBitwiseMin(t *testing.T) { + tests := getTestCases() + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + result := Bitwise(test.base, 999, test.numbers...) + if result != test.min { + t.Errorf("Wrong result! Expected:%v, returned:%v ", test.min, result) + } + }) + } +} + +func TestMin(t *testing.T) { + for _, test := range getTestCases() { + t.Run(test.name, func(t *testing.T) { + actualMin := Int(test.numbers...) + if actualMin != test.min { + t.Errorf("Wrong result! Expected:%v, returned:%v ", test.min, actualMin) + } + }) + } +} + +func BenchmarkTestMinInt(b *testing.B) { + for i := 0; i < b.N; i++ { + Int(0, 10, 9, 7, 2, 1, 4, 3, 5, 6) + } +} + +func BenchmarkTestBitwiseMin(b *testing.B) { + for i := 0; i < b.N; i++ { + Bitwise(32, 10, 9, 7, 2, 1, 4, 3, 5, 6) + } +} diff --git a/math/mobius.go b/math/mobius.go new file mode 100644 index 000000000..0f9fac639 --- /dev/null +++ b/math/mobius.go @@ -0,0 +1,40 @@ +// mobius.go +// description: Returns μ(n) +// details: +// For any positive integer n, define μ(n) as the sum of the primitive nth roots of unity. +// It has values in {−1, 0, 1} depending on the factorization of n into prime factors: +// μ(n) = +1 if n is a square-free positive integer with an even number of prime factors. +// μ(n) = −1 if n is a square-free positive integer with an odd number of prime factors. +// μ(n) = 0 if n has a squared prime factor. +// wikipedia: https://en.wikipedia.org/wiki/M%C3%B6bius_function +// time complexity: O(n) +// space complexity: O(1) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see mobius_test.go + +package math + +import ( + "github.com/TheAlgorithms/Go/math/prime" +) + +// Mu is the Mobius function +// This function returns μ(n) for given number +func Mu(n int) int { + if n <= 1 { + return 1 + } + var primeFactorCount int + for i := 1; i <= n; i++ { + if n%i == 0 && prime.OptimizedTrialDivision(int64(i)) { + if n%(i*i) == 0 { + return 0 + } + primeFactorCount += 1 + } + } + if primeFactorCount%2 == 0 { + return 1 + } + return -1 +} diff --git a/math/mobius_test.go b/math/mobius_test.go new file mode 100644 index 000000000..271b9c74f --- /dev/null +++ b/math/mobius_test.go @@ -0,0 +1,41 @@ +// mobius_test.go +// description: Returns μ(n) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see mobius.go + +package math_test + +import ( + "testing" + + algmath "github.com/TheAlgorithms/Go/math" +) + +func TestMu(t *testing.T) { + var tests = []struct { + n int + expected int + }{ + {-1, 1}, + {0, 1}, + {2, -1}, + {3, -1}, + {95, 1}, + {97, -1}, + {98, 0}, + {99, 0}, + {100, 0}, + } + for _, test := range tests { + result := algmath.Mu(test.n) + t.Log(test.n, " ", result) + if result != test.expected { + t.Errorf("Wrong result! Expected:%v, returned:%v ", test.expected, result) + } + } +} +func BenchmarkMu(b *testing.B) { + for i := 0; i < b.N; i++ { + algmath.Mu(65536) + } +} diff --git a/math/mode.go b/math/mode.go new file mode 100644 index 000000000..87f233304 --- /dev/null +++ b/math/mode.go @@ -0,0 +1,47 @@ +// mode.go +// author(s): [CalvinNJK] (https://github.com/CalvinNJK) +// time complexity: O(n) +// space complexity: O(n) +// description: Finding Mode Value In an Array +// see mode.go + +package math + +import ( + "errors" + + "github.com/TheAlgorithms/Go/constraints" +) + +// ErrEmptySlice is the error returned by functions in math package when +// an empty slice is provided to it as argument when the function expects +// a non-empty slice. +var ErrEmptySlice = errors.New("empty slice provided") + +func Mode[T constraints.Number](numbers []T) (T, error) { + + countMap := make(map[T]int) + + n := len(numbers) + + if n == 0 { + return 0, ErrEmptySlice + } + + for _, number := range numbers { + countMap[number]++ + } + + var mode T + count := 0 + + for k, v := range countMap { + if v > count { + count = v + mode = k + } + } + + return mode, nil + +} diff --git a/math/mode_test.go b/math/mode_test.go new file mode 100644 index 000000000..5db0eb5df --- /dev/null +++ b/math/mode_test.go @@ -0,0 +1,94 @@ +// mode.go +// author(s): [CalvinNJK] (https://github.com/CalvinNJK) +// description: Test for Finding Mode Value In an Array + +package math_test + +import ( + "errors" + "testing" + + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/math" +) + +type testCase[T constraints.Number] struct { + name string + numbers []T + mode T + err error +} + +func testModeFramework[T constraints.Number](t *testing.T, testCases []testCase[T]) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + returnMode, err := math.Mode(test.numbers) + if returnMode != test.mode { + t.Errorf("\n Failed test %s,\n Numbers: %v,\n Correct Mode: %v,\n Returned Mode: %v\n", + test.name, test.numbers, test.mode, returnMode) + } + if !errors.Is(err, test.err) { + t.Errorf("\n Failed test %s,\n Numbers: %v,\n Correct Error: %v,\n Returned Error: %v\n", + test.name, test.numbers, test.err, err) + } + }) + } +} +func TestMode(t *testing.T) { + // test cases for integer values + intTestCases := []testCase[int]{ + { + name: "An array of positive whole numbers", + numbers: []int{10, 52, 10, 92, 10, 75, 60, 10, 44, 29}, + mode: 10, + err: nil, + }, + { + name: "An array of negative whole numbers", + numbers: []int{-19, -12, -74, -19, -22, -56, -19, -19, -68, -93}, + mode: -19, + err: nil, + }, + { + name: "An array of positive & negative whole numbers", + numbers: []int{18, -28, 33, -28, 2, 39, 48, -49, -87, 78, -28}, + mode: -28, + err: nil, + }, + { + name: "If array has no value", + numbers: []int{}, + mode: 0, + err: math.ErrEmptySlice, + }, + } + testModeFramework(t, intTestCases) + // test cases for float64 values + floatTestCases := []testCase[float64]{ + { + name: "An array of positive real numbers", + numbers: []float64{1.5, 2.88, 84.4, 77.2, 29.8, 46.2, 33.7, 88.4, 88.4}, + mode: 88.4, + err: nil, + }, + { + name: "An array of negative real numbers", + numbers: []float64{-98.1, -26.8, -54.45, -26.8, -1.5, -26.8, -33, -19.5, -26.8}, + mode: -26.8, + err: nil, + }, + { + name: "An array of positive and negative real numbers", + numbers: []float64{-17, 28.9, -5.2, -19.5, 77.3, -5.2, 39.3, 28.5, -59.77, -5.2}, + mode: -5.2, + err: nil, + }, + { + name: "If array has no value", + numbers: []float64{}, + mode: 0, + err: math.ErrEmptySlice, + }, + } + testModeFramework(t, floatTestCases) +} diff --git a/math/modular/exponentiation.go b/math/modular/exponentiation.go new file mode 100644 index 000000000..85a397e4f --- /dev/null +++ b/math/modular/exponentiation.go @@ -0,0 +1,58 @@ +// exponentiation.go +// description: Implementation of Modular Exponentiation Algorithm +// details: +// A simple implementation of Modular Exponentiation - [Modular Exponenetation wiki](https://en.wikipedia.org/wiki/Modular_exponentiation) +// time complexity: O(log(n)) where n is the exponent +// space complexity: O(1) +// author(s) [Taj](https://github.com/tjgurwara99) +// see exponentiation_test.go + +package modular + +import ( + "errors" + "math" +) + +// ErrorIntOverflow For asserting that the values do not overflow in Int64 +var ErrorIntOverflow = errors.New("integer overflow") + +// ErrorNegativeExponent for asserting that the exponent we receive is positive +var ErrorNegativeExponent = errors.New("negative Exponent provided") + +// Exponentiation returns base^exponent % mod +func Exponentiation(base, exponent, mod int64) (int64, error) { + if mod == 1 { + return 0, nil + } + + if exponent < 0 { + return -1, ErrorNegativeExponent + } + _, err := Multiply64BitInt(mod-1, mod-1) + + if err != nil { + return -1, err + } + + var result int64 = 1 + + base = base % mod + + for exponent > 0 { + if exponent%2 == 1 { + result = (result * base) % mod + } + exponent = exponent >> 1 + base = (base * base) % mod + } + return result, nil +} + +// Multiply64BitInt Checking if the integer multiplication overflows +func Multiply64BitInt(left, right int64) (int64, error) { + if math.Abs(float64(left)) > float64(math.MaxInt64)/math.Abs(float64(right)) { + return 0, ErrorIntOverflow + } + return left * right, nil +} diff --git a/math/modular/exponentiation_test.go b/math/modular/exponentiation_test.go new file mode 100644 index 000000000..2c25ac22b --- /dev/null +++ b/math/modular/exponentiation_test.go @@ -0,0 +1,89 @@ +// exponentiation_test.go +// description: Test for ModularExponentiation +// author(s) [Taj](https://github.com/tjgurwara99) +// see exponentiation.go + +package modular + +import "testing" + +type cases struct { + name string + description string + base int64 + exponent int64 + mod int64 + expected int64 + expectedError error +} + +var testCases = []cases{ + { + name: "Test 1", + description: "Test 1: 3^6 % 3 == 0", + base: 3, + exponent: 6, + mod: 3, + expected: 0, + expectedError: nil, + }, + { + name: "Test 2", + description: "Test 2: 33^60 % 25 == 1", + base: 33, + exponent: 60, + mod: 25, + expected: 1, + expectedError: nil, + }, + { + name: "Test 3", + description: "Test 3: 17^60 % 23 == 2", + base: 17, + exponent: 60, + mod: 23, + expected: 2, + expectedError: nil, + }, + { + name: "Test 4", + description: "Test 4: 17^60 % 1 == 0", // handling result when we get mod = 1 + base: 17, + exponent: 60, + mod: 1, + expected: 0, + expectedError: nil, + }, + { + name: "Error test 1", + description: "Testing whether we receive the expected errors gracefully", + base: 50, + exponent: -1, + mod: 2, + expected: -1, + expectedError: ErrorNegativeExponent, + }, +} + +func TestExponentiation(t *testing.T) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + result, err := Exponentiation(test.base, test.exponent, test.mod) + if err != test.expectedError { + t.Logf("Test Failed for %s", test.name) + t.Logf("Unexpected error occurred") + t.Errorf("Expected error: %v, Received error: %v", test.expectedError, err) + } + if result != test.expected { + t.Logf("Test Failed for %s", test.description) + t.Fatalf("Expected: %d, Received: %d", test.expected, result) + } + }) + } +} + +func BenchmarkExponentiation(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = Exponentiation(17, 60, 23) + } +} diff --git a/math/modular/inverse.go b/math/modular/inverse.go new file mode 100644 index 000000000..f20d70b11 --- /dev/null +++ b/math/modular/inverse.go @@ -0,0 +1,28 @@ +// inverse.go +// description: Implementation of Modular Inverse Algorithm +// details: +// A simple implementation of Modular Inverse - [Modular Inverse wiki](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse) +// time complexity: O(log(min(a, b))) where a and b are the two numbers +// space complexity: O(1) +// author(s) [Taj](https://github.com/tjgurwara99) +// see inverse_test.go + +package modular + +import ( + "errors" + + "github.com/TheAlgorithms/Go/math/gcd" +) + +var ErrorInverse = errors.New("no Modular Inverse exists") + +// Inverse Modular function +func Inverse(a, m int64) (int64, error) { + gcd, x, _ := gcd.Extended(a, m) + if gcd != 1 || m == 0 { + return 0, ErrorInverse + } + + return ((m + (x % m)) % m), nil // this is necessary because of Go's use of architecture specific instruction for the % operator. +} diff --git a/math/modular/inverse_test.go b/math/modular/inverse_test.go new file mode 100644 index 000000000..a8025e97c --- /dev/null +++ b/math/modular/inverse_test.go @@ -0,0 +1,39 @@ +// inverse_test.go +// description: Test for Modular Inverse +// author(s) [Taj](https://github.com/tjgurwara99) +// see inverse.go + +package modular + +import "testing" +import "fmt" + +func TestInverse(t *testing.T) { + testCases := []struct { + a int64 + m int64 + expectedValue int64 + expectedError error + }{ + {3, 11, 4, nil}, + {10, 17, 12, nil}, + {2, 6, 0, ErrorInverse}, + {1, 0, 0, ErrorInverse}, + } + for _, tc := range testCases { + testName := fmt.Sprintf("Testing a = %d and m = %d: ", tc.a, tc.m) + t.Run(testName, func(t *testing.T) { + inv, err := Inverse(tc.a, tc.m) + if err != tc.expectedError { + if tc.expectedError == nil { + t.Fatalf("Error was raised when it shouldn't: %v", err) + } else { + t.Fatalf("Error was not raised when it should") + } + } + if inv != tc.expectedValue { + t.Fatalf("expected: %d, got: %d", tc.expectedValue, inv) + } + }) + } +} diff --git a/math/moserdebruijnsequence/sequence.go b/math/moserdebruijnsequence/sequence.go new file mode 100644 index 000000000..09d2c7776 --- /dev/null +++ b/math/moserdebruijnsequence/sequence.go @@ -0,0 +1,32 @@ +// The Moser-de Bruijn sequence is the sequence obtained by +// adding up the distinct powers of the number 4 (For example 1, 4, 16, 64, etc). +// time complexity: O(n) +// space complexity: O(n) +// You can get more details on https://en.wikipedia.org/wiki/Moser%E2%80%93de_Bruijn_sequence. + +package moserdebruijnsequence + +func MoserDeBruijnSequence(number int) []int { + sequence := []int{} + + for i := 0; i < number; i++ { + res := generateNthTerm(i) + sequence = append(sequence, res) + } + + return sequence +} + +func generateNthTerm(num int) int { + if num == 0 || num == 1 { + return num + } + + //number is even + if num%2 == 0 { + return 4 * generateNthTerm(num/2) + } + + //number is odd + return 4*generateNthTerm(num/2) + 1 +} diff --git a/math/moserdebruijnsequence/sequence_test.go b/math/moserdebruijnsequence/sequence_test.go new file mode 100644 index 000000000..8036ddc47 --- /dev/null +++ b/math/moserdebruijnsequence/sequence_test.go @@ -0,0 +1,25 @@ +package moserdebruijnsequence + +import ( + "reflect" + "testing" +) + +var testCases = []struct { + name string + inputNum int + expected []int +}{ + {"first 15 terms", 15, []int{0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84}}, +} + +func TestMoserDeBruijnSequence(t *testing.T) { + + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + if output := MoserDeBruijnSequence(test.inputNum); !reflect.DeepEqual(output, test.expected) { + t.Errorf("For input: %d, expected: %v, but got: %v", test.inputNum, test.expected, output) + } + }) + } +} diff --git a/math/pascal/pascaltriangle.go b/math/pascal/pascaltriangle.go new file mode 100644 index 000000000..742b735d7 --- /dev/null +++ b/math/pascal/pascaltriangle.go @@ -0,0 +1,36 @@ +// pascaltriangle.go +// description: Pascal's triangle +// details: +// Pascal's triangle is a triangular array of the binomial coefficients that arises in probability theory, combinatorics, and algebra. - [Pascal's triangle](https://en.wikipedia.org/wiki/Pascal%27s_triangle) +// example: +//1 +//1 1 +//1 2 1 +//1 3 3 1 +//1 4 6 4 1 +//1 5 10 10 5 1 +//1 6 15 20 15 6 1 +//1 7 21 35 35 21 7 1 +//1 8 28 56 70 56 28 8 1 +//1 9 36 84 126 126 84 36 9 1 +//1 10 45 120 210 252 210 120 45 10 1 +//... +// author(s) [red_byte](https://github.com/i-redbyte) +// time complexity: O(n^2) +// space complexity: O(n^2) +// see pascaltriangle_test.go + +package pascal + +// GenerateTriangle This function generates a Pascal's triangle of n lines +func GenerateTriangle(n int) [][]int { + var triangle = make([][]int, n) + for i := 0; i < n; i++ { + triangle[i] = make([]int, i+1) + triangle[i][0], triangle[i][i] = 1, 1 + for j := 1; j < i; j++ { + triangle[i][j] = triangle[i-1][j] + triangle[i-1][j-1] + } + } + return triangle +} diff --git a/math/pascal/pascaltriangle_test.go b/math/pascal/pascaltriangle_test.go new file mode 100644 index 000000000..33fe53e2c --- /dev/null +++ b/math/pascal/pascaltriangle_test.go @@ -0,0 +1,37 @@ +// pascaltriangle_test.go +// description: Test for Pascal's triangle +// author(s) [red_byte](https://github.com/i-redbyte) +// see pascaltriangle.go + +package pascal + +import ( + "reflect" + "testing" +) + +func TestGenerateTriangle(t *testing.T) { + tests := []struct { + name string + n int + want [][]int + }{ + {name: "Pascal's three-line triangle", n: 3, want: [][]int{{1}, {1, 1}, {1, 2, 1}}}, + {name: "Pascal's 0-line triangle", n: 0, want: [][]int{}}, + {name: "Pascal's one-line triangle", n: 1, want: [][]int{{1}}}, + {name: "Pascal's 7-line triangle", n: 7, want: [][]int{{1}, {1, 1}, {1, 2, 1}, {1, 3, 3, 1}, {1, 4, 6, 4, 1}, {1, 5, 10, 10, 5, 1}, {1, 6, 15, 20, 15, 6, 1}}}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := GenerateTriangle(test.n); !reflect.DeepEqual(got, test.want) { + t.Errorf("GenerateTriangle() = %v, want %v", got, test.want) + } + }) + } +} + +func BenchmarkGenerateTriangle(b *testing.B) { + for i := 0; i < b.N; i++ { + GenerateTriangle(10) + } +} diff --git a/math/perfectnumber.go b/math/perfectnumber.go new file mode 100644 index 000000000..37be71a2b --- /dev/null +++ b/math/perfectnumber.go @@ -0,0 +1,38 @@ +// perfectnumber.go +// description: provides the function IsPerfectNumber and related utilities +// details: +// provides the functions +// - IsPerfectNumber which checks if the input is a perfect number, +// - SumOfProperDivisors which returns the sum of proper divisors of the input. +// A number is called perfect, if it is a sum of its proper divisors, +// cf. https://en.wikipedia.org/wiki/Perfect_number, +// https://mathworld.wolfram.com/PerfectNumber.html +// time complexity: O(sqrt(n)) +// space complexity: O(1) +// https://oeis.org/A000396 +// author(s) [Piotr Idzik](https://github.com/vil02) +// see perfectnumber_test.go + +package math + +// Returns the sum of proper divisors of inNumber. +func SumOfProperDivisors(inNumber uint) uint { + var res = uint(0) + if inNumber > 1 { + res = uint(1) + } + for curDivisor := uint(2); curDivisor*curDivisor <= inNumber; curDivisor++ { + if inNumber%curDivisor == 0 { + res += curDivisor + if curDivisor*curDivisor != inNumber { + res += inNumber / curDivisor + } + } + } + return res +} + +// Checks if inNumber is a perfect number +func IsPerfectNumber(inNumber uint) bool { + return inNumber > 0 && SumOfProperDivisors(inNumber) == inNumber +} diff --git a/math/perfectnumber_test.go b/math/perfectnumber_test.go new file mode 100644 index 000000000..c0041d0ae --- /dev/null +++ b/math/perfectnumber_test.go @@ -0,0 +1,151 @@ +package math_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math" +) + +type testCaseSumOfProperDivisors struct { + input uint + expected uint +} + +// getSumOfProperDivisorsTestCases returns an array of test data +// for the tests of the function SumOfProperDivisors. +// Data was verified using [A001065]. +// [A001065]: https://oeis.org/A001065/b001065.txt +func getSumOfProperDivisorsTestCases() []testCaseSumOfProperDivisors { + return []testCaseSumOfProperDivisors{ + {0, 0}, + {1, 0}, + {2, 1}, + {3, 1}, + {4, 3}, + {5, 1}, + {6, 6}, + {7, 1}, + {8, 7}, + {9, 4}, + {10, 8}, + {11, 1}, + {12, 16}, + {13, 1}, + {14, 10}, + {15, 9}, + {16, 15}, + {17, 1}, + {18, 21}, + {19, 1}, + {20, 22}, + {21, 11}, + {22, 14}, + {23, 1}, + {24, 36}, + {25, 6}, + {26, 16}, + {27, 13}, + {28, 28}, + {29, 1}, + {30, 42}, + {31, 1}, + {32, 31}, + {33, 15}, + {34, 20}, + {35, 13}, + {36, 55}, + {37, 1}, + {38, 22}, + {39, 17}, + {40, 50}, + {41, 1}, + {42, 54}, + {43, 1}, + {44, 40}, + {45, 33}, + {46, 26}, + {47, 1}, + {48, 76}, + {49, 8}, + {50, 43}, + {51, 21}, + {52, 46}, + {53, 1}, + {54, 66}, + {55, 17}, + {56, 64}, + {57, 23}, + {58, 32}, + {59, 1}, + {60, 108}, + {800, 1153}, + {8204, 8260}, + {9646, 8498}, + {9756, 14996}, + {9829, 1}, + {9954, 15006}, + {10000, 14211}, + } +} + +func TestSumOfProperDivisors(t *testing.T) { + for _, tc := range getSumOfProperDivisorsTestCases() { + actual := math.SumOfProperDivisors(tc.input) + if actual != tc.expected { + t.Errorf( + "Expected SumOfProperDivisors(%d) to be: %d, but got: %d", + tc.input, tc.expected, actual) + } + } +} + +func BenchmarkSumOfProperDivisors(b *testing.B) { + for i := 0; i < b.N; i++ { + math.SumOfProperDivisors(800) + } +} + +type isPerfectNumberTestCase struct { + number uint + isPerfect bool +} + +// getIsPerfectNumberTestCases returns an array of test data +// for the tests of the function IsPerfectNumber +// Data was verified using [A000396]. +// [A000396]: https://oeis.org/A000396 +func getIsPerfectNumberTestCases() []isPerfectNumberTestCase { + return []isPerfectNumberTestCase{ + {6, true}, + {28, true}, + {496, true}, + {8128, true}, + {33550336, true}, + {0, false}, + {1, false}, + {2, false}, + {3, false}, + {4, false}, + {5, false}, + {7, false}, + {100, false}, + {219, false}, + {997, false}, + {33550335, false}, + {33550337, false}, + } +} + +func TestIsPerfectNumber(t *testing.T) { + for _, tc := range getIsPerfectNumberTestCases() { + if math.IsPerfectNumber(tc.number) != tc.isPerfect { + t.Errorf("Unexpected output for %d", tc.number) + } + } +} + +func BenchmarkIsPerfectNumber(b *testing.B) { + for i := 0; i < b.N; i++ { + math.IsPerfectNumber(8128) + } +} diff --git a/math/permutation/heaps.go b/math/permutation/heaps.go new file mode 100644 index 000000000..5f4ebaed3 --- /dev/null +++ b/math/permutation/heaps.go @@ -0,0 +1,48 @@ +// heaps.go +// description: Implementation of Heap's Algorithm for generating all permutations of n objects +// time complexity: O(n!) +// space complexity: O(n) + +package permutation + +import ( + "strings" +) + +// Heap's Algorithm for generating all permutations of n objects +func Heaps(out chan []string, n int) { + elementSetCh := make(chan []string) + go GenerateElementSet(elementSetCh, n) + elementSet := <-elementSetCh + + var recursiveGenerate func([]string, int, []string) + var permutations []string + recursiveGenerate = func(previousIteration []string, n int, elements []string) { + if n == 1 { + permutations = append(permutations, strings.Join(elements, "")) + } else { + for i := 0; i < n; i++ { + recursiveGenerate(previousIteration, n-1, elements) + if n%2 == 1 { + tmp := elements[i] + elements[i] = elements[n-1] + elements[n-1] = tmp + } else { + tmp := elements[0] + elements[0] = elements[n-1] + elements[n-1] = tmp + } + } + } + } + recursiveGenerate(permutations, n, elementSet) + out <- permutations +} + +func GenerateElementSet(out chan []string, n int) { + elementSet := make([]string, n) + for i := range elementSet { + elementSet[i] = string(rune(i + 49)) // Adjust this if you want to change your charset + } + out <- elementSet +} diff --git a/math/permutation/heaps_test.go b/math/permutation/heaps_test.go new file mode 100644 index 000000000..224ea15b2 --- /dev/null +++ b/math/permutation/heaps_test.go @@ -0,0 +1,31 @@ +package permutation + +import ( + "reflect" + "sort" + "testing" +) + +func TestHeaps(t *testing.T) { + t.Run("Should generate permutations for various size sets", func(t *testing.T) { + expectedValues := [][]string{ + {"1"}, + {"12", "21"}, + {"123", "213", "321", "231", "312", "132"}, + {"1234", "1243", "1324", "1342", "1423", "1432", "2134", "2143", "2314", "2341", "2413", "2431", "3124", "3142", "3214", "3241", "3412", "3421", "4123", "4132", "4213", "4231", "4312", "4321"}, + {"12345", "12354", "12435", "12453", "12534", "12543", "13245", "13254", "13425", "13452", "13524", "13542", "14235", "14253", "14325", "14352", "14523", "14532", "15234", "15243", "15324", "15342", "15423", "15432", "21345", "21354", "21435", "21453", "21534", "21543", "23145", "23154", "23415", "23451", "23514", "23541", "24135", "24153", "24315", "24351", "24513", "24531", "25134", "25143", "25314", "25341", "25413", "25431", "31245", "31254", "31425", "31452", "31524", "31542", "32145", "32154", "32415", "32451", "32514", "32541", "34125", "34152", "34215", "34251", "34512", "34521", "35124", "35142", "35214", "35241", "35412", "35421", "41235", "41253", "41325", "41352", "41523", "41532", "42135", "42153", "42315", "42351", "42513", "42531", "43125", "43152", "43215", "43251", "43512", "43521", "45123", "45132", "45213", "45231", "45312", "45321", "51234", "51243", "51324", "51342", "51423", "51432", "52134", "52143", "52314", "52341", "52413", "52431", "53124", "53142", "53214", "53241", "53412", "53421", "54123", "54132", "54213", "54231", "54312", "54321"}, + } + permutationsCh := make(chan []string) + var value []string + + for i := 1; i <= 5; i++ { + go Heaps(permutationsCh, i) + value = <-permutationsCh + sort.Strings(value) + sort.Strings(expectedValues[i-1]) + if !reflect.DeepEqual(value, expectedValues[i-1]) { + t.Errorf("Permutation set is incorrect for element size of %v. Expected (%v) and received (%v)", i, expectedValues[i-1], value) + } + } + }) +} diff --git a/math/permutation/next_permutation.go b/math/permutation/next_permutation.go new file mode 100644 index 000000000..6aff11296 --- /dev/null +++ b/math/permutation/next_permutation.go @@ -0,0 +1,39 @@ +// A practice to find lexicographically next greater permutation of the given array of integers. +// If there does not exist any greater permutation, then print the lexicographically smallest permutation of the given array. +// The implementation below, finds the next permutation in linear time and constant memory and returns in place +// time complexity: O(n) +// space complexity: O(1) +// Useful reference: https://www.geeksforgeeks.org/next-permutation/ + +package permutation + +func NextPermutation(nums []int) { + pivot := 0 + for pivot = len(nums) - 2; pivot >= 0; pivot-- { + if nums[pivot] < nums[pivot+1] { + break + } + } + if pivot < 0 { + // current permutation is the last and must be reversed totally + for l, r := 0, len(nums)-1; l < r; l, r = l+1, r-1 { + nums[l], nums[r] = nums[r], nums[l] + } + } else { + succ := 0 + for succ = len(nums) - 1; succ > pivot; succ = succ - 1 { + if nums[succ] > nums[pivot] { + break + } + } + + // Swap the pivot and successor + nums[pivot], nums[succ] = nums[succ], nums[pivot] + + // Reverse the suffix part to minimize it + for l, r := pivot+1, len(nums)-1; l < r; l, r = l+1, r-1 { + nums[l], nums[r] = nums[r], nums[l] + } + } + +} diff --git a/math/permutation/next_permutation_test.go b/math/permutation/next_permutation_test.go new file mode 100644 index 000000000..8246876b4 --- /dev/null +++ b/math/permutation/next_permutation_test.go @@ -0,0 +1,40 @@ +package permutation + +import ( + "reflect" + "testing" +) + +func TestNextPermutation(t *testing.T) { + var nextPermutationTestData = []struct { + description string + numbers []int + next []int + }{ + { + description: "Basic case", + numbers: []int{1, 2, 3}, + next: []int{1, 3, 2}, + }, + { + description: "Should reverse the whole slice", + numbers: []int{3, 2, 1}, + next: []int{1, 2, 3}, + }, + { + description: "A more complex test", + numbers: []int{2, 4, 1, 7, 5, 0}, + next: []int{2, 4, 5, 0, 1, 7}, + }, + } + for _, test := range nextPermutationTestData { + t.Run(test.description, func(t *testing.T) { + NextPermutation(test.numbers) + + if !reflect.DeepEqual(test.numbers, test.next) { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expected result:%v\nFound: %v", test.next, test.numbers) + } + }) + } +} diff --git a/math/pi/montecarlopi.go b/math/pi/montecarlopi.go new file mode 100644 index 000000000..a2e140f08 --- /dev/null +++ b/math/pi/montecarlopi.go @@ -0,0 +1,95 @@ +// montecarlopi.go +// description: Calculating pi by the Monte Carlo method +// details: +// implementations of Monte Carlo Algorithm for the calculating of Pi - [Monte Carlo method](https://en.wikipedia.org/wiki/Monte_Carlo_method) +// time complexity: O(n) +// space complexity: O(1) +// author(s): [red_byte](https://github.com/i-redbyte), [Paul Leydier] (https://github.com/paul-leydier) +// see montecarlopi_test.go + +package pi + +import ( + "fmt" // Used for error formatting + "math/rand" // Used for random number generation in Monte Carlo method + "runtime" // Used to get information on available CPUs + "time" // Used for seeding the random number generation +) + +func MonteCarloPi(randomPoints int) float64 { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + inside := 0 + for i := 0; i < randomPoints; i++ { + x := rnd.Float64() + y := rnd.Float64() + if x*x+y*y <= 1 { + inside += 1 + } + } + pi := float64(inside) / float64(randomPoints) * 4 + return pi +} + +// MonteCarloPiConcurrent approximates the value of pi using the Monte Carlo method. +// Unlike the MonteCarloPi function (first version), this implementation uses +// goroutines and channels to parallelize the computation. +// More details on the Monte Carlo method available at https://en.wikipedia.org/wiki/Monte_Carlo_method. +// More details on goroutines parallelization available at https://go.dev/doc/effective_go#parallel. +func MonteCarloPiConcurrent(n int) (float64, error) { + numCPU := runtime.GOMAXPROCS(0) + c := make(chan int, numCPU) + pointsToDraw, err := splitInt(n, numCPU) // split the task in sub-tasks of approximately equal sizes + if err != nil { + return 0, err + } + + // launch numCPU parallel tasks + for _, p := range pointsToDraw { + go drawPoints(p, c) + } + + // collect the tasks results + inside := 0 + for i := 0; i < numCPU; i++ { + inside += <-c + } + return float64(inside) / float64(n) * 4, nil +} + +// drawPoints draws n random two-dimensional points in the interval [0, 1), [0, 1) and sends through c +// the number of points which where within the circle of center 0 and radius 1 (unit circle) +func drawPoints(n int, c chan<- int) { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + inside := 0 + for i := 0; i < n; i++ { + x, y := rnd.Float64(), rnd.Float64() + if x*x+y*y <= 1 { + inside++ + } + } + c <- inside +} + +// splitInt takes an integer x and splits it within an integer slice of length n in the most uniform +// way possible. +// For example, splitInt(10, 3) will return []int{4, 3, 3}, nil +func splitInt(x int, n int) ([]int, error) { + if x < n { + return nil, fmt.Errorf("x must be < n - given values are x=%d, n=%d", x, n) + } + split := make([]int, n) + if x%n == 0 { + for i := 0; i < n; i++ { + split[i] = x / n + } + } else { + limit := x % n + for i := 0; i < limit; i++ { + split[i] = x/n + 1 + } + for i := limit; i < n; i++ { + split[i] = x / n + } + } + return split, nil +} diff --git a/math/pi/montecarlopi_test.go b/math/pi/montecarlopi_test.go new file mode 100644 index 000000000..acf862453 --- /dev/null +++ b/math/pi/montecarlopi_test.go @@ -0,0 +1,83 @@ +// montecarlopi_test.go +// description: Test for calculating pi by the Monte Carlo method +// author(s) [red_byte](https://github.com/i-redbyte) +// see montecarlopi.go + +package pi + +import ( + "fmt" + "testing" +) + +func TestMonteCarloPi(t *testing.T) { + t.Run("Monte Carlo Pi", func(t *testing.T) { + result := fmt.Sprintf("%.2f", MonteCarloPi(100000000)) + t.Log(result) + if result != "3.14" { + t.Errorf("Wrong result! Expected:%f, returned:%s ", 3.1415, result) + } + }) +} + +func BenchmarkMonteCarloPi(b *testing.B) { + for i := 0; i < b.N; i++ { + MonteCarloPi(100000000) + } +} + +func TestSplitInt(t *testing.T) { + testCases := []struct { + name string + x int + n int + expectedResult []int + expectedError bool + }{ + {"multiple", 10, 5, []int{2, 2, 2, 2, 2}, false}, + {"n=1", 10, 1, []int{10}, false}, + {"x=10, n=3", 10, 3, []int{4, 3, 3}, false}, + {"x=10, n=7", 10, 7, []int{2, 2, 2, 1, 1, 1, 1}, false}, + {"n>x", 10, 11, nil, true}, + } + for _, testCase := range testCases { + t.Run(testCase.name, func(t *testing.T) { + res, err := splitInt(testCase.x, testCase.n) + for i := 0; i < len(testCase.expectedResult); i++ { + if res[i] != testCase.expectedResult[i] { + t.Fatalf("unexpected result at index %d: %d - expected %d", i, res[i], testCase.expectedResult[i]) + } + } + if testCase.expectedError { + if err == nil { + t.Fatal("expected an error, got nil") + } + } else { + if err != nil { + t.Fatalf("unexpected error - %s", err) + } + } + }) + } +} + +func TestMonteCarloPi2(t *testing.T) { + res, err := MonteCarloPiConcurrent(100000000) + if err != nil { + t.Errorf("unexpected error %s", err) + } + result := fmt.Sprintf("%.2f", res) + t.Log(result) + if result != "3.14" { + t.Errorf("Wrong result! Expected:%f, returned:%s ", 3.1415, result) + } +} + +func BenchmarkMonteCarloPi2(b *testing.B) { + for i := 0; i < b.N; i++ { + _, err := MonteCarloPiConcurrent(100000000) + if err != nil { + b.Fatalf("unexpected error - %s", err) + } + } +} diff --git a/math/pi/spigotpi.go b/math/pi/spigotpi.go new file mode 100644 index 000000000..349602a32 --- /dev/null +++ b/math/pi/spigotpi.go @@ -0,0 +1,61 @@ +// spigotpi.go +// description: A Spigot Algorithm for the Digits of Pi +// details: +// implementation of Spigot Algorithm for the Digits of Pi - [Spigot algorithm](https://en.wikipedia.org/wiki/Spigot_algorithm) +// time complexity: O(n) +// space complexity: O(n) +// author(s) [red_byte](https://github.com/i-redbyte) +// see spigotpi_test.go + +package pi + +import "strconv" + +func Spigot(n int) string { + pi := "" + boxes := n * 10 / 3 + remainders := make([]int, boxes) + for i := 0; i < boxes; i++ { + remainders[i] = 2 + } + digitsHeld := 0 + for i := 0; i < n; i++ { + carriedOver := 0 + sum := 0 + for j := boxes - 1; j >= 0; j-- { + remainders[j] *= 10 + sum = remainders[j] + carriedOver + quotient := sum / (j*2 + 1) + remainders[j] = sum % (j*2 + 1) + carriedOver = quotient * j + } + remainders[0] = sum % 10 + q := sum / 10 + switch q { + case 9: + digitsHeld++ + case 10: + q = 0 + for k := 1; k <= digitsHeld; k++ { + replaced, _ := strconv.Atoi(pi[i-k : i-k+1]) + if replaced == 9 { + replaced = 0 + } else { + replaced++ + } + pi = delChar(pi, i-k) + pi = pi[:i-k] + strconv.Itoa(replaced) + pi[i-k:] + } + digitsHeld = 1 + default: + digitsHeld = 1 + } + pi += strconv.Itoa(q) + } + return pi +} + +func delChar(s string, index int) string { + tmp := []rune(s) + return string(append(tmp[0:index], tmp[index+1:]...)) +} diff --git a/math/pi/spigotpi_test.go b/math/pi/spigotpi_test.go new file mode 100644 index 000000000..c48b7dc24 --- /dev/null +++ b/math/pi/spigotpi_test.go @@ -0,0 +1,60 @@ +// spigotpi_test.go +// description: Test for Spigot Algorithm for the Digits of Pi +// author(s) [red_byte](https://github.com/i-redbyte) +// see spigotpi.go +package pi + +import ( + "strconv" + "testing" +) + +func TestSpigot(t *testing.T) { + var tests = []struct { + result string + n int + }{ + {"314", 3}, + {"31415", 5}, + {"314159", 6}, + {"31415926535", 11}, + {"314159265358", 12}, + {"314159265358979323846", 21}, + {"3141592653589793238462643", 25}, + {"314159265358979323846264338327950", 33}, + {"31415926535897932384626433832795028841971693993751" + + "05820974944592307816406286208998628034825342117067" + + "98214808651328230664709384460955058223172535940812" + + "84811174502841027019385211055596446229489549303819" + + "64428810975665933446128475648233786783165271201909" + + "14564856692346034861045432664821339360726024914127" + + "37245870066063155881748815209209628292540917153643" + + "678925903600", 362}, + } + for _, tv := range tests { + t.Run(strconv.Itoa(tv.n)+":"+tv.result, func(t *testing.T) { + result := Spigot(tv.n) + if result != tv.result { + t.Errorf("Bad result %d:%s", tv.n, tv.result) + } + }) + } +} + +func BenchmarkPiSpigotN10(b *testing.B) { + for i := 0; i < b.N; i++ { + Spigot(10) + } +} + +func BenchmarkPiSpigotN100(b *testing.B) { + for i := 0; i < b.N; i++ { + Spigot(100) + } +} + +func BenchmarkPiSpigotN1000(b *testing.B) { + for i := 0; i < b.N; i++ { + Spigot(1000) + } +} diff --git a/math/pollard.go b/math/pollard.go new file mode 100644 index 000000000..a2cc42df1 --- /dev/null +++ b/math/pollard.go @@ -0,0 +1,45 @@ +// pollard.go +// description: Pollard's rho algorithm +// details: +// implementation of Pollard's rho algorithm for integer factorization-[Pollard's rho algorithm](https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm) +// time complexity: O(n^(1/4)) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see pollard_test.go + +package math + +import ( + "errors" + "math/big" +) + +// DefaultPolynomial is the commonly used polynomial g(x) = (x^2 + 1) mod n +func DefaultPolynomial(n *big.Int) func(*big.Int) *big.Int { + bigOne := big.NewInt(1) + bigTwo := big.NewInt(2) + return func(x *big.Int) *big.Int { + xSquared := new(big.Int).Exp(x, bigTwo, n) // see: https://en.wikipedia.org/wiki/Pollard%27s_rho_algorithm#Core_ideas + xSquared.Add(xSquared, bigOne) + xSquared.Mod(xSquared, n) + return xSquared + } +} + +// PollardsRhoFactorization is an implementation of Pollard's rho factorization algorithm +// using the default parameters x = y = 2 +func PollardsRhoFactorization(n *big.Int, f func(n *big.Int) func(x *big.Int) *big.Int) (*big.Int, error) { + x, y, d := big.NewInt(2), big.NewInt(2), big.NewInt(1) + bigOne := big.NewInt(1) + g := f(n) + for d.Cmp(bigOne) == 0 { + x = g(x) + y = g(g(y)) + sub := new(big.Int).Sub(x, y) + d.GCD(nil, nil, sub.Abs(sub), n) + } + if d.Cmp(n) == 0 { + return nil, errors.New("factorization failed") + } + return d, nil +} diff --git a/math/pollard_test.go b/math/pollard_test.go new file mode 100644 index 000000000..d77d81b22 --- /dev/null +++ b/math/pollard_test.go @@ -0,0 +1,79 @@ +// pollard_test.go +// description: Test for Pollard's rho algorithm +// author(s) [red_byte](https://github.com/i-redbyte) +// see pollard.go + +package math + +import ( + "math/big" + "reflect" + "testing" +) + +func TestDefaultPolynomial(t *testing.T) { + tests := []struct { + name string + x *big.Int + n *big.Int + want *big.Int + }{ + {"Polynomial for n = 1772; x = 535", big.NewInt(535), big.NewInt(1772), big.NewInt(934)}, + {"Polynomial for n = 666; x = 53135", big.NewInt(53135), big.NewInt(666), big.NewInt(380)}, + {"Polynomial for n = 666; x = 13", big.NewInt(13), big.NewInt(666), big.NewInt(170)}, + {"Polynomial for n = 1917; x = 2510", big.NewInt(2510), big.NewInt(1917), big.NewInt(839)}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + if got := DefaultPolynomial(test.n)(test.x); !reflect.DeepEqual(got, test.want) { + t.Errorf("DefaultPolynomial() = %v, want %v", got, test.want) + } + }) + } +} + +func TestRho(t *testing.T) { + tests := []struct { + name string + n *big.Int + g func(n *big.Int) func(*big.Int) *big.Int + want *big.Int + wantErr bool + }{ + {"Factor of n: 11235 ", big.NewInt(11235), DefaultPolynomial, big.NewInt(21), false}, + {"Factor of n: 111155 ", big.NewInt(111155), DefaultPolynomial, big.NewInt(11), false}, + {"Factor of n: 8080 ", big.NewInt(8080), DefaultPolynomial, big.NewInt(16), false}, + {"Factor of n: 8536 ", big.NewInt(8536), DefaultPolynomial, big.NewInt(88), false}, + {"Factor of n: 666 ", big.NewInt(666), DefaultPolynomial, big.NewInt(3), false}, + {"Factor of n: 2 ", big.NewInt(2), DefaultPolynomial, big.NewInt(2), true}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + got, err := PollardsRhoFactorization(test.n, test.g) + if err != nil && !test.wantErr { + t.Errorf("PollardsRhoFactorization() error = %v, wantErr %v", err, test.wantErr) + return + } else if err != nil && test.wantErr { + return + } + if !reflect.DeepEqual(got, test.want) { + t.Errorf("PollardsRhoFactorization() got = %v, want %v", got, test.want) + } + }) + } +} + +func BenchmarkDefaultPolynomial(b *testing.B) { + for i := 0; i < b.N; i++ { + DefaultPolynomial(big.NewInt(535))(big.NewInt(11235)) + } +} + +func BenchmarkRho(b *testing.B) { + for i := 0; i < b.N; i++ { + _, err := PollardsRhoFactorization(big.NewInt(535), DefaultPolynomial) + if err != nil { + return + } + } +} diff --git a/math/power/fastexponent.go b/math/power/fastexponent.go new file mode 100644 index 000000000..c7626b045 --- /dev/null +++ b/math/power/fastexponent.go @@ -0,0 +1,38 @@ +package power + +// IterativePower is iterative O(logn) function for pow(x, y) +func IterativePower(n uint, power uint) uint { + var res uint = 1 + for power > 0 { + if (power & 1) != 0 { + res = res * n + } + + power = power >> 1 + n *= n + } + return res +} + +// RecursivePower is recursive O(logn) function for pow(x, y) +func RecursivePower(n uint, power uint) uint { + if power == 0 { + return 1 + } + var temp = RecursivePower(n, power/2) + if power%2 == 0 { + return temp * temp + } + return n * temp * temp +} + +// RecursivePower1 is recursive O(n) function for pow(x, y) +func RecursivePower1(n uint, power uint) uint { + if power == 0 { + return 1 + } else if power%2 == 0 { + return RecursivePower1(n, power/2) * RecursivePower1(n, power/2) + } else { + return n * RecursivePower1(n, power/2) * RecursivePower1(n, power/2) + } +} diff --git a/math/power/fastexponent_test.go b/math/power/fastexponent_test.go new file mode 100644 index 000000000..6a2f671eb --- /dev/null +++ b/math/power/fastexponent_test.go @@ -0,0 +1,67 @@ +package power + +import "testing" + +var testCases = []struct { + name string + base uint + power uint + expected uint +}{ + {"0^2", 0, 2, 0}, + {"2^0", 2, 0, 1}, + {"2^3", 2, 3, 8}, + {"8^3", 8, 3, 512}, + {"10^5", 10, 5, 100000}, +} + +func TestIterativePower(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := IterativePower(tc.base, tc.power) + if actual != tc.expected { + t.Errorf("Expected %d to the power of %d to be: %d, but got: %d", tc.base, tc.power, tc.expected, actual) + } + }) + } +} + +func TestRecursivePower(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := RecursivePower(tc.base, tc.power) + if actual != tc.expected { + t.Errorf("Expected %d to the power of %d to be: %d, but got: %d", tc.base, tc.power, tc.expected, actual) + } + }) + } +} + +func TestRecursivePower1(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := RecursivePower1(tc.base, tc.power) + if actual != tc.expected { + t.Errorf("Expected %d to the power of %d to be: %d, but got: %d", tc.base, tc.power, tc.expected, actual) + } + }) + } +} + +func BenchmarkIterativePower(b *testing.B) { + for i := 0; i < b.N; i++ { + IterativePower(10, 5) + } +} + +func BenchmarkRecursivePower(b *testing.B) { + for i := 0; i < b.N; i++ { + RecursivePower(10, 5) + } +} + +func BenchmarkRecursivePower1(b *testing.B) { + for i := 0; i < b.N; i++ { + RecursivePower1(10, 5) + } +} diff --git a/math/power/powvialogarithm.go b/math/power/powvialogarithm.go new file mode 100644 index 000000000..c2a395e3b --- /dev/null +++ b/math/power/powvialogarithm.go @@ -0,0 +1,26 @@ +// powvialogarithm.go +// description: Powers in terms of logarithms +// details: +// implementation of exponentiation using exponent and logarithm, without using loops - [Powers via logarithms wiki](https://en.wikipedia.org/wiki/Exponentiation#Powers_via_logarithms) +// time complexity: O(1) +// space complexity: O(1) +// author(s) [red_byte](https://github.com/i-redbyte) +// see powvialogarithm_test.go + +package power + +import ( + "math" +) + +func UsingLog(a float64, b float64) float64 { + var p float64 + p = 1 + if a < 0 && int(b)&1 != 0 { + p = -1 + } + log := math.Log(math.Abs(a)) + exp := math.Exp(b * log) + result := exp * p + return math.Round(result) +} diff --git a/math/power/powvialogarithm_test.go b/math/power/powvialogarithm_test.go new file mode 100644 index 000000000..e38046c9c --- /dev/null +++ b/math/power/powvialogarithm_test.go @@ -0,0 +1,44 @@ +// powvialogarithm_test.go +// description: Test for UsingLog +// author(s) [red_byte](https://github.com/i-redbyte) +// see powvialogarithm.go + +package power + +import "testing" + +func TestUsingLog(t *testing.T) { + var tests = []struct { + name string + base float64 + power float64 + expected float64 + }{ + {"0^0", 99, 1, 99}, + {"-3^9", -3, 9, -19683}, + {"0^2", 0, 2, 0}, + {"2^0", 2, 0, 1}, + {"2^3", 2, 3, 8}, + {"8^3", 8, 3, 512}, + {"11^11", 11, 11, 285311670611}, + {"5^5", 5, 5, 3125}, + {"-7^2", -7, 2, 49}, + {"-6^3", -6, 3, -216}, + } + + for _, tc := range tests { + t.Run(tc.name, func(t *testing.T) { + result := UsingLog(tc.base, tc.power) + t.Log(result) + if result != tc.expected { + t.Errorf("Expected %.2f to the power of %.2f to be: %.2f, but got: %.2f", tc.base, tc.power, tc.expected, result) + } + }) + } +} + +func BenchmarkUsingLog(b *testing.B) { + for i := 0; i < b.N; i++ { + UsingLog(10, 5) + } +} diff --git a/math/prime/millerrabintest.go b/math/prime/millerrabintest.go new file mode 100644 index 000000000..5357bc45c --- /dev/null +++ b/math/prime/millerrabintest.go @@ -0,0 +1,162 @@ +// This file implements two versions of the Miller-Rabin primality test. +// One of the implementations is deterministic and the other is probabilistic. +// The Miller-Rabin test is one of the simplest and fastest known primality +// tests and is widely used. +// time complexity: O(k * log(n)^3) +// space complexity: O(1) +// Authors: +// [Taj](https://github.com/tjgurwara99) +// [Rak](https://github.com/raklaptudirm) + +package prime + +import ( + "math/rand" + + "github.com/TheAlgorithms/Go/math/modular" +) + +// formatNum accepts a number and returns the +// odd number d such that num = 2^s * d + 1 +func formatNum(num int64) (d int64, s int64) { + d = num - 1 + for num%2 == 0 { + d /= 2 + s++ + } + return +} + +// isTrivial checks if num's primality is easy to determine. +// If it is, it returns true and num's primality. Otherwise +// it returns false and false. +func isTrivial(num int64) (prime bool, trivial bool) { + if num <= 4 { + // 2 and 3 are primes + prime = num == 2 || num == 3 + trivial = true + } else { + prime = false + // number is trivial prime if + // it is divisible by 2 + trivial = num%2 == 0 + } + + return +} + +// MillerTest tests whether num is a strong probable prime to a witness. +// Formally: a^d ≡ 1 (mod n) or a^(2^r * d) ≡ -1 (mod n), 0 <= r <= s +func MillerTest(num, witness int64) (bool, error) { + d, _ := formatNum(num) + res, err := modular.Exponentiation(witness, d, num) + + if err != nil { + return false, err + } + // miller conditions checks + if res == 1 || res == num-1 { + return true, nil + } + + for d != num-1 { + res = (res * res) % num + d *= 2 + if res == 1 { + return false, nil + } + if res == num-1 { + return true, nil + } + } + return false, nil +} + +// MillerRandomTest This is the intermediate step that repeats within the +// miller rabin primality test for better probabilitic chances of +// receiving the correct result with random witnesses. +func MillerRandomTest(num int64) (bool, error) { + random := rand.Int63n(num-2) + 2 + return MillerTest(num, random) +} + +// MillerTestMultiple is like MillerTest but runs the test for multiple +// witnesses. +func MillerTestMultiple(num int64, witnesses ...int64) (bool, error) { + for _, witness := range witnesses { + prime, err := MillerTest(num, witness) + if err != nil { + return false, err + } + + if !prime { + return false, nil + } + } + + return true, nil +} + +// MillerRabinProbabilistic is a probabilistic test for primality +// of an integer based of the algorithm devised by Miller and Rabin. +func MillerRabinProbabilistic(num, rounds int64) (bool, error) { + if prime, trivial := isTrivial(num); trivial { + // num is a trivial number + return prime, nil + } + + for i := int64(0); i < rounds; i++ { + val, err := MillerRandomTest(num) + if err != nil { + return false, err + } + if !val { + return false, nil + } + } + return true, nil +} + +// MillerRabinDeterministic is a Deterministic version of the Miller-Rabin +// test, which returns correct results for all valid int64 numbers. +func MillerRabinDeterministic(num int64) (bool, error) { + if prime, trivial := isTrivial(num); trivial { + // num is a trivial number + return prime, nil + } + + switch { + case num < 2047: + // witness 2 can determine the primality of any number less than 2047 + return MillerTest(num, 2) + case num < 1_373_653: + // witnesses 2 and 3 can determine the primality + // of any number less than 1,373,653 + return MillerTestMultiple(num, 2, 3) + case num < 9_080_191: + // witnesses 31 and 73 can determine the primality + // of any number less than 9,080,191 + return MillerTestMultiple(num, 31, 73) + case num < 25_326_001: + // witnesses 2, 3, and 5 can determine the + // primality of any number less than 25,326,001 + return MillerTestMultiple(num, 2, 3, 5) + case num < 1_122_004_669_633: + // witnesses 2, 13, 23, and 1,662,803 can determine the + // primality of any number less than 1,122,004,669,633 + return MillerTestMultiple(num, 2, 13, 23, 1_662_803) + case num < 2_152_302_898_747: + // witnesses 2, 3, 5, 7, and 11 can determine the primality + // of any number less than 2,152,302,898,747 + return MillerTestMultiple(num, 2, 3, 5, 7, 11) + case num < 341_550_071_728_321: + // witnesses 2, 3, 5, 7, 11, 13, and 17 can determine the + // primality of any number less than 341,550,071,728,321 + return MillerTestMultiple(num, 2, 3, 5, 7, 11, 13, 17) + default: + // witnesses 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, and 37 can determine + // the primality of any number less than 318,665,857,834,031,151,167,461 + // which is well above the max int64 9,223,372,036,854,775,807 + return MillerTestMultiple(num, 2, 3, 5, 7, 11, 13, 17, 19, 23, 31, 37) + } +} diff --git a/math/prime/prime_test.go b/math/prime/prime_test.go new file mode 100644 index 000000000..e06f4a6de --- /dev/null +++ b/math/prime/prime_test.go @@ -0,0 +1,95 @@ +package prime + +import ( + "fmt" + "testing" +) + +var primeList = []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127} +var testLimit = 127 + +type primalityTest func(int64) bool + +func primalityTestTestingHelper(t *testing.T, name string, f primalityTest) { + arrayIndex := 0 + for i := 1; i <= testLimit; i++ { + isPrime := i == primeList[arrayIndex] + + testName := fmt.Sprintf("%s(%d)", name, i) + t.Run(testName, func(t *testing.T) { + result := f(int64(i)) + + if isPrime { + arrayIndex++ + } + + if result != isPrime { + t.Errorf("%d: %s function returned %v\n", i, name, result) + } + }) + } +} + +func primalityTestBenchmarkHelper(b *testing.B, f primalityTest) { + for i := 0; i < b.N; i++ { + f(104729) + } +} + +// Miller-Rabin Probabilistic test + +func millerRabinProbabilisticTester(n int64) bool { + result, err := MillerRabinProbabilistic(n, 40) + if err != nil { + panic(err) + } + + return result +} + +func TestMillerRabinProbabilistic(t *testing.T) { + primalityTestTestingHelper(t, "Miller-Rabin Probabilistic", millerRabinProbabilisticTester) +} + +func BenchmarkMillerRabinProbabilistic(b *testing.B) { + primalityTestBenchmarkHelper(b, millerRabinProbabilisticTester) +} + +// Miller-Rabin deterministic test + +func millerRabinDeterministicTester(n int64) bool { + result, err := MillerRabinDeterministic(n) + if err != nil { + panic(err) + } + + return result +} + +func TestMillerRabinDeterministic(t *testing.T) { + primalityTestTestingHelper(t, "Miller-Rabin Deterministic", millerRabinDeterministicTester) +} + +func BenchmarkMillerRabinDeterministic(b *testing.B) { + primalityTestBenchmarkHelper(b, millerRabinDeterministicTester) +} + +// Trial Division test + +func TestTrialDivision(t *testing.T) { + primalityTestTestingHelper(t, "Trial Division", TrialDivision) +} + +func BenchmarkTrialDivision(b *testing.B) { + primalityTestBenchmarkHelper(b, TrialDivision) +} + +// Trial Division (optimized) + +func TestOptimizedTrialDivision(t *testing.T) { + primalityTestTestingHelper(t, "Trial Division (optimized)", OptimizedTrialDivision) +} + +func BenchmarkOptimizedTrialDivision(b *testing.B) { + primalityTestBenchmarkHelper(b, OptimizedTrialDivision) +} diff --git a/math/prime/primecheck.go b/math/prime/primecheck.go new file mode 100644 index 000000000..7671c9cd0 --- /dev/null +++ b/math/prime/primecheck.go @@ -0,0 +1,50 @@ +package prime + +// A primality test is an algorithm for determining whether an input number is prime. Among other +// fields of mathematics, it is used for cryptography. Unlike integer factorization, primality +// tests do not generally give prime factors, only stating whether the input number is prime or not. +// time complexity: O(sqrt(n)) +// space complexity: O(1) +// Source - Wikipedia https://en.wikipedia.org/wiki/Primality_test + +// TrialDivision tests whether a number is prime by trying to divide it by the numbers less than it. +func TrialDivision(n int64) bool { + if n < 2 { + return false + } + + for i := int64(2); i < n; i++ { + + if n%i == 0 { + return false + } + } + return true +} + +// OptimizedTrialDivision checks primality of an integer using an optimized trial division method. +// The optimizations include not checking divisibility by the even numbers and only checking up to +// the square root of the given number. +func OptimizedTrialDivision(n int64) bool { + // 0 and 1 are not prime + if n < 2 { + return false + } + + // 2 and 3 are prime + if n < 4 { + return true + } + + // all numbers divisible by 2 except 2 are not prime + if n%2 == 0 { + return false + } + + for i := int64(3); i*i <= n; i += 2 { + if n%i == 0 { + return false + } + } + return true +} diff --git a/math/prime/primefactorization.go b/math/prime/primefactorization.go new file mode 100644 index 000000000..43479e439 --- /dev/null +++ b/math/prime/primefactorization.go @@ -0,0 +1,27 @@ +// primefactorization.go +// description: Prime factorization of a number +// time complexity: O(sqrt(n)) +// space complexity: O(sqrt(n)) + +package prime + +// Factorize is a function that computes the exponents +// of each prime in the prime factorization of n +func Factorize(n int64) map[int64]int64 { + result := make(map[int64]int64) + + for i := int64(2); i*i <= n; i += 1 { + for { + if n%i != 0 { + break + } + result[i] += 1 + n /= i + } + + } + if n > 1 { + result[n] += 1 + } + return result +} diff --git a/math/prime/primefactorization_test.go b/math/prime/primefactorization_test.go new file mode 100644 index 000000000..a5c900fe8 --- /dev/null +++ b/math/prime/primefactorization_test.go @@ -0,0 +1,33 @@ +package prime + +import ( + "reflect" + "testing" +) + +func TestFactorize(t *testing.T) { + var tests = []struct { + n int64 + expected map[int64]int64 + }{ + {4, map[int64]int64{2: 2}}, + {5, map[int64]int64{5: 1}}, + {7, map[int64]int64{7: 1}}, + {10, map[int64]int64{2: 1, 5: 1}}, + {999, map[int64]int64{3: 3, 37: 1}}, + {999999999999878, map[int64]int64{2: 1, 19: 1, 26315789473681: 1}}, + } + for _, test := range tests { + result := Factorize(test.n) + t.Log(test.n, " ", result) + if !reflect.DeepEqual(result, test.expected) { + t.Errorf("Wrong result! Expected:%v, returned:%v ", test.expected, result) + } + } +} + +func BenchmarkFactorize(b *testing.B) { + for i := 0; i < b.N; i++ { + Factorize(1000000007) + } +} diff --git a/math/prime/sieve.go b/math/prime/sieve.go new file mode 100644 index 000000000..e6b216a68 --- /dev/null +++ b/math/prime/sieve.go @@ -0,0 +1,40 @@ +// sieve.go +// description: Algorithms for generating prime numbers efficiently +// author(s) [Taj](https://github.com/tjgurwara99) +// see sieve_test.go + +package prime + +// Generate generates the sequence of integers starting at 2 and sends it to the channel `ch` +func GenerateChannel(ch chan<- int) { + for i := 2; ; i++ { + ch <- i + } +} + +// Sieve Sieving the numbers that are not prime from the channel - basically removing them from the channels +func Sieve(in <-chan int, out chan<- int, prime int) { + for { + i := <-in + if i%prime != 0 { + out <- i + } + } +} + +// Generate returns a int slice of prime numbers up to the limit +func Generate(limit int) []int { + var primes []int + + ch := make(chan int) + go GenerateChannel(ch) + + for i := 0; i < limit; i++ { + primes = append(primes, <-ch) + ch1 := make(chan int) + go Sieve(ch, ch1, primes[i]) + ch = ch1 + } + + return primes +} diff --git a/math/prime/sieve2.go b/math/prime/sieve2.go new file mode 100644 index 000000000..881ca20f5 --- /dev/null +++ b/math/prime/sieve2.go @@ -0,0 +1,23 @@ +/* sieve2.go - Sieve of Eratosthenes + * Algorithm to generate prime numbers up to a limit + * time complexity: O(n log log n) + * space complexity: O(n) + * Author: ddaniel27 + */ +package prime + +func SieveEratosthenes(limit int) []int { + primes := make([]int, 0) + sieve := make([]int, limit+1) // make a slice of size limit+1 + + for i := 2; i <= limit; i++ { + if sieve[i] == 0 { // if the number is not marked as composite + primes = append(primes, i) // add it to the list of primes + for j := i * i; j <= limit; j += i { // mark all multiples of i as composite + sieve[j] = 1 + } + } + } + + return primes +} diff --git a/math/prime/sieve2_test.go b/math/prime/sieve2_test.go new file mode 100644 index 000000000..24912e3d0 --- /dev/null +++ b/math/prime/sieve2_test.go @@ -0,0 +1,43 @@ +package prime_test + +import ( + "reflect" + "testing" + + "github.com/TheAlgorithms/Go/math/prime" +) + +func TestSieveEratosthenes(t *testing.T) { + tests := []struct { + name string + limit int + want []int + }{ + { + name: "First 10 primes test", + limit: 30, + want: []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29}, + }, + { + name: "First 20 primes test", + limit: 71, + want: []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71}, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + got := prime.SieveEratosthenes(tt.limit) + + if !reflect.DeepEqual(got, tt.want) { + t.Errorf("SieveEratosthenes() = %v, want %v", got, tt.want) + } + }) + } +} + +func BenchmarkSieveEratosthenes(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = prime.SieveEratosthenes(10) + } +} diff --git a/math/prime/sieve_test.go b/math/prime/sieve_test.go new file mode 100644 index 000000000..36a1c5811 --- /dev/null +++ b/math/prime/sieve_test.go @@ -0,0 +1,52 @@ +// sieve_test.go +// description: Testing all the algorithms related to the generation of prime numbers in sieve.go +// author(s) [Taj](https://github.com/tjgurwara99) +// see sieve.go + +package prime + +import ( + "reflect" + "testing" +) + +func TestSieve(t *testing.T) { + firstTenPrimes := [10]int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29} + + t.Run("First 10 primes test", func(t *testing.T) { + var testTenPrimes [10]int + + ch := make(chan int) + go GenerateChannel(ch) + + for i := 0; i < 10; i++ { + testTenPrimes[i] = <-ch + ch1 := make(chan int) + go Sieve(ch, ch1, testTenPrimes[i]) + ch = ch1 + } + + if firstTenPrimes != testTenPrimes { + t.Errorf("The first 10 primes do not match") + } + + }) +} + +func TestGeneratePrimes(t *testing.T) { + firstTenPrimes := []int{2, 3, 5, 7, 11, 13, 17, 19, 23, 29} + + t.Run("Testing GeneratePrimes Function", func(t *testing.T) { + testPrimes := Generate(10) + + if !reflect.DeepEqual(firstTenPrimes, testPrimes) { + t.Fatal("GeneratePrimes function failed") + } + }) +} + +func BenchmarkSieve10(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Generate(10) + } +} diff --git a/math/prime/twin.go b/math/prime/twin.go new file mode 100644 index 000000000..dfd861510 --- /dev/null +++ b/math/prime/twin.go @@ -0,0 +1,22 @@ +// twin.go +// description: Returns Twin Prime of n +// details: +// For any integer n, twin prime is (n + 2) +// if and only if both n and (n + 2) both are prime +// wikipedia: https://en.wikipedia.org/wiki/Twin_prime +// time complexity: O(log n) +// space complexity: O(1) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see twin_test.go + +package prime + +// This function returns twin prime for given number +// returns (n + 2) if both n and (n + 2) are prime +// -1 otherwise +func Twin(n int) (int, bool) { + if OptimizedTrialDivision(int64(n)) && OptimizedTrialDivision(int64(n+2)) { + return n + 2, true + } + return -1, false +} diff --git a/math/prime/twin_test.go b/math/prime/twin_test.go new file mode 100644 index 000000000..7c1923dcb --- /dev/null +++ b/math/prime/twin_test.go @@ -0,0 +1,39 @@ +// twin_test.go +// description: Returns Twin Prime of n +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see twin.go + +package prime_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math/prime" +) + +func TestTwin(t *testing.T) { + var tests = []struct { + name string + n int + expectedValue int + hasTwin bool + }{ + {"n = 3, should return 5", 3, 5, true}, + {"n = 4, should return -1", 4, -1, false}, + {"n = 5, should return 7", 5, 7, true}, + {"n = 17, should return 19", 17, 19, true}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + result, hasTwin := prime.Twin(test.n) + if result != test.expectedValue || hasTwin != test.hasTwin { + t.Errorf("expected value: %v and %v, got: %v and %v", test.expectedValue, test.hasTwin, result, hasTwin) + } + }) + } +} +func BenchmarkTwin(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = prime.Twin(65536) + } +} diff --git a/math/pronicnumber.go b/math/pronicnumber.go new file mode 100644 index 000000000..47d25d17c --- /dev/null +++ b/math/pronicnumber.go @@ -0,0 +1,23 @@ +// pronicnumber.go +// description: Returns true if the number is pronic and false otherwise +// details: +// Pronic number: For any integer n, if there exists integer m +// such that n = m * (m + 1) then n is called a pronic number. +// wikipedia: https://en.wikipedia.org/wiki/Pronic_number +// time complexity: O(1) +// space complexity: O(1) +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see pronicnumber_test.go + +package math + +import "math" + +// PronicNumber returns true if argument passed to the function is pronic and false otherwise. +func PronicNumber(n int) bool { + if n < 0 || n%2 == 1 { + return false + } + x := int(math.Sqrt(float64(n))) + return n == x*(x+1) +} diff --git a/math/pronicnumber_test.go b/math/pronicnumber_test.go new file mode 100644 index 000000000..34880d68e --- /dev/null +++ b/math/pronicnumber_test.go @@ -0,0 +1,438 @@ +// pronicnumber_test.go +// author: Akshay Dubey (https://github.com/itsAkshayDubey) +// see pronicnumber.go + +package math_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/math" +) + +func TestPronicNumber(t *testing.T) { + var tests = []struct { + name string + n int + expectedValue bool + }{ + {"-12 is not pronic", -12, false}, + {"0 is pronic", 0, true}, + {"1 is not pronic", 1, false}, + {"2 is pronic", 2, true}, + {"3 is not pronic", 3, false}, + {"4 is not pronic", 4, false}, + {"5 is not pronic", 5, false}, + {"6 is pronic", 6, true}, + {"7 is not pronic", 7, false}, + {"8 is not pronic", 8, false}, + {"9 is not pronic", 9, false}, + {"10 is not pronic", 10, false}, + {"11 is not pronic", 11, false}, + {"12 is pronic", 12, true}, + {"13 is not pronic", 13, false}, + {"14 is not pronic", 14, false}, + {"15 is not pronic", 15, false}, + {"16 is not pronic", 16, false}, + {"17 is not pronic", 17, false}, + {"18 is not pronic", 18, false}, + {"19 is not pronic", 19, false}, + {"20 is pronic", 20, true}, + {"21 is not pronic", 21, false}, + {"22 is not pronic", 22, false}, + {"23 is not pronic", 23, false}, + {"24 is not pronic", 24, false}, + {"25 is not pronic", 25, false}, + {"26 is not pronic", 26, false}, + {"27 is not pronic", 27, false}, + {"28 is not pronic", 28, false}, + {"29 is not pronic", 29, false}, + {"30 is pronic", 30, true}, + {"31 is not pronic", 31, false}, + {"32 is not pronic", 32, false}, + {"33 is not pronic", 33, false}, + {"34 is not pronic", 34, false}, + {"35 is not pronic", 35, false}, + {"36 is not pronic", 36, false}, + {"37 is not pronic", 37, false}, + {"38 is not pronic", 38, false}, + {"39 is not pronic", 39, false}, + {"40 is not pronic", 40, false}, + {"41 is not pronic", 41, false}, + {"42 is pronic", 42, true}, + {"43 is not pronic", 43, false}, + {"44 is not pronic", 44, false}, + {"45 is not pronic", 45, false}, + {"46 is not pronic", 46, false}, + {"47 is not pronic", 47, false}, + {"48 is not pronic", 48, false}, + {"49 is not pronic", 49, false}, + {"50 is not pronic", 50, false}, + {"51 is not pronic", 51, false}, + {"52 is not pronic", 52, false}, + {"53 is not pronic", 53, false}, + {"54 is not pronic", 54, false}, + {"55 is not pronic", 55, false}, + {"56 is pronic", 56, true}, + {"57 is not pronic", 57, false}, + {"58 is not pronic", 58, false}, + {"59 is not pronic", 59, false}, + {"60 is not pronic", 60, false}, + {"61 is not pronic", 61, false}, + {"62 is not pronic", 62, false}, + {"63 is not pronic", 63, false}, + {"64 is not pronic", 64, false}, + {"65 is not pronic", 65, false}, + {"66 is not pronic", 66, false}, + {"67 is not pronic", 67, false}, + {"68 is not pronic", 68, false}, + {"69 is not pronic", 69, false}, + {"70 is not pronic", 70, false}, + {"71 is not pronic", 71, false}, + {"72 is pronic", 72, true}, + {"73 is not pronic", 73, false}, + {"74 is not pronic", 74, false}, + {"75 is not pronic", 75, false}, + {"76 is not pronic", 76, false}, + {"77 is not pronic", 77, false}, + {"78 is not pronic", 78, false}, + {"79 is not pronic", 79, false}, + {"80 is not pronic", 80, false}, + {"81 is not pronic", 81, false}, + {"82 is not pronic", 82, false}, + {"83 is not pronic", 83, false}, + {"84 is not pronic", 84, false}, + {"85 is not pronic", 85, false}, + {"86 is not pronic", 86, false}, + {"87 is not pronic", 87, false}, + {"88 is not pronic", 88, false}, + {"89 is not pronic", 89, false}, + {"90 is pronic", 90, true}, + {"91 is not pronic", 91, false}, + {"92 is not pronic", 92, false}, + {"93 is not pronic", 93, false}, + {"94 is not pronic", 94, false}, + {"95 is not pronic", 95, false}, + {"96 is not pronic", 96, false}, + {"97 is not pronic", 97, false}, + {"98 is not pronic", 98, false}, + {"99 is not pronic", 99, false}, + {"100 is not pronic", 100, false}, + {"101 is not pronic", 101, false}, + {"102 is not pronic", 102, false}, + {"103 is not pronic", 103, false}, + {"104 is not pronic", 104, false}, + {"105 is not pronic", 105, false}, + {"106 is not pronic", 106, false}, + {"107 is not pronic", 107, false}, + {"108 is not pronic", 108, false}, + {"109 is not pronic", 109, false}, + {"110 is pronic", 110, true}, + {"111 is not pronic", 111, false}, + {"112 is not pronic", 112, false}, + {"113 is not pronic", 113, false}, + {"114 is not pronic", 114, false}, + {"115 is not pronic", 115, false}, + {"116 is not pronic", 116, false}, + {"117 is not pronic", 117, false}, + {"118 is not pronic", 118, false}, + {"119 is not pronic", 119, false}, + {"120 is not pronic", 120, false}, + {"121 is not pronic", 121, false}, + {"122 is not pronic", 122, false}, + {"123 is not pronic", 123, false}, + {"124 is not pronic", 124, false}, + {"125 is not pronic", 125, false}, + {"126 is not pronic", 126, false}, + {"127 is not pronic", 127, false}, + {"128 is not pronic", 128, false}, + {"129 is not pronic", 129, false}, + {"130 is not pronic", 130, false}, + {"131 is not pronic", 131, false}, + {"132 is pronic", 132, true}, + {"133 is not pronic", 133, false}, + {"134 is not pronic", 134, false}, + {"135 is not pronic", 135, false}, + {"136 is not pronic", 136, false}, + {"137 is not pronic", 137, false}, + {"138 is not pronic", 138, false}, + {"139 is not pronic", 139, false}, + {"140 is not pronic", 140, false}, + {"141 is not pronic", 141, false}, + {"142 is not pronic", 142, false}, + {"143 is not pronic", 143, false}, + {"144 is not pronic", 144, false}, + {"145 is not pronic", 145, false}, + {"146 is not pronic", 146, false}, + {"147 is not pronic", 147, false}, + {"148 is not pronic", 148, false}, + {"149 is not pronic", 149, false}, + {"150 is not pronic", 150, false}, + {"151 is not pronic", 151, false}, + {"152 is not pronic", 152, false}, + {"153 is not pronic", 153, false}, + {"154 is not pronic", 154, false}, + {"155 is not pronic", 155, false}, + {"156 is pronic", 156, true}, + {"157 is not pronic", 157, false}, + {"158 is not pronic", 158, false}, + {"159 is not pronic", 159, false}, + {"160 is not pronic", 160, false}, + {"161 is not pronic", 161, false}, + {"162 is not pronic", 162, false}, + {"163 is not pronic", 163, false}, + {"164 is not pronic", 164, false}, + {"165 is not pronic", 165, false}, + {"166 is not pronic", 166, false}, + {"167 is not pronic", 167, false}, + {"168 is not pronic", 168, false}, + {"169 is not pronic", 169, false}, + {"170 is not pronic", 170, false}, + {"171 is not pronic", 171, false}, + {"172 is not pronic", 172, false}, + {"173 is not pronic", 173, false}, + {"174 is not pronic", 174, false}, + {"175 is not pronic", 175, false}, + {"176 is not pronic", 176, false}, + {"177 is not pronic", 177, false}, + {"178 is not pronic", 178, false}, + {"179 is not pronic", 179, false}, + {"180 is not pronic", 180, false}, + {"181 is not pronic", 181, false}, + {"182 is pronic", 182, true}, + {"183 is not pronic", 183, false}, + {"184 is not pronic", 184, false}, + {"185 is not pronic", 185, false}, + {"186 is not pronic", 186, false}, + {"187 is not pronic", 187, false}, + {"188 is not pronic", 188, false}, + {"189 is not pronic", 189, false}, + {"190 is not pronic", 190, false}, + {"191 is not pronic", 191, false}, + {"192 is not pronic", 192, false}, + {"193 is not pronic", 193, false}, + {"194 is not pronic", 194, false}, + {"195 is not pronic", 195, false}, + {"196 is not pronic", 196, false}, + {"197 is not pronic", 197, false}, + {"198 is not pronic", 198, false}, + {"199 is not pronic", 199, false}, + {"200 is not pronic", 200, false}, + {"201 is not pronic", 201, false}, + {"202 is not pronic", 202, false}, + {"203 is not pronic", 203, false}, + {"204 is not pronic", 204, false}, + {"205 is not pronic", 205, false}, + {"206 is not pronic", 206, false}, + {"207 is not pronic", 207, false}, + {"208 is not pronic", 208, false}, + {"209 is not pronic", 209, false}, + {"210 is pronic", 210, true}, + {"211 is not pronic", 211, false}, + {"212 is not pronic", 212, false}, + {"213 is not pronic", 213, false}, + {"214 is not pronic", 214, false}, + {"215 is not pronic", 215, false}, + {"216 is not pronic", 216, false}, + {"217 is not pronic", 217, false}, + {"218 is not pronic", 218, false}, + {"219 is not pronic", 219, false}, + {"220 is not pronic", 220, false}, + {"221 is not pronic", 221, false}, + {"222 is not pronic", 222, false}, + {"223 is not pronic", 223, false}, + {"224 is not pronic", 224, false}, + {"225 is not pronic", 225, false}, + {"226 is not pronic", 226, false}, + {"227 is not pronic", 227, false}, + {"228 is not pronic", 228, false}, + {"229 is not pronic", 229, false}, + {"230 is not pronic", 230, false}, + {"231 is not pronic", 231, false}, + {"232 is not pronic", 232, false}, + {"233 is not pronic", 233, false}, + {"234 is not pronic", 234, false}, + {"235 is not pronic", 235, false}, + {"236 is not pronic", 236, false}, + {"237 is not pronic", 237, false}, + {"238 is not pronic", 238, false}, + {"239 is not pronic", 239, false}, + {"240 is pronic", 240, true}, + {"241 is not pronic", 241, false}, + {"242 is not pronic", 242, false}, + {"243 is not pronic", 243, false}, + {"244 is not pronic", 244, false}, + {"245 is not pronic", 245, false}, + {"246 is not pronic", 246, false}, + {"247 is not pronic", 247, false}, + {"248 is not pronic", 248, false}, + {"249 is not pronic", 249, false}, + {"250 is not pronic", 250, false}, + {"251 is not pronic", 251, false}, + {"252 is not pronic", 252, false}, + {"253 is not pronic", 253, false}, + {"254 is not pronic", 254, false}, + {"255 is not pronic", 255, false}, + {"256 is not pronic", 256, false}, + {"257 is not pronic", 257, false}, + {"258 is not pronic", 258, false}, + {"259 is not pronic", 259, false}, + {"260 is not pronic", 260, false}, + {"261 is not pronic", 261, false}, + {"262 is not pronic", 262, false}, + {"263 is not pronic", 263, false}, + {"264 is not pronic", 264, false}, + {"265 is not pronic", 265, false}, + {"266 is not pronic", 266, false}, + {"267 is not pronic", 267, false}, + {"268 is not pronic", 268, false}, + {"269 is not pronic", 269, false}, + {"270 is not pronic", 270, false}, + {"271 is not pronic", 271, false}, + {"272 is pronic", 272, true}, + {"273 is not pronic", 273, false}, + {"274 is not pronic", 274, false}, + {"275 is not pronic", 275, false}, + {"276 is not pronic", 276, false}, + {"277 is not pronic", 277, false}, + {"278 is not pronic", 278, false}, + {"279 is not pronic", 279, false}, + {"280 is not pronic", 280, false}, + {"281 is not pronic", 281, false}, + {"282 is not pronic", 282, false}, + {"283 is not pronic", 283, false}, + {"284 is not pronic", 284, false}, + {"285 is not pronic", 285, false}, + {"286 is not pronic", 286, false}, + {"287 is not pronic", 287, false}, + {"288 is not pronic", 288, false}, + {"289 is not pronic", 289, false}, + {"290 is not pronic", 290, false}, + {"291 is not pronic", 291, false}, + {"292 is not pronic", 292, false}, + {"293 is not pronic", 293, false}, + {"294 is not pronic", 294, false}, + {"295 is not pronic", 295, false}, + {"296 is not pronic", 296, false}, + {"297 is not pronic", 297, false}, + {"298 is not pronic", 298, false}, + {"299 is not pronic", 299, false}, + {"300 is not pronic", 300, false}, + {"301 is not pronic", 301, false}, + {"302 is not pronic", 302, false}, + {"303 is not pronic", 303, false}, + {"304 is not pronic", 304, false}, + {"305 is not pronic", 305, false}, + {"306 is pronic", 306, true}, + {"307 is not pronic", 307, false}, + {"308 is not pronic", 308, false}, + {"309 is not pronic", 309, false}, + {"310 is not pronic", 310, false}, + {"311 is not pronic", 311, false}, + {"312 is not pronic", 312, false}, + {"313 is not pronic", 313, false}, + {"314 is not pronic", 314, false}, + {"315 is not pronic", 315, false}, + {"316 is not pronic", 316, false}, + {"317 is not pronic", 317, false}, + {"318 is not pronic", 318, false}, + {"319 is not pronic", 319, false}, + {"320 is not pronic", 320, false}, + {"321 is not pronic", 321, false}, + {"322 is not pronic", 322, false}, + {"323 is not pronic", 323, false}, + {"324 is not pronic", 324, false}, + {"325 is not pronic", 325, false}, + {"326 is not pronic", 326, false}, + {"327 is not pronic", 327, false}, + {"328 is not pronic", 328, false}, + {"329 is not pronic", 329, false}, + {"330 is not pronic", 330, false}, + {"331 is not pronic", 331, false}, + {"332 is not pronic", 332, false}, + {"333 is not pronic", 333, false}, + {"334 is not pronic", 334, false}, + {"335 is not pronic", 335, false}, + {"336 is not pronic", 336, false}, + {"337 is not pronic", 337, false}, + {"338 is not pronic", 338, false}, + {"339 is not pronic", 339, false}, + {"340 is not pronic", 340, false}, + {"341 is not pronic", 341, false}, + {"342 is pronic", 342, true}, + {"343 is not pronic", 343, false}, + {"344 is not pronic", 344, false}, + {"345 is not pronic", 345, false}, + {"346 is not pronic", 346, false}, + {"347 is not pronic", 347, false}, + {"348 is not pronic", 348, false}, + {"349 is not pronic", 349, false}, + {"350 is not pronic", 350, false}, + {"351 is not pronic", 351, false}, + {"352 is not pronic", 352, false}, + {"353 is not pronic", 353, false}, + {"354 is not pronic", 354, false}, + {"355 is not pronic", 355, false}, + {"356 is not pronic", 356, false}, + {"357 is not pronic", 357, false}, + {"358 is not pronic", 358, false}, + {"359 is not pronic", 359, false}, + {"360 is not pronic", 360, false}, + {"361 is not pronic", 361, false}, + {"362 is not pronic", 362, false}, + {"363 is not pronic", 363, false}, + {"364 is not pronic", 364, false}, + {"365 is not pronic", 365, false}, + {"366 is not pronic", 366, false}, + {"367 is not pronic", 367, false}, + {"368 is not pronic", 368, false}, + {"369 is not pronic", 369, false}, + {"370 is not pronic", 370, false}, + {"371 is not pronic", 371, false}, + {"372 is not pronic", 372, false}, + {"373 is not pronic", 373, false}, + {"374 is not pronic", 374, false}, + {"375 is not pronic", 375, false}, + {"376 is not pronic", 376, false}, + {"377 is not pronic", 377, false}, + {"378 is not pronic", 378, false}, + {"379 is not pronic", 379, false}, + {"380 is pronic", 380, true}, + {"381 is not pronic", 381, false}, + {"382 is not pronic", 382, false}, + {"383 is not pronic", 383, false}, + {"384 is not pronic", 384, false}, + {"385 is not pronic", 385, false}, + {"386 is not pronic", 386, false}, + {"387 is not pronic", 387, false}, + {"388 is not pronic", 388, false}, + {"389 is not pronic", 389, false}, + {"390 is not pronic", 390, false}, + {"391 is not pronic", 391, false}, + {"392 is not pronic", 392, false}, + {"393 is not pronic", 393, false}, + {"394 is not pronic", 394, false}, + {"395 is not pronic", 395, false}, + {"396 is not pronic", 396, false}, + {"397 is not pronic", 397, false}, + {"398 is not pronic", 398, false}, + {"399 is not pronic", 399, false}, + {"400 is not pronic", 400, false}, + {"2147441940 is pronic", 2147441940, true}, + {"9223372033963249500 is pronic", 9223372033963249500, true}, + {"9223372033963249664 is not pronic", 9223372033963249664, false}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + result := math.PronicNumber(test.n) + if result != test.expectedValue { + t.Errorf("expected value: %v, got: %v", test.expectedValue, result) + } + }) + } +} +func BenchmarkPronicNumber(b *testing.B) { + for i := 0; i < b.N; i++ { + math.PronicNumber(65536) + } +} diff --git a/math/pythagoras/pythagoras.go b/math/pythagoras/pythagoras.go new file mode 100644 index 000000000..54e6ef0ca --- /dev/null +++ b/math/pythagoras/pythagoras.go @@ -0,0 +1,18 @@ +package pythagoras + +import ( + "math" +) + +// Vector defines a tuple with 3 values in 3d-space +type Vector struct { + x float64 + y float64 + z float64 +} + +// Distance calculates the distance between to vectors with the Pythagoras theorem +func Distance(a, b Vector) float64 { + res := math.Pow(b.x-a.x, 2.0) + math.Pow(b.y-a.y, 2.0) + math.Pow(b.z-a.z, 2.0) + return math.Sqrt(res) +} diff --git a/math/pythagoras/pythagoras_test.go b/math/pythagoras/pythagoras_test.go new file mode 100644 index 000000000..3365c4a31 --- /dev/null +++ b/math/pythagoras/pythagoras_test.go @@ -0,0 +1,37 @@ +package pythagoras + +import ( + "math" + "testing" +) + +// TableDrivenTest for checking multiple values against our Test Function +var distanceTest = []struct { + name string + v1 Vector + v2 Vector + res float64 +}{ + {"random negative vector", Vector{2, -1, 7}, Vector{1, -3, 5}, 3.0}, + {"random wide vectors", Vector{4, 10, 9}, Vector{4, 3, 5}, 8.06}, + {"random wide vectors", Vector{8, 5, 5}, Vector{1, 1, 12}, 10.67}, + {"random short vectors", Vector{1, 1, 1}, Vector{2, 2, 2}, 1.73}, +} + +// TestDistance tests the Function Distance with 2 vectors +func TestDistance(t *testing.T) { + t.Parallel() // marks TestDistance as capable of running in parallel with other tests + for _, tt := range distanceTest { + tt := tt // NOTE: https://github.com/golang/go/wiki/CommonMistakes#using-goroutines-on-loop-iterator-variables + t.Run(tt.name, func(t *testing.T) { + t.Parallel() + res := Distance(tt.v1, tt.v2) // Calculate result for + roundRes := (math.Floor(res*100) / 100) // Round to 2 decimal places because we can't compare an infinite number of places + // Check result + if roundRes != tt.res { + t.Errorf("Distance(%v, %v) = %f, expected %f", + tt.v1, tt.v2, roundRes, tt.res) + } + }) + } +} diff --git a/math/sin.go b/math/sin.go new file mode 100644 index 000000000..e9713cf5e --- /dev/null +++ b/math/sin.go @@ -0,0 +1,11 @@ +// author(s) [red_byte](https://github.com/i-redbyte) +// see sin_test.go + +package math + +import "math" + +// Sin returns the sine of the radian argument x. [See more](https://en.wikipedia.org/wiki/Sine_and_cosine) +func Sin(x float64) float64 { + return Cos((math.Pi / 2) - x) +} diff --git a/math/sin_test.go b/math/sin_test.go new file mode 100644 index 000000000..0dc89428f --- /dev/null +++ b/math/sin_test.go @@ -0,0 +1,43 @@ +package math_test + +import ( + algmath "github.com/TheAlgorithms/Go/math" + stdmath "math" + "testing" +) + +func TestSin(t *testing.T) { + tests := []struct { + name string + n float64 + want float64 + }{ + {"sin(0)", 0, 0}, + {"sin(3π/2)", (3 * stdmath.Pi) / 2, -1}, + {"sin(π/2)", stdmath.Pi / 2, 1}, + {"sin(π/6)", stdmath.Pi / 6, 0.5}, + {"sin(90)", 90, 0.893996663600558}, + } + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + got := algmath.Sin(test.n) + if stdmath.Abs(got-test.want) >= epsilon { + t.Errorf("Sin() = %v, want %v", got, test.want) + t.Errorf("MATH Sin() = %v", stdmath.Sin(test.n)) + } + }) + } +} + +func BenchmarkSin(b *testing.B) { + for i := 0; i < b.N; i++ { + algmath.Sin(180) + } +} + +// BenchmarkMathSin is slower because the standard library `math.Sin` calculates a more accurate value. +func BenchmarkMathSin(b *testing.B) { + for i := 0; i < b.N; i++ { + stdmath.Sin(180) + } +} diff --git a/other/NestedBrackets.go b/other/NestedBrackets.go deleted file mode 100644 index c3951ebba..000000000 --- a/other/NestedBrackets.go +++ /dev/null @@ -1,54 +0,0 @@ -// The nested brackets problem is a problem that determines if a sequence of -// brackets are properly nested. A sequence of brackets s is considered properly nested -// if any of the following conditions are true: -// - s is empty -// - s has the form (U) or [U] or {U} where U is a properly nested string -// - s has the form VW where V and W are properly nested strings -// For example, the string "()()[()]" is properly nested but "[(()]" is not. -// The function called isBalanced takes as input a string which is a sequence of brackets and -// returns true if input is nested and false otherwise. - -package main - -import ( - "bufio" - "fmt" - "os" - "strings" -) - -func isBalanced(input string) string { - - if len(input) > 0 { - var stack []byte - for i := 0; i < len(input); i++ { - if input[i] == '(' || input[i] == '{' || input[i] == '[' { - stack = append(stack, input[i]) - } else { - if len(stack) > 0 { - pair := string(stack[len(stack)-1]) + string(input[i]) - stack = stack[:len(stack)-1] - - if pair != "[]" && pair != "{}" && pair != "()" { - return input + " is not balanced." - } - } else { - return input + " is not balanced." - } - } - } - if len(stack) == 0 { - return input + " is balanced." - } - } - return "Please enter a sequence of brackets." -} - -func main() { - reader := bufio.NewReader(os.Stdin) - fmt.Print("Enter sequence of brackets: ") - text, _ := reader.ReadString('\n') - - text = strings.TrimSpace(text) - fmt.Println(isBalanced(text)) -} \ No newline at end of file diff --git a/other/PasswordGenerator.go b/other/PasswordGenerator.go deleted file mode 100644 index 5dd30dff0..000000000 --- a/other/PasswordGenerator.go +++ /dev/null @@ -1,54 +0,0 @@ -// This program generates a password from a list of possible chars -// You must provide a minimum length and a maximum length -// This length is not fixed if you generate multiple passwords for the same range - -package main - -import ( - crand "crypto/rand" - "fmt" - "io" - "math/rand" - "time" -) - -func generatePassword(minLength int, maxLength int) string { - var chars = []byte("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789!@#$%^&*()-_=+,.?/:;{}[]`~") - - var length = rand.Intn(maxLength-minLength) + minLength - - newPassword := make([]byte, length) - randomData := make([]byte, length+(length/4)) - clen := byte(len(chars)) - maxrb := byte(256 - (256 % len(chars))) - i := 0 - for { - if _, err := io.ReadFull(crand.Reader, randomData); err != nil { - panic(err) - } - for _, c := range randomData { - if c >= maxrb { - continue - } - newPassword[i] = chars[c%clen] - i++ - if i == length { - return string(newPassword) - } - } - } -} - -func main() { - rand.Seed(time.Now().Unix()) - - fmt.Print("Please specify a minimum length: ") - var minLength int - fmt.Scanf("%d", &minLength) - - fmt.Print("Please specify a maximum length: ") - var maxLength int - fmt.Scanf("%d", &maxLength) - - fmt.Printf("Your generated password is %v\n", generatePassword(minLength, maxLength)) -} diff --git a/other/PrimeNumbers.go b/other/PrimeNumbers.go deleted file mode 100644 index 4fb7364c7..000000000 --- a/other/PrimeNumbers.go +++ /dev/null @@ -1,86 +0,0 @@ -package main - -import ( - "fmt" - "math" - "os" - "strconv" - "github.com/douglasmakey/golang-algorithms-/utils" - "time" -) - -// Define struct -type numberResult struct { - number int64 - isPrime bool -} - -// Define functions - -// isPrime: validate N number is prime -func isPrime(n int64) bool { - var i, limit int64 - if n <= 1 { - return false - } - - if n == 2 { - return true - } - - if math.Mod(float64(n), 2) == 0 { - return false - } - - - limit = int64(math.Ceil(math.Sqrt(float64(n)))) - for i = 3; i <= limit; i += 2 { - if math.Mod(float64(n), float64(i)) == 0 { - return false - } - } - return true -} - -// createNrAndValidate: Receive number and validate if is prime, send channel this same -func createNrAndValidate(n int64, c chan numberResult) { - - result := new(numberResult) - result.number = n - result.isPrime = isPrime(n) - c <- *result -} - -func initGoCalculations(min int64, max int64, c chan numberResult) { - var i int64 - for i = min; i <= max; i++ { - go createNrAndValidate(i, c) - } -} - -func primesInRange(min int64, max int64) (primeArr []int64) { - defer utils.TimeTrack(time.Now(), "primesInRange") - - // Create channels and defer close - c := make(chan numberResult) - defer close(c) - - // Execute N goroutines in range number - go initGoCalculations(min, max, c) - - for i := min; i <= max; i++ { - // Receive numberResult - r := <-c - if r.isPrime { - primeArr = append(primeArr, r.number) - } - } - return -} - -func main() { - // Receive arguments min max - min, _ := strconv.ParseInt(os.Args[1], 10, 64) - max, _ := strconv.ParseInt(os.Args[2], 10, 64) - fmt.Println(primesInRange(min, max)) -} diff --git a/other/doc.go b/other/doc.go new file mode 100644 index 000000000..dbe11e339 --- /dev/null +++ b/other/doc.go @@ -0,0 +1,3 @@ +// Package other is dedicated to algorithms that +// do not quite fit into any of the other subpackages in this repository. +package other diff --git a/other/maxSubarraySum.go b/other/maxSubarraySum.go deleted file mode 100644 index a336dd378..000000000 --- a/other/maxSubarraySum.go +++ /dev/null @@ -1,30 +0,0 @@ -/* O(n) solution, for calculating -maximum contiguous sum in the given array. */ - -package main - -import ( - "fmt" -) - -func Max(x int, y int) int { - if x < y { - return y - } - return x -} - -func maxSubarraySum(array []int) int { - var currentMax int = 0 - var maxTillNow int = 0 - for i := 0; i < len(array); i++ { - currentMax = Max(array[i], currentMax + array[i]) - maxTillNow = Max(maxTillNow, currentMax) - } - return maxTillNow -} - -func main() { - array := []int{-2, -5, 6, 0, -2, 0, -3, 1, 0, 5, -6} - fmt.Println("Maximum contiguous sum: ", maxSubarraySum(array)) -} diff --git a/other/maxsubarraysum/maxsubarraysum.go b/other/maxsubarraysum/maxsubarraysum.go new file mode 100644 index 000000000..731907284 --- /dev/null +++ b/other/maxsubarraysum/maxsubarraysum.go @@ -0,0 +1,25 @@ +/* O(n) solution, for calculating +maximum contiguous sum in the given array. */ + +// Package maxsubarraysum is a package containing a solution to a common +// problem of finding max contiguous sum within a array of ints. +package maxsubarraysum + +import ( + "github.com/TheAlgorithms/Go/math/max" +) + +// MaxSubarraySum returns the maximum subarray sum +func MaxSubarraySum(array []int) int { + var currentMax int + var maxTillNow int + if len(array) != 0 { + currentMax = array[0] + maxTillNow = array[0] + } + for _, v := range array { + currentMax = max.Int(v, currentMax+v) + maxTillNow = max.Int(maxTillNow, currentMax) + } + return maxTillNow +} diff --git a/other/maxsubarraysum/maxsubarraysum_test.go b/other/maxsubarraysum/maxsubarraysum_test.go new file mode 100644 index 000000000..013ba1d88 --- /dev/null +++ b/other/maxsubarraysum/maxsubarraysum_test.go @@ -0,0 +1,41 @@ +package maxsubarraysum + +import ( + "testing" +) + +func TestMaxSubarraySum(t *testing.T) { + testCases := []struct { + name string + slice []int + expected int + }{ + { + name: "Empty slice", + slice: []int{}, + expected: 0, + }, + { + name: "Max is 0", + slice: []int{0, -1, -2, -4, -5}, + expected: 0, + }, + { + name: "Max is -1", + slice: []int{-1, -3, -2, -5, -7}, + expected: -1, + }, + { + name: "Max is 7", + slice: []int{-2, -5, 6, 0, -2, 0, -3, 1, 0, 5, -6}, + expected: 7, + }, + } + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + if result := MaxSubarraySum(test.slice); result != test.expected { + t.Fatalf("%s\n\tslice: %v, expected: %v, returned: %v", test.name, test.slice, test.expected, result) + } + }) + } +} diff --git a/other/nested/nestedbrackets.go b/other/nested/nestedbrackets.go new file mode 100644 index 000000000..7f220a332 --- /dev/null +++ b/other/nested/nestedbrackets.go @@ -0,0 +1,65 @@ +// Package nested provides functions for testing +// strings proper brackets nesting. +package nested + +// IsBalanced returns true if provided input string is properly nested. +// +// Input is a sequence of brackets: '(', ')', '[', ']', '{', '}'. +// +// A sequence of brackets `s` is considered properly nested +// if any of the following conditions are true: +// - `s` is empty; +// - `s` has the form (U) or [U] or {U} where U is a properly nested string; +// - `s` has the form VW where V and W are properly nested strings. +// +// For example, the string "()()[()]" is properly nested but "[(()]" is not. +// +// **Note** Providing characters other then brackets would return false, +// despite brackets sequence in the string. Make sure to filter +// input before usage. +// time complexity: O(n) +// space complexity: O(n) + +func IsBalanced(input string) bool { + if len(input) == 0 { + return true + } + + if len(input)%2 != 0 { + return false + } + + // Brackets such as '{', '[', '(' are valid UTF-8 characters, + // which means that only one byte is required to code them, + // so can be stored as bytes. + var stack []byte + + for i := 0; i < len(input); i++ { + if input[i] == '(' || input[i] == '{' || input[i] == '[' { + stack = append(stack, input[i]) + } else { + if len(stack) > 0 { + pair := string(stack[len(stack)-1]) + string(input[i]) + stack = stack[:len(stack)-1] + + if pair != "[]" && pair != "{}" && pair != "()" { + // This means that two types of brackets has + // been mixed together, for example "([)]", + // which makes seuqence invalid by definition. + return false + } + } else { + // This means that closing bracket is encountered + // before opening one, which makes all sequence + // invalid by definition. + return false + } + } + } + + // If sequence is properly nested, all elements in stack + // has been paired with closing elements. If even one + // element has not been paired with a closing bracket, + // means that sequence is invalid by definition. + return len(stack) == 0 +} diff --git a/other/nested/nestedbrackets_test.go b/other/nested/nestedbrackets_test.go new file mode 100644 index 000000000..52fc41cfb --- /dev/null +++ b/other/nested/nestedbrackets_test.go @@ -0,0 +1,79 @@ +package nested + +import ( + "testing" +) + +func TestIsBalancedSimple(t *testing.T) { + input := "{[()]}" + + got := IsBalanced(input) + want := true + + if got != want { + t.Errorf("\nInput: %s\nGot: %v\nWant: %v\n", input, got, want) + } +} + +func TestIsBalancedFalty(t *testing.T) { + input := "{([()]}" + + got := IsBalanced(input) + want := false + + if got != want { + t.Errorf("\nInput: %s\nGot: %v\nWant: %v\n", input, got, want) + } +} + +func TestIsBalancedHandlesEmpty(t *testing.T) { + input := "" + + got := IsBalanced(input) + want := true + + if got != want { + t.Errorf("\nInput: %s\nGot: %v\nWant: %v\n", input, got, want) + } +} + +func TestIsBalancedHandlesOneChar(t *testing.T) { + input := "{" + + got := IsBalanced(input) + want := false + + if got != want { + t.Errorf("\nInput: %s\nGot: %v\nWant: %v\n", input, got, want) + } +} + +func TestIsBalancedHandlesNonBracketsCorrectly(t *testing.T) { + input := "aaaa" + + got := IsBalanced(input) + want := false + + if got != want { + t.Errorf("\nInput: %s\nGot: %v\nWant: %v\n", input, got, want) + } +} + +func TestIsBalancedHandlesOrdering(t *testing.T) { + input := "([)]" + + got := IsBalanced(input) + want := false + + if got != want { + t.Errorf("\nInput: %s\nGot: %v\nWant: %v\n", input, got, want) + } +} + +func BenchmarkIsBalanced(b *testing.B) { + input := "{[()]}" + + for i := 0; i < b.N; i++ { + IsBalanced(input) + } +} diff --git a/other/other_test.go b/other/other_test.go new file mode 100644 index 000000000..35aa59143 --- /dev/null +++ b/other/other_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package other diff --git a/other/password/generator.go b/other/password/generator.go new file mode 100644 index 000000000..71bfdbd65 --- /dev/null +++ b/other/password/generator.go @@ -0,0 +1,49 @@ +// This program generates a password from a list of possible chars +// You must provide a minimum length and a maximum length +// This length is not fixed if you generate multiple passwords for the same range + +// Package password contains functions to help generate random passwords +// time complexity: O(n) +// space complexity: O(n) + +package password + +import ( + "crypto/rand" + "io" + "math/big" +) + +// Generate returns a newly generated password +func Generate(minLength int, maxLength int) string { + var chars = []byte("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789!@#$%^&*()-_=+,.?/:;{}[]`~") + + length, err := rand.Int(rand.Reader, big.NewInt(int64(maxLength-minLength))) + if err != nil { + panic(err) // handle this gracefully + } + length.Add(length, big.NewInt(int64(minLength))) + + intLength := int(length.Int64()) + + newPassword := make([]byte, intLength) + randomData := make([]byte, intLength+intLength/4) + charLen := byte(len(chars)) + maxrb := byte(256 - (256 % len(chars))) + i := 0 + for { + if _, err := io.ReadFull(rand.Reader, randomData); err != nil { + panic(err) + } + for _, c := range randomData { + if c >= maxrb { + continue + } + newPassword[i] = chars[c%charLen] + i++ + if i == intLength { + return string(newPassword) + } + } + } +} diff --git a/other/prime_numbers.go b/other/prime_numbers.go deleted file mode 100644 index 4fb7364c7..000000000 --- a/other/prime_numbers.go +++ /dev/null @@ -1,86 +0,0 @@ -package main - -import ( - "fmt" - "math" - "os" - "strconv" - "github.com/douglasmakey/golang-algorithms-/utils" - "time" -) - -// Define struct -type numberResult struct { - number int64 - isPrime bool -} - -// Define functions - -// isPrime: validate N number is prime -func isPrime(n int64) bool { - var i, limit int64 - if n <= 1 { - return false - } - - if n == 2 { - return true - } - - if math.Mod(float64(n), 2) == 0 { - return false - } - - - limit = int64(math.Ceil(math.Sqrt(float64(n)))) - for i = 3; i <= limit; i += 2 { - if math.Mod(float64(n), float64(i)) == 0 { - return false - } - } - return true -} - -// createNrAndValidate: Receive number and validate if is prime, send channel this same -func createNrAndValidate(n int64, c chan numberResult) { - - result := new(numberResult) - result.number = n - result.isPrime = isPrime(n) - c <- *result -} - -func initGoCalculations(min int64, max int64, c chan numberResult) { - var i int64 - for i = min; i <= max; i++ { - go createNrAndValidate(i, c) - } -} - -func primesInRange(min int64, max int64) (primeArr []int64) { - defer utils.TimeTrack(time.Now(), "primesInRange") - - // Create channels and defer close - c := make(chan numberResult) - defer close(c) - - // Execute N goroutines in range number - go initGoCalculations(min, max, c) - - for i := min; i <= max; i++ { - // Receive numberResult - r := <-c - if r.isPrime { - primeArr = append(primeArr, r.number) - } - } - return -} - -func main() { - // Receive arguments min max - min, _ := strconv.ParseInt(os.Args[1], 10, 64) - max, _ := strconv.ParseInt(os.Args[2], 10, 64) - fmt.Println(primesInRange(min, max)) -} diff --git a/project_euler/problem_1/problem1.go b/project_euler/problem_1/problem1.go new file mode 100644 index 000000000..e41fbf468 --- /dev/null +++ b/project_euler/problem_1/problem1.go @@ -0,0 +1,24 @@ +/** + * Problem 1 - Multiples of 3 and 5 + * + * @see {@link https://projecteuler.net/problem=1} + * + * If we list all the natural numbers below 10 that are multiples of 3 or 5, + * we get 3, 5, 6 and 9. The sum of these multiples is 23. + * Find the sum of all the multiples of 3 or 5 below 1000. + * + * @author ddaniel27 + */ +package problem1 + +func Problem1(n uint) uint { + sum := uint(0) + + for i := uint(1); i < n; i++ { + if i%3 == 0 || i%5 == 0 { + sum += i + } + } + + return sum +} diff --git a/project_euler/problem_1/problem1_test.go b/project_euler/problem_1/problem1_test.go new file mode 100644 index 000000000..c2d649b02 --- /dev/null +++ b/project_euler/problem_1/problem1_test.go @@ -0,0 +1,45 @@ +package problem1 + +import "testing" + +// Tests +func TestProblem1_Func(t *testing.T) { + tests := []struct { + name string + threshold uint + want uint + }{ + { + name: "Testcase 1 - threshold 10", + threshold: 10, + want: 23, + }, + { + name: "Testcase 2 - threshold 100", + threshold: 100, + want: 2318, + }, + { + name: "Testcase 3 - threshold 1000", + threshold: 1000, + want: 233168, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem1(tt.threshold) + + if n != tt.want { + t.Errorf("Problem1() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem1(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem1(1000) + } +} diff --git a/project_euler/problem_10/problem10.go b/project_euler/problem_10/problem10.go new file mode 100644 index 000000000..342c79d24 --- /dev/null +++ b/project_euler/problem_10/problem10.go @@ -0,0 +1,23 @@ +/** +* Problem 10 - Summation of primes +* @see {@link https://projecteuler.net/problem=10} +* +* The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17. +* Find the sum of all the primes below two million. +* +* @author ddaniel27 + */ +package problem10 + +import "github.com/TheAlgorithms/Go/math/prime" + +func Problem10(n int) uint { + sum := uint(0) + sieve := prime.SieveEratosthenes(n) + + for _, v := range sieve { + sum += uint(v) + } + + return sum +} diff --git a/project_euler/problem_10/problem10_test.go b/project_euler/problem_10/problem10_test.go new file mode 100644 index 000000000..d82e6f29e --- /dev/null +++ b/project_euler/problem_10/problem10_test.go @@ -0,0 +1,40 @@ +package problem10 + +import "testing" + +// Tests +func TestProblem10_Func(t *testing.T) { + tests := []struct { + name string + input int + want uint + }{ + { + name: "Testcase 1 - input 10", + input: 10, + want: 17, + }, + { + name: "Testcase 2 - input 2000000", + input: 2000000, + want: 142913828922, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem10(tt.input) + + if n != tt.want { + t.Errorf("Problem10() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem10(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem10(2000000) + } +} diff --git a/project_euler/problem_11/problem11.go b/project_euler/problem_11/problem11.go new file mode 100644 index 000000000..5ddaea8e2 --- /dev/null +++ b/project_euler/problem_11/problem11.go @@ -0,0 +1,80 @@ +/** +* Problem 11 - Largest product in a grid +* @see {@link https://projecteuler.net/problem=11} +* +* In the 20×20 grid below, four numbers along a diagonal line have been marked in red. +* +* The product of these numbers is 26 × 63 × 78 × 14 = 1788696. +* +* What is the greatest product of four adjacent numbers in the same direction +* (up, down, left, right, or diagonally) in the 20×20 grid? +* +* @author ddaniel27 + */ +package problem11 + +var grid = [20][20]uint{ + {8, 2, 22, 97, 38, 15, 0, 40, 0, 75, 4, 5, 7, 78, 52, 12, 50, 77, 91, 8}, + {49, 49, 99, 40, 17, 81, 18, 57, 60, 87, 17, 40, 98, 43, 69, 48, 4, 56, 62, 0}, + {81, 49, 31, 73, 55, 79, 14, 29, 93, 71, 40, 67, 53, 88, 30, 3, 49, 13, 36, 65}, + {52, 70, 95, 23, 4, 60, 11, 42, 69, 24, 68, 56, 1, 32, 56, 71, 37, 2, 36, 91}, + {22, 31, 16, 71, 51, 67, 63, 89, 41, 92, 36, 54, 22, 40, 40, 28, 66, 33, 13, 80}, + {24, 47, 32, 60, 99, 3, 45, 2, 44, 75, 33, 53, 78, 36, 84, 20, 35, 17, 12, 50}, + {32, 98, 81, 28, 64, 23, 67, 10, 26, 38, 40, 67, 59, 54, 70, 66, 18, 38, 64, 70}, + {67, 26, 20, 68, 2, 62, 12, 20, 95, 63, 94, 39, 63, 8, 40, 91, 66, 49, 94, 21}, + {24, 55, 58, 5, 66, 73, 99, 26, 97, 17, 78, 78, 96, 83, 14, 88, 34, 89, 63, 72}, + {21, 36, 23, 9, 75, 0, 76, 44, 20, 45, 35, 14, 0, 61, 33, 97, 34, 31, 33, 95}, + {78, 17, 53, 28, 22, 75, 31, 67, 15, 94, 3, 80, 4, 62, 16, 14, 9, 53, 56, 92}, + {16, 39, 5, 42, 96, 35, 31, 47, 55, 58, 88, 24, 0, 17, 54, 24, 36, 29, 85, 57}, + {86, 56, 0, 48, 35, 71, 89, 7, 5, 44, 44, 37, 44, 60, 21, 58, 51, 54, 17, 58}, + {19, 80, 81, 68, 5, 94, 47, 69, 28, 73, 92, 13, 86, 52, 17, 77, 4, 89, 55, 40}, + {4, 52, 8, 83, 97, 35, 99, 16, 7, 97, 57, 32, 16, 26, 26, 79, 33, 27, 98, 66}, + {88, 36, 68, 87, 57, 62, 20, 72, 3, 46, 33, 67, 46, 55, 12, 32, 63, 93, 53, 69}, + {4, 42, 16, 73, 38, 25, 39, 11, 24, 94, 72, 18, 8, 46, 29, 32, 40, 62, 76, 36}, + {20, 69, 36, 41, 72, 30, 23, 88, 34, 62, 99, 69, 82, 67, 59, 85, 74, 4, 36, 16}, + {20, 73, 35, 29, 78, 31, 90, 1, 74, 31, 49, 71, 48, 86, 81, 16, 23, 57, 5, 54}, + {1, 70, 54, 71, 83, 51, 54, 69, 16, 92, 33, 48, 61, 43, 52, 1, 89, 19, 67, 48}, +} + +func Problem11() uint { + max := uint(0) + + for i := 0; i < 20; i++ { + for j := 0; j < 20; j++ { + + // Vertical + if i+3 < 20 { + product := grid[i][j] * grid[i+1][j] * grid[i+2][j] * grid[i+3][j] + if product > max { + max = product + } + } + + // Horizontal + if j+3 < 20 { + product := grid[i][j] * grid[i][j+1] * grid[i][j+2] * grid[i][j+3] + if product > max { + max = product + } + } + + if i+3 < 20 && j+3 < 20 { + // Diagonal + product := grid[i][j] * grid[i+1][j+1] * grid[i+2][j+2] * grid[i+3][j+3] + if product > max { + max = product + } + } + + if i+3 < 20 && j-3 >= 0 { + // Diagonal + product := grid[i][j] * grid[i+1][j-1] * grid[i+2][j-2] * grid[i+3][j-3] + if product > max { + max = product + } + } + } + } + + return max +} diff --git a/project_euler/problem_11/problem11_test.go b/project_euler/problem_11/problem11_test.go new file mode 100644 index 000000000..b6ae99e05 --- /dev/null +++ b/project_euler/problem_11/problem11_test.go @@ -0,0 +1,29 @@ +package problem11 + +import "testing" + +// Tests +func TestProblem11_Func(t *testing.T) { + testCases := []struct { + name string + expected uint + }{ + {"Test Case 1", 70600674}, + } + + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := Problem11() + if actual != tc.expected { + t.Errorf("Expected: %v, but got %v", tc.expected, actual) + } + }) + } +} + +// Benchmark +func BenchmarkProblem11_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem11() + } +} diff --git a/project_euler/problem_12/problem12.go b/project_euler/problem_12/problem12.go new file mode 100644 index 000000000..803add5b7 --- /dev/null +++ b/project_euler/problem_12/problem12.go @@ -0,0 +1,46 @@ +/** +* Problem 12 - Highly divisible triangular number +* @see {@link https://projecteuler.net/problem=12} +* +* The sequence of triangle numbers is generated by adding the natural numbers. +* So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. +* The first ten terms would be: +* +* 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... +* +* Let us list the factors of the first seven triangle numbers: +* +* 1: 1 +* 3: 1,3 +* 6: 1,2,3,6 +* 10: 1,2,5,10 +* 15: 1,3,5,15 +* 21: 1,3,7,21 +* 28: 1,2,4,7,14,28 +* +* We can see that 28 is the first triangle number to have over five divisors. +* What is the value of the first triangle number to have over five hundred divisors? +* +* @author ddaniel27 + */ +package problem12 + +func Problem12(limit uint) uint { + triangle := uint(0) + for i := uint(1); ; i++ { + triangle += i + if numDivisors(triangle) >= limit { + return triangle + } + } +} + +func numDivisors(n uint) uint { + divisors := uint(0) + for i := uint(1); i*i <= n; i++ { + if n%i == 0 { + divisors += 2 + } + } + return divisors +} diff --git a/project_euler/problem_12/problem12_test.go b/project_euler/problem_12/problem12_test.go new file mode 100644 index 000000000..2659fb1e9 --- /dev/null +++ b/project_euler/problem_12/problem12_test.go @@ -0,0 +1,31 @@ +package problem12 + +import "testing" + +func TestProblem12_Func(t *testing.T) { + tests := []struct { + name string + input uint + want uint + }{ + {"Test Case 1", 6, 28}, + {"Test Case 2", 7, 36}, + {"Test Case 3", 11, 120}, + {"Test Case 4", 500, 76576500}, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + actual := Problem12(tt.input) + if actual != tt.want { + t.Errorf("Expected: %v, but got %v", tt.want, actual) + } + }) + } +} + +func BenchmarkProblem12_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem12(500) + } +} diff --git a/project_euler/problem_13/problem13.go b/project_euler/problem_13/problem13.go new file mode 100644 index 000000000..d5669d271 --- /dev/null +++ b/project_euler/problem_13/problem13.go @@ -0,0 +1,150 @@ +/** +* Problem 13 - Large sum +* @see {@link https://projecteuler.net/problem=13} +* +* Work out the first ten digits of the sum of the following one-hundred 50-digit numbers. +* +* @author ddaniel27 + */ +package problem13 + +var numbers = [100]string{ + "37107287533902102798797998220837590246510135740250", + "46376937677490009712648124896970078050417018260538", + "74324986199524741059474233309513058123726617309629", + "91942213363574161572522430563301811072406154908250", + "23067588207539346171171980310421047513778063246676", + "89261670696623633820136378418383684178734361726757", + "28112879812849979408065481931592621691275889832738", + "44274228917432520321923589422876796487670272189318", + "47451445736001306439091167216856844588711603153276", + "70386486105843025439939619828917593665686757934951", + "62176457141856560629502157223196586755079324193331", + "64906352462741904929101432445813822663347944758178", + "92575867718337217661963751590579239728245598838407", + "58203565325359399008402633568948830189458628227828", + "80181199384826282014278194139940567587151170094390", + "35398664372827112653829987240784473053190104293586", + "86515506006295864861532075273371959191420517255829", + "71693888707715466499115593487603532921714970056938", + "54370070576826684624621495650076471787294438377604", + "53282654108756828443191190634694037855217779295145", + "36123272525000296071075082563815656710885258350721", + "45876576172410976447339110607218265236877223636045", + "17423706905851860660448207621209813287860733969412", + "81142660418086830619328460811191061556940512689692", + "51934325451728388641918047049293215058642563049483", + "62467221648435076201727918039944693004732956340691", + "15732444386908125794514089057706229429197107928209", + "55037687525678773091862540744969844508330393682126", + "18336384825330154686196124348767681297534375946515", + "80386287592878490201521685554828717201219257766954", + "78182833757993103614740356856449095527097864797581", + "16726320100436897842553539920931837441497806860984", + "48403098129077791799088218795327364475675590848030", + "87086987551392711854517078544161852424320693150332", + "59959406895756536782107074926966537676326235447210", + "69793950679652694742597709739166693763042633987085", + "41052684708299085211399427365734116182760315001271", + "65378607361501080857009149939512557028198746004375", + "35829035317434717326932123578154982629742552737307", + "94953759765105305946966067683156574377167401875275", + "88902802571733229619176668713819931811048770190271", + "25267680276078003013678680992525463401061632866526", + "36270218540497705585629946580636237993140746255962", + "24074486908231174977792365466257246923322810917141", + "91430288197103288597806669760892938638285025333403", + "34413065578016127815921815005561868836468420090470", + "23053081172816430487623791969842487255036638784583", + "11487696932154902810424020138335124462181441773470", + "63783299490636259666498587618221225225512486764533", + "67720186971698544312419572409913959008952310058822", + "95548255300263520781532296796249481641953868218774", + "76085327132285723110424803456124867697064507995236", + "37774242535411291684276865538926205024910326572967", + "23701913275725675285653248258265463092207058596522", + "29798860272258331913126375147341994889534765745501", + "18495701454879288984856827726077713721403798879715", + "38298203783031473527721580348144513491373226651381", + "34829543829199918180278916522431027392251122869539", + "40957953066405232632538044100059654939159879593635", + "29746152185502371307642255121183693803580388584903", + "41698116222072977186158236678424689157993532961922", + "62467957194401269043877107275048102390895523597457", + "23189706772547915061505504953922979530901129967519", + "86188088225875314529584099251203829009407770775672", + "11306739708304724483816533873502340845647058077308", + "82959174767140363198008187129011875491310547126581", + "97623331044818386269515456334926366572897563400500", + "42846280183517070527831839425882145521227251250327", + "55121603546981200581762165212827652751691296897789", + "32238195734329339946437501907836945765883352399886", + "75506164965184775180738168837861091527357929701337", + "62177842752192623401942399639168044983993173312731", + "32924185707147349566916674687634660915035914677504", + "99518671430235219628894890102423325116913619626622", + "73267460800591547471830798392868535206946944540724", + "76841822524674417161514036427982273348055556214818", + "97142617910342598647204516893989422179826088076852", + "87783646182799346313767754307809363333018982642090", + "10848802521674670883215120185883543223812876952786", + "71329612474782464538636993009049310363619763878039", + "62184073572399794223406235393808339651327408011116", + "66627891981488087797941876876144230030984490851411", + "60661826293682836764744779239180335110989069790714", + "85786944089552990653640447425576083659976645795096", + "66024396409905389607120198219976047599490197230297", + "64913982680032973156037120041377903785566085089252", + "16730939319872750275468906903707539413042652315011", + "94809377245048795150954100921645863754710598436791", + "78639167021187492431995700641917969777599028300699", + "15368713711936614952811305876380278410754449733078", + "40789923115535562561142322423255033685442488917353", + "44889911501440648020369068063960672322193204149535", + "41503128880339536053299340368006977710650566631954", + "81234880673210146739058568557934581403627822703280", + "82616570773948327592232845941706525094512325230608", + "22918802058777319719839450180888072429661980811197", + "77158542502016545090413245809786882778948721859617", + "72107838435069186155435662884062257473692284509516", + "20849603980134001723930671666823555245252804609722", + "53503534226472524250874054075591789781264330331690", +} + +func Problem13() string { + sum := "0" + + for _, n := range numbers { + sum = add(sum, n) + } + + return sum[:10] +} + +func add(a, b string) string { + if len(a) < len(b) { + a, b = b, a + } + + carry := 0 + sum := make([]byte, len(a)+1) + + for i := 0; i < len(a); i++ { + d := int(a[len(a)-1-i] - '0') + if i < len(b) { + d += int(b[len(b)-1-i] - '0') + } + d += carry + + sum[len(sum)-1-i] = byte(d%10) + '0' + carry = d / 10 + } + + if carry > 0 { + sum[0] = byte(carry) + '0' + } else { + sum = sum[1:] + } + + return string(sum) +} diff --git a/project_euler/problem_13/problem13_test.go b/project_euler/problem_13/problem13_test.go new file mode 100644 index 000000000..e776cbb04 --- /dev/null +++ b/project_euler/problem_13/problem13_test.go @@ -0,0 +1,27 @@ +package problem13 + +import "testing" + +func TestProblem13_Func(t *testing.T) { + tests := []struct { + name string + expected string + }{ + {"Test Case 1", "5537376230"}, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + actual := Problem13() + if actual != tt.expected { + t.Errorf("Expected: %v, but got %v", tt.expected, actual) + } + }) + } +} + +func BenchmarkProblem13_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem13() + } +} diff --git a/project_euler/problem_14/problem14.go b/project_euler/problem_14/problem14.go new file mode 100644 index 000000000..aa5702c12 --- /dev/null +++ b/project_euler/problem_14/problem14.go @@ -0,0 +1,56 @@ +/** +* Problem 14 - Longest Collatz sequence +* @see {@link https://projecteuler.net/problem=14} +* +* The following iterative sequence is defined for the set of positive integers: +* n → n/2 (n is even) +* n → 3n + 1 (n is odd) +* +* Using the rule above and starting with 13, we generate the following sequence: +* 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 +* +* Which starting number, under one million, produces the longest chain? +* +* NOTE: Once the chain starts the terms are allowed to go above one million. +* +* @author ddaniel27 + */ +package problem14 + +type dict map[uint64]uint64 + +var dictionary = dict{ + 1: 1, +} + +func Problem14(limit uint64) uint64 { + for i := uint64(2); i <= limit; i++ { + weightNextNode(i) + } + + var max, maxWeight uint64 + for k, v := range dictionary { + if v > maxWeight { + max = k + maxWeight = v + } + } + + return max +} + +func weightNextNode(current uint64) uint64 { + var next, weight uint64 + if current%2 == 0 { + next = current / 2 + } else { + next = (3 * current) + 1 + } + if v, ok := dictionary[next]; !ok { + weight = weightNextNode(next) + 1 + } else { + weight = v + 1 + } + dictionary[current] = weight + return weight +} diff --git a/project_euler/problem_14/problem14_test.go b/project_euler/problem_14/problem14_test.go new file mode 100644 index 000000000..801ff0fdd --- /dev/null +++ b/project_euler/problem_14/problem14_test.go @@ -0,0 +1,31 @@ +package problem14 + +import "testing" + +// Tests +func TestProblem14_Func(t *testing.T) { + tests := []struct { + name string + input uint64 + want uint64 + }{ + {"Input 30", 30, 27}, + {"Input 1e6", 1e6, 837799}, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + got := Problem14(tt.input) + if got != tt.want { + t.Errorf("Problem14() = %v, want %v", got, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem14_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem14(1e6) + } +} diff --git a/project_euler/problem_15/problem15.go b/project_euler/problem_15/problem15.go new file mode 100644 index 000000000..6adbd6977 --- /dev/null +++ b/project_euler/problem_15/problem15.go @@ -0,0 +1,42 @@ +/** +* Problem 15 - Lattice paths +* @see {@link https://projecteuler.net/problem=15} +* +* Starting in the top left corner of a 2×2 grid, +* and only being able to move to the right and down, +* there are exactly 6 routes to the bottom right corner. +* +* How many such routes are there through a 20×20 grid? +* +* @author ddaniel27 + */ +package problem15 + +import ( + "github.com/TheAlgorithms/Go/math/factorial" +) + +func Problem15(gridSize int) int { + /** + Author note: + We can solve this problem using combinatorics. + Here is a good blog post that explains the solution: + + [link](https://stemhash.com/counting-lattice-paths/) + + Btw, I'm not related to the author of the blog post. + + After some simplification, we can see that the solution is: + (2n)! / (n!)^2 + + We can use the factorial package to calculate the factorials. + */ + + n := gridSize + + numerator, _ := factorial.Iterative(2 * n) + denominator, _ := factorial.Iterative(n) + denominator *= denominator + + return numerator / denominator +} diff --git a/project_euler/problem_15/problem15_test.go b/project_euler/problem_15/problem15_test.go new file mode 100644 index 000000000..a5b729428 --- /dev/null +++ b/project_euler/problem_15/problem15_test.go @@ -0,0 +1,34 @@ +package problem15 + +import "testing" + +// Tests +func TestProblem15_Func(t *testing.T) { + tests := []struct { + name string + input int + want int + }{ + {"Input 2", 2, 6}, + // This test case is disabled + // because it needs a big integer to run successfully + // and factorial package doesn't support it + // {"Input 20", 20, 137846528820}, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + got := Problem15(tt.input) + if got != tt.want { + t.Errorf("Problem15() = %v, want %v", got, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem15_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem15(20) + } +} diff --git a/project_euler/problem_16/problem16.go b/project_euler/problem_16/problem16.go new file mode 100644 index 000000000..cc0471c66 --- /dev/null +++ b/project_euler/problem_16/problem16.go @@ -0,0 +1,33 @@ +/** +* Problem 16 - Power digit sum +* @see {@link https://projecteuler.net/problem=16} +* +* 2^15 = 32768 and the sum of its digits is 3 + 2 + 7 + 6 + 8 = 26. +* +* What is the sum of the digits of the number 2^1000? +* +* @author ddaniel27 + */ +package problem16 + +import ( + "math/big" +) + +func Problem16(exponent int64) int64 { + var result big.Int + + bigTwo := big.NewInt(2) + bigExponent := big.NewInt(exponent) + + result.Exp(bigTwo, bigExponent, nil) + + resultStr := result.String() + + var sum int64 + for _, digit := range resultStr { + sum += int64(digit - '0') + } + + return sum +} diff --git a/project_euler/problem_16/problem16_test.go b/project_euler/problem_16/problem16_test.go new file mode 100644 index 000000000..31e3f9a02 --- /dev/null +++ b/project_euler/problem_16/problem16_test.go @@ -0,0 +1,30 @@ +package problem16 + +import "testing" + +// Tests +func TestProblem16_Func(t *testing.T) { + tests := []struct { + name string + exponent int64 + want int64 + }{ + {"2^15", 15, 26}, + {"2^1000", 1000, 1366}, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := Problem16(tt.exponent); got != tt.want { + t.Errorf("Problem16() = %v, want %v", got, tt.want) + } + }) + } +} + +// Benchmark +func BenchmarkProblem16_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem16(1000) + } +} diff --git a/project_euler/problem_17/input.go b/project_euler/problem_17/input.go new file mode 100644 index 000000000..3a16f8c3a --- /dev/null +++ b/project_euler/problem_17/input.go @@ -0,0 +1,8 @@ +/** +* I put this code in a separate file because it is too long. +* Also it took me a lot of time to parsing this input from +* a random html page, so, I don't want to lose it. + */ +package problem17 + +const INPUT = "One Two Three Four Five Six Seven Eight Nine Ten Eleven Twelve Thirteen Fourteen Fifteen Sixteen Seventeen Eighteen Nineteen Twenty Twenty one Twenty two Twenty three Twenty four Twenty five Twenty six Twenty seven Twenty eight Twenty nine Thirty Thirty one Thirty two Thirty three Thirty four Thirty five Thirty six Thirty seven Thirty eight Thirty nine Forty Forty one Forty two Forty three Forty four Forty five Forty six Forty seven Forty eight Forty nine Fifty Fifty one Fifty two Fifty three Fifty four Fifty five Fifty six Fifty seven Fifty eight Fifty nine Sixty Sixty one Sixty two Sixty three Sixty four Sixty five Sixty six Sixty seven Sixty eight Sixty nine Seventy Seventy one Seventy two Seventy three Seventy four Seventy five Seventy six Seventy seven Seventy eight Seventy nine Eighty Eighty one Eighty two Eighty three Eighty four Eighty five Eighty six Eighty seven Eighty eight Eighty nine Ninety Ninety one Ninety two Ninety three Ninety four Ninety five Ninety six Ninety seven Ninety eight Ninety nine One hundred One hundred and one One hundred and two One hundred and three One hundred and four One hundred and five One hundred and six One hundred and seven One hundred and eight One hundred and nine One hundred and ten One hundred and eleven One hundred and twelve One hundred and thirteen One hundred and fourteen One hundred and fifteen One hundred and sixteen One hundred and seventeen One hundred and eighteen One hundred and nineteen One hundred and twenty One hundred and twenty one One hundred and twenty two One hundred and twenty three One hundred and twenty four One hundred and twenty five One hundred and twenty six One hundred and twenty seven One hundred and twenty eight One hundred and twenty nine One hundred and thirty One hundred and thirty one One hundred and thirty two One hundred and thirty three One hundred and thirty four One hundred and thirty five One hundred and thirty six One hundred and thirty seven One hundred and thirty eight One hundred and thirty nine One hundred and forty One hundred and forty one One hundred and forty two One hundred and forty three One hundred and forty four One hundred and forty five One hundred and forty six One hundred and forty seven One hundred and forty eight One hundred and forty nine One hundred and fifty One hundred and fifty one One hundred and fifty two One hundred and fifty three One hundred and fifty four One hundred and fifty five One hundred and fifty six One hundred and fifty seven One hundred and fifty eight One hundred and fifty nine One hundred and sixty One hundred and sixty one One hundred and sixty two One hundred and sixty three One hundred and sixty four One hundred and sixty five One hundred and sixty six One hundred and sixty seven One hundred and sixty eight One hundred and sixty nine One hundred and seventy One hundred and seventy one One hundred and seventy two One hundred and seventy three One hundred and seventy four One hundred and seventy five One hundred and seventy six One hundred and seventy seven One hundred and seventy eight One hundred and seventy nine One hundred and eighty One hundred and eighty one One hundred and eighty two One hundred and eighty three One hundred and eighty four One hundred and eighty five One hundred and eighty six One hundred and eighty seven One hundred and eighty eight One hundred and eighty nine One hundred and ninety One hundred and ninety one One hundred and ninety two One hundred and ninety three One hundred and ninety four One hundred and ninety five One hundred and ninety six One hundred and ninety seven One hundred and ninety eight One hundred and ninety nine Two hundred Two hundred and one Two hundred and two Two hundred and three Two hundred and four Two hundred and five Two hundred and six Two hundred and seven Two hundred and eight Two hundred and nine Two hundred and ten Two hundred and eleven Two hundred and twelve Two hundred and thirteen Two hundred and fourteen Two hundred and fifteen Two hundred and sixteen Two hundred and seventeen Two hundred and eighteen Two hundred and nineteen Two hundred and twenty Two hundred and twenty one Two hundred and twenty two Two hundred and twenty three Two hundred and twenty four Two hundred and twenty five Two hundred and twenty six Two hundred and twenty seven Two hundred and twenty eight Two hundred and twenty nine Two hundred and thirty Two hundred and thirty one Two hundred and thirty two Two hundred and thirty three Two hundred and thirty four Two hundred and thirty five Two hundred and thirty six Two hundred and thirty seven Two hundred and thirty eight Two hundred and thirty nine Two hundred and forty Two hundred and forty one Two hundred and forty two Two hundred and forty three Two hundred and forty four Two hundred and forty five Two hundred and forty six Two hundred and forty seven Two hundred and forty eight Two hundred and forty nine Two hundred and fifty Two hundred and fifty one Two hundred and fifty two Two hundred and fifty three Two hundred and fifty four Two hundred and fifty five Two hundred and fifty six Two hundred and fifty seven Two hundred and fifty eight Two hundred and fifty nine Two hundred and sixty Two hundred and sixty one Two hundred and sixty two Two hundred and sixty three Two hundred and sixty four Two hundred and sixty five Two hundred and sixty six Two hundred and sixty seven Two hundred and sixty eight Two hundred and sixty nine Two hundred and seventy Two hundred and seventy one Two hundred and seventy two Two hundred and seventy three Two hundred and seventy four Two hundred and seventy five Two hundred and seventy six Two hundred and seventy seven Two hundred and seventy eight Two hundred and seventy nine Two hundred and eighty Two hundred and eighty one Two hundred and eighty two Two hundred and eighty three Two hundred and eighty four Two hundred and eighty five Two hundred and eighty six Two hundred and eighty seven Two hundred and eighty eight Two hundred and eighty nine Two hundred and ninety Two hundred and ninety one Two hundred and ninety two Two hundred and ninety three Two hundred and ninety four Two hundred and ninety five Two hundred and ninety six Two hundred and ninety seven Two hundred and ninety eight Two hundred and ninety nine Three hundred Three hundred and one Three hundred and two Three hundred and three Three hundred and four Three hundred and five Three hundred and six Three hundred and seven Three hundred and eight Three hundred and nine Three hundred and ten Three hundred and eleven Three hundred and twelve Three hundred and thirteen Three hundred and fourteen Three hundred and fifteen Three hundred and sixteen Three hundred and seventeen Three hundred and eighteen Three hundred and nineteen Three hundred and twenty Three hundred and twenty one Three hundred and twenty two Three hundred and twenty three Three hundred and twenty four Three hundred and twenty five Three hundred and twenty six Three hundred and twenty seven Three hundred and twenty eight Three hundred and twenty nine Three hundred and thirty Three hundred and thirty one Three hundred and thirty two Three hundred and thirty three Three hundred and thirty four Three hundred and thirty five Three hundred and thirty six Three hundred and thirty seven Three hundred and thirty eight Three hundred and thirty nine Three hundred and forty Three hundred and forty one Three hundred and forty two Three hundred and forty three Three hundred and forty four Three hundred and forty five Three hundred and forty six Three hundred and forty seven Three hundred and forty eight Three hundred and forty nine Three hundred and fifty Three hundred and fifty one Three hundred and fifty two Three hundred and fifty three Three hundred and fifty four Three hundred and fifty five Three hundred and fifty six Three hundred and fifty seven Three hundred and fifty eight Three hundred and fifty nine Three hundred and sixty Three hundred and sixty one Three hundred and sixty two Three hundred and sixty three Three hundred and sixty four Three hundred and sixty five Three hundred and sixty six Three hundred and sixty seven Three hundred and sixty eight Three hundred and sixty nine Three hundred and seventy Three hundred and seventy one Three hundred and seventy two Three hundred and seventy three Three hundred and seventy four Three hundred and seventy five Three hundred and seventy six Three hundred and seventy seven Three hundred and seventy eight Three hundred and seventy nine Three hundred and eighty Three hundred and eighty one Three hundred and eighty two Three hundred and eighty three Three hundred and eighty four Three hundred and eighty five Three hundred and eighty six Three hundred and eighty seven Three hundred and eighty eight Three hundred and eighty nine Three hundred and ninety Three hundred and ninety one Three hundred and ninety two Three hundred and ninety three Three hundred and ninety four Three hundred and ninety five Three hundred and ninety six Three hundred and ninety seven Three hundred and ninety eight Three hundred and ninety nine Four hundred Four hundred and one Four hundred and two Four hundred and three Four hundred and four Four hundred and five Four hundred and six Four hundred and seven Four hundred and eight Four hundred and nine Four hundred and ten Four hundred and eleven Four hundred and twelve Four hundred and thirteen Four hundred and fourteen Four hundred and fifteen Four hundred and sixteen Four hundred and seventeen Four hundred and eighteen Four hundred and nineteen Four hundred and twenty Four hundred and twenty one Four hundred and twenty two Four hundred and twenty three Four hundred and twenty four Four hundred and twenty five Four hundred and twenty six Four hundred and twenty seven Four hundred and twenty eight Four hundred and twenty nine Four hundred and thirty Four hundred and thirty one Four hundred and thirty two Four hundred and thirty three Four hundred and thirty four Four hundred and thirty five Four hundred and thirty six Four hundred and thirty seven Four hundred and thirty eight Four hundred and thirty nine Four hundred and forty Four hundred and forty one Four hundred and forty two Four hundred and forty three Four hundred and forty four Four hundred and forty five Four hundred and forty six Four hundred and forty seven Four hundred and forty eight Four hundred and forty nine Four hundred and fifty Four hundred and fifty one Four hundred and fifty two Four hundred and fifty three Four hundred and fifty four Four hundred and fifty five Four hundred and fifty six Four hundred and fifty seven Four hundred and fifty eight Four hundred and fifty nine Four hundred and sixty Four hundred and sixty one Four hundred and sixty two Four hundred and sixty three Four hundred and sixty four Four hundred and sixty five Four hundred and sixty six Four hundred and sixty seven Four hundred and sixty eight Four hundred and sixty nine Four hundred and seventy Four hundred and seventy one Four hundred and seventy two Four hundred and seventy three Four hundred and seventy four Four hundred and seventy five Four hundred and seventy six Four hundred and seventy seven Four hundred and seventy eight Four hundred and seventy nine Four hundred and eighty Four hundred and eighty one Four hundred and eighty two Four hundred and eighty three Four hundred and eighty four Four hundred and eighty five Four hundred and eighty six Four hundred and eighty seven Four hundred and eighty eight Four hundred and eighty nine Four hundred and ninety Four hundred and ninety one Four hundred and ninety two Four hundred and ninety three Four hundred and ninety four Four hundred and ninety five Four hundred and ninety six Four hundred and ninety seven Four hundred and ninety eight Four hundred and ninety nine Five hundred Five hundred and one Five hundred and two Five hundred and three Five hundred and four Five hundred and five Five hundred and six Five hundred and seven Five hundred and eight Five hundred and nine Five hundred and ten Five hundred and eleven Five hundred and twelve Five hundred and thirteen Five hundred and fourteen Five hundred and fifteen Five hundred and sixteen Five hundred and seventeen Five hundred and eighteen Five hundred and nineteen Five hundred and twenty Five hundred and twenty one Five hundred and twenty two Five hundred and twenty three Five hundred and twenty four Five hundred and twenty five Five hundred and twenty six Five hundred and twenty seven Five hundred and twenty eight Five hundred and twenty nine Five hundred and thirty Five hundred and thirty one Five hundred and thirty two Five hundred and thirty three Five hundred and thirty four Five hundred and thirty five Five hundred and thirty six Five hundred and thirty seven Five hundred and thirty eight Five hundred and thirty nine Five hundred and forty Five hundred and forty one Five hundred and forty two Five hundred and forty three Five hundred and forty four Five hundred and forty five Five hundred and forty six Five hundred and forty seven Five hundred and forty eight Five hundred and forty nine Five hundred and fifty Five hundred and fifty one Five hundred and fifty two Five hundred and fifty three Five hundred and fifty four Five hundred and fifty five Five hundred and fifty six Five hundred and fifty seven Five hundred and fifty eight Five hundred and fifty nine Five hundred and sixty Five hundred and sixty one Five hundred and sixty two Five hundred and sixty three Five hundred and sixty four Five hundred and sixty five Five hundred and sixty six Five hundred and sixty seven Five hundred and sixty eight Five hundred and sixty nine Five hundred and seventy Five hundred and seventy one Five hundred and seventy two Five hundred and seventy three Five hundred and seventy four Five hundred and seventy five Five hundred and seventy six Five hundred and seventy seven Five hundred and seventy eight Five hundred and seventy nine Five hundred and eighty Five hundred and eighty one Five hundred and eighty two Five hundred and eighty three Five hundred and eighty four Five hundred and eighty five Five hundred and eighty six Five hundred and eighty seven Five hundred and eighty eight Five hundred and eighty nine Five hundred and ninety Five hundred and ninety one Five hundred and ninety two Five hundred and ninety three Five hundred and ninety four Five hundred and ninety five Five hundred and ninety six Five hundred and ninety seven Five hundred and ninety eight Five hundred and ninety nine Six hundred Six hundred and one Six hundred and two Six hundred and three Six hundred and four Six hundred and five Six hundred and six Six hundred and seven Six hundred and eight Six hundred and nine Six hundred and ten Six hundred and eleven Six hundred and twelve Six hundred and thirteen Six hundred and fourteen Six hundred and fifteen Six hundred and sixteen Six hundred and seventeen Six hundred and eighteen Six hundred and nineteen Six hundred and twenty Six hundred and twenty one Six hundred and twenty two Six hundred and twenty three Six hundred and twenty four Six hundred and twenty five Six hundred and twenty six Six hundred and twenty seven Six hundred and twenty eight Six hundred and twenty nine Six hundred and thirty Six hundred and thirty one Six hundred and thirty two Six hundred and thirty three Six hundred and thirty four Six hundred and thirty five Six hundred and thirty six Six hundred and thirty seven Six hundred and thirty eight Six hundred and thirty nine Six hundred and forty Six hundred and forty one Six hundred and forty two Six hundred and forty three Six hundred and forty four Six hundred and forty five Six hundred and forty six Six hundred and forty seven Six hundred and forty eight Six hundred and forty nine Six hundred and fifty Six hundred and fifty one Six hundred and fifty two Six hundred and fifty three Six hundred and fifty four Six hundred and fifty five Six hundred and fifty six Six hundred and fifty seven Six hundred and fifty eight Six hundred and fifty nine Six hundred and sixty Six hundred and sixty one Six hundred and sixty two Six hundred and sixty three Six hundred and sixty four Six hundred and sixty five Six hundred and sixty six Six hundred and sixty seven Six hundred and sixty eight Six hundred and sixty nine Six hundred and seventy Six hundred and seventy one Six hundred and seventy two Six hundred and seventy three Six hundred and seventy four Six hundred and seventy five Six hundred and seventy six Six hundred and seventy seven Six hundred and seventy eight Six hundred and seventy nine Six hundred and eighty Six hundred and eighty one Six hundred and eighty two Six hundred and eighty three Six hundred and eighty four Six hundred and eighty five Six hundred and eighty six Six hundred and eighty seven Six hundred and eighty eight Six hundred and eighty nine Six hundred and ninety Six hundred and ninety one Six hundred and ninety two Six hundred and ninety three Six hundred and ninety four Six hundred and ninety five Six hundred and ninety six Six hundred and ninety seven Six hundred and ninety eight Six hundred and ninety nine Seven hundred Seven hundred and one Seven hundred and two Seven hundred and three Seven hundred and four Seven hundred and five Seven hundred and six Seven hundred and seven Seven hundred and eight Seven hundred and nine Seven hundred and ten Seven hundred and eleven Seven hundred and twelve Seven hundred and thirteen Seven hundred and fourteen Seven hundred and fifteen Seven hundred and sixteen Seven hundred and seventeen Seven hundred and eighteen Seven hundred and nineteen Seven hundred and twenty Seven hundred and twenty one Seven hundred and twenty two Seven hundred and twenty three Seven hundred and twenty four Seven hundred and twenty five Seven hundred and twenty six Seven hundred and twenty seven Seven hundred and twenty eight Seven hundred and twenty nine Seven hundred and thirty Seven hundred and thirty one Seven hundred and thirty two Seven hundred and thirty three Seven hundred and thirty four Seven hundred and thirty five Seven hundred and thirty six Seven hundred and thirty seven Seven hundred and thirty eight Seven hundred and thirty nine Seven hundred and forty Seven hundred and forty one Seven hundred and forty two Seven hundred and forty three Seven hundred and forty four Seven hundred and forty five Seven hundred and forty six Seven hundred and forty seven Seven hundred and forty eight Seven hundred and forty nine Seven hundred and fifty Seven hundred and fifty one Seven hundred and fifty two Seven hundred and fifty three Seven hundred and fifty four Seven hundred and fifty five Seven hundred and fifty six Seven hundred and fifty seven Seven hundred and fifty eight Seven hundred and fifty nine Seven hundred and sixty Seven hundred and sixty one Seven hundred and sixty two Seven hundred and sixty three Seven hundred and sixty four Seven hundred and sixty five Seven hundred and sixty six Seven hundred and sixty seven Seven hundred and sixty eight Seven hundred and sixty nine Seven hundred and seventy Seven hundred and seventy one Seven hundred and seventy two Seven hundred and seventy three Seven hundred and seventy four Seven hundred and seventy five Seven hundred and seventy six Seven hundred and seventy seven Seven hundred and seventy eight Seven hundred and seventy nine Seven hundred and eighty Seven hundred and eighty one Seven hundred and eighty two Seven hundred and eighty three Seven hundred and eighty four Seven hundred and eighty five Seven hundred and eighty six Seven hundred and eighty seven Seven hundred and eighty eight Seven hundred and eighty nine Seven hundred and ninety Seven hundred and ninety one Seven hundred and ninety two Seven hundred and ninety three Seven hundred and ninety four Seven hundred and ninety five Seven hundred and ninety six Seven hundred and ninety seven Seven hundred and ninety eight Seven hundred and ninety nine Eight hundred Eight hundred and one Eight hundred and two Eight hundred and three Eight hundred and four Eight hundred and five Eight hundred and six Eight hundred and seven Eight hundred and eight Eight hundred and nine Eight hundred and ten Eight hundred and eleven Eight hundred and twelve Eight hundred and thirteen Eight hundred and fourteen Eight hundred and fifteen Eight hundred and sixteen Eight hundred and seventeen Eight hundred and eighteen Eight hundred and nineteen Eight hundred and twenty Eight hundred and twenty one Eight hundred and twenty two Eight hundred and twenty three Eight hundred and twenty four Eight hundred and twenty five Eight hundred and twenty six Eight hundred and twenty seven Eight hundred and twenty eight Eight hundred and twenty nine Eight hundred and thirty Eight hundred and thirty one Eight hundred and thirty two Eight hundred and thirty three Eight hundred and thirty four Eight hundred and thirty five Eight hundred and thirty six Eight hundred and thirty seven Eight hundred and thirty eight Eight hundred and thirty nine Eight hundred and forty Eight hundred and forty one Eight hundred and forty two Eight hundred and forty three Eight hundred and forty four Eight hundred and forty five Eight hundred and forty six Eight hundred and forty seven Eight hundred and forty eight Eight hundred and forty nine Eight hundred and fifty Eight hundred and fifty one Eight hundred and fifty two Eight hundred and fifty three Eight hundred and fifty four Eight hundred and fifty five Eight hundred and fifty six Eight hundred and fifty seven Eight hundred and fifty eight Eight hundred and fifty nine Eight hundred and sixty Eight hundred and sixty one Eight hundred and sixty two Eight hundred and sixty three Eight hundred and sixty four Eight hundred and sixty five Eight hundred and sixty six Eight hundred and sixty seven Eight hundred and sixty eight Eight hundred and sixty nine Eight hundred and seventy Eight hundred and seventy one Eight hundred and seventy two Eight hundred and seventy three Eight hundred and seventy four Eight hundred and seventy five Eight hundred and seventy six Eight hundred and seventy seven Eight hundred and seventy eight Eight hundred and seventy nine Eight hundred and eighty Eight hundred and eighty one Eight hundred and eighty two Eight hundred and eighty three Eight hundred and eighty four Eight hundred and eighty five Eight hundred and eighty six Eight hundred and eighty seven Eight hundred and eighty eight Eight hundred and eighty nine Eight hundred and ninety Eight hundred and ninety one Eight hundred and ninety two Eight hundred and ninety three Eight hundred and ninety four Eight hundred and ninety five Eight hundred and ninety six Eight hundred and ninety seven Eight hundred and ninety eight Eight hundred and ninety nine Nine hundred Nine hundred and one Nine hundred and two Nine hundred and three Nine hundred and four Nine hundred and five Nine hundred and six Nine hundred and seven Nine hundred and eight Nine hundred and nine Nine hundred and ten Nine hundred and eleven Nine hundred and twelve Nine hundred and thirteen Nine hundred and fourteen Nine hundred and fifteen Nine hundred and sixteen Nine hundred and seventeen Nine hundred and eighteen Nine hundred and nineteen Nine hundred and twenty Nine hundred and twenty one Nine hundred and twenty two Nine hundred and twenty three Nine hundred and twenty four Nine hundred and twenty five Nine hundred and twenty six Nine hundred and twenty seven Nine hundred and twenty eight Nine hundred and twenty nine Nine hundred and thirty Nine hundred and thirty one Nine hundred and thirty two Nine hundred and thirty three Nine hundred and thirty four Nine hundred and thirty five Nine hundred and thirty six Nine hundred and thirty seven Nine hundred and thirty eight Nine hundred and thirty nine Nine hundred and forty Nine hundred and forty one Nine hundred and forty two Nine hundred and forty three Nine hundred and forty four Nine hundred and forty five Nine hundred and forty six Nine hundred and forty seven Nine hundred and forty eight Nine hundred and forty nine Nine hundred and fifty Nine hundred and fifty one Nine hundred and fifty two Nine hundred and fifty three Nine hundred and fifty four Nine hundred and fifty five Nine hundred and fifty six Nine hundred and fifty seven Nine hundred and fifty eight Nine hundred and fifty nine Nine hundred and sixty Nine hundred and sixty one Nine hundred and sixty two Nine hundred and sixty three Nine hundred and sixty four Nine hundred and sixty five Nine hundred and sixty six Nine hundred and sixty seven Nine hundred and sixty eight Nine hundred and sixty nine Nine hundred and seventy Nine hundred and seventy one Nine hundred and seventy two Nine hundred and seventy three Nine hundred and seventy four Nine hundred and seventy five Nine hundred and seventy six Nine hundred and seventy seven Nine hundred and seventy eight Nine hundred and seventy nine Nine hundred and eighty Nine hundred and eighty one Nine hundred and eighty two Nine hundred and eighty three Nine hundred and eighty four Nine hundred and eighty five Nine hundred and eighty six Nine hundred and eighty seven Nine hundred and eighty eight Nine hundred and eighty nine Nine hundred and ninety Nine hundred and ninety one Nine hundred and ninety two Nine hundred and ninety three Nine hundred and ninety four Nine hundred and ninety five Nine hundred and ninety six Nine hundred and ninety seven Nine hundred and ninety eight Nine hundred and ninety nine One thousand" diff --git a/project_euler/problem_17/problem17.go b/project_euler/problem_17/problem17.go new file mode 100644 index 000000000..a5e2beee7 --- /dev/null +++ b/project_euler/problem_17/problem17.go @@ -0,0 +1,31 @@ +/** +* Problem 17 - Number letter counts +* @see {@link https://projecteuler.net/problem=17} +* +* If the numbers 1 to 5 are written out in words: one, two, three, four, five, +* then there are 3 + 3 + 5 + 4 + 4 = 19 letters used in total. +* +* If all the numbers from 1 to 1000 (one thousand) inclusive were written out in words, +* how many letters would be used? +* +* NOTE: Do not count spaces or hyphens. For example, 342 (three hundred and forty-two) +* contains 23 letters and 115 (one hundred and fifteen) contains 20 letters. +* The use of "and" when writing out numbers is in compliance with British usage. +* +* @author ddaniel27 + */ +package problem17 + +import "strings" + +func Problem17(input string) int { + var sum int + + parsed := strings.Split(input, " ") + + for _, word := range parsed { + sum += len(word) + } + + return sum +} diff --git a/project_euler/problem_17/problem17_test.go b/project_euler/problem_17/problem17_test.go new file mode 100644 index 000000000..13cf68bf4 --- /dev/null +++ b/project_euler/problem_17/problem17_test.go @@ -0,0 +1,30 @@ +package problem17 + +import "testing" + +// Tests +func TestProblem17_Func(t *testing.T) { + tests := []struct { + name string + input string + want int + }{ + {"1 to 5", "one two three four five", 19}, + {"1 to 1000", INPUT, 21124}, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := Problem17(tt.input); got != tt.want { + t.Errorf("Problem17() = %v, want %v", got, tt.want) + } + }) + } +} + +// Benchmark +func BenchmarkProblem17_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem17(INPUT) + } +} diff --git a/project_euler/problem_18/edge.go b/project_euler/problem_18/edge.go new file mode 100644 index 000000000..90f44b082 --- /dev/null +++ b/project_euler/problem_18/edge.go @@ -0,0 +1,100 @@ +package problem18 + +type Edge struct { + ID int + NodeValue NodeValue + NodeLeft Node + NodeRight Node + Parent Node +} + +func (n *Edge) Value() NodeValue { + return n.NodeValue +} + +func (n *Edge) Left() Node { + return n.NodeLeft +} + +func (n *Edge) Right() Node { + return n.NodeRight +} + +func (n *Edge) Kind() string { + return "edge" +} + +func (n *Edge) CreateChild(value NodeValue, id int) Node { + // When the left child is nil, it's a left edge + if n.NodeLeft == nil { + return &Edge{ + ID: id, + NodeValue: value, + Parent: n, + NodeLeft: nil, + NodeRight: nil, + } + } + + // When the left child is a leaf, it's a right edge + if n.NodeLeft.Kind() == "leaf" { + return &Edge{ + ID: id, + NodeValue: value, + Parent: n, + NodeLeft: nil, + NodeRight: nil, + } + } + + return &Leaf{ + ID: id, + NodeValue: value, + Parent: n, + NodeLeft: nil, + NodeRight: nil, + } +} + +func (n *Edge) GetID() int { + return n.ID +} + +func (n *Edge) Insert(node Node) { + // If Left is nil, always simply insert the node + if n.NodeLeft == nil { + node.SetParent(n) + n.NodeLeft = node + + return + } + + // If Right is nil, insert the node + n.NodeRight = node + + // If the node to insert is an edge, set the parent + if node.Kind() == "edge" { + node.SetParent(n) + + return + } + + // If the node to insert is a leaf, send it to the sibling right + n.Parent.Right().Insert(node) +} + +func (n *Edge) HasSpace() bool { + return n.NodeLeft == nil || n.NodeRight == nil +} + +func (n *Edge) LeftIsNil() bool { + return n.NodeLeft == nil +} + +func (n *Edge) RightIsNil() bool { + return n.NodeRight == nil +} + +func (n *Edge) SetParent(node Node) { + n.Parent = node +} diff --git a/project_euler/problem_18/input.go b/project_euler/problem_18/input.go new file mode 100644 index 000000000..e11dcc41f --- /dev/null +++ b/project_euler/problem_18/input.go @@ -0,0 +1,42 @@ +package problem18 + +import "strings" + +const problem18_input_string = ` +75 +95 64 +17 47 82 +18 35 87 10 +20 04 82 47 65 +19 01 23 75 03 34 +88 02 77 73 07 63 67 +99 65 04 28 06 16 70 92 +41 41 26 56 83 40 80 70 33 +41 48 72 33 47 32 37 16 94 29 +53 71 44 65 25 43 91 52 97 51 14 +70 11 33 28 77 73 17 78 39 68 17 57 +91 71 52 38 17 14 91 43 58 50 27 29 48 +63 66 04 68 89 53 67 30 73 16 69 87 40 31 +04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 +` + +var problem18_input_parsed_string []string = strings.Split( + strings.Trim( + strings.ReplaceAll(problem18_input_string, "\n", " "), + " ", + ), + " ") + +const problem18_test_string = ` +3 +7 4 +2 4 6 +8 5 9 3 +` + +var problem18_test_parsed_string []string = strings.Split( + strings.Trim( + strings.ReplaceAll(problem18_test_string, "\n", " "), + " ", + ), + " ") diff --git a/project_euler/problem_18/leaf.go b/project_euler/problem_18/leaf.go new file mode 100644 index 000000000..8dd452602 --- /dev/null +++ b/project_euler/problem_18/leaf.go @@ -0,0 +1,75 @@ +package problem18 + +type Leaf struct { + ID int + NodeValue NodeValue + NodeLeft *Leaf + NodeRight *Leaf + Parent Node +} + +func (n *Leaf) Value() NodeValue { + return n.NodeValue +} + +func (n *Leaf) Left() Node { + if n.NodeLeft != nil { + n.NodeLeft.Parent = n // Leaf is the parent of its left child always + } + + return n.NodeLeft +} + +func (n *Leaf) Right() Node { + return n.NodeRight +} + +func (n *Leaf) Kind() string { + return "leaf" +} + +func (n *Leaf) CreateChild(value NodeValue, id int) Node { + // Leafs only have leaf children + return &Leaf{ + ID: id, + NodeValue: value, + Parent: n, + NodeLeft: nil, + NodeRight: nil, + } +} + +func (n *Leaf) GetID() int { + return n.ID +} + +func (n *Leaf) Insert(node Node) { + // If Left is nil, always simply insert the node + if n.NodeLeft == nil { + node.SetParent(n) + n.NodeLeft = node.(*Leaf) + + return + } + + // If Right is nil, insert the node + n.NodeRight = node.(*Leaf) + // Send it to the sibling right + n.Parent.Right().Insert(node) +} + +func (n *Leaf) HasSpace() bool { + return n.NodeLeft == nil || n.NodeRight == nil +} + +func (n *Leaf) LeftIsNil() bool { + return n.NodeLeft == nil +} + +func (n *Leaf) RightIsNil() bool { + return n.NodeRight == nil +} + +func (n *Leaf) SetParent(node Node) { + n.Parent = node +} diff --git a/project_euler/problem_18/problem18.go b/project_euler/problem_18/problem18.go new file mode 100644 index 000000000..1775c6bd0 --- /dev/null +++ b/project_euler/problem_18/problem18.go @@ -0,0 +1,63 @@ +/** +* Problem 18 - Maximum path sum I +* @see {@link https://projecteuler.net/problem=18} +* +* By starting at the top of the triangle below and +* moving to adjacent numbers on the row below, +* the maximum total from top to bottom is 23. +* +* 3 +* 7 4 +* 2 4 6 +* 8 5 9 3 +* +* That is, 3 + 7 + 4 + 9 = 23. +* +* Find the maximum total from top to bottom of the triangle below: +* [refer to the problem link] +* +* NOTE: As there are only 16384 routes, it is possible +* to solve this problem by trying every route. +* However, Problem 67, is the same challenge with a triangle +* containing one-hundred rows; it cannot be solved by brute force, +* and requires a clever method! ;o) +* +* @author ddaniel27 + */ +package problem18 + +import "strconv" + +type ( + NodeValue int + NodeType string + + Node interface { + Value() NodeValue + GetID() int + Left() Node + Right() Node + LeftIsNil() bool + RightIsNil() bool + HasSpace() bool + Kind() string + SetParent(Node) + CreateChild(NodeValue, int) Node + Insert(Node) + } +) + +func Problem18(input []string, deep int) int { + tree := &Tree{} + + for _, num := range input { + v, err := strconv.Atoi(num) + if err != nil { + panic(err) + } + + tree.BFSInsert(NodeValue(v)) + } + + return tree.MaxPathValueSearch(deep) +} diff --git a/project_euler/problem_18/problem18_test.go b/project_euler/problem_18/problem18_test.go new file mode 100644 index 000000000..50baab2ed --- /dev/null +++ b/project_euler/problem_18/problem18_test.go @@ -0,0 +1,42 @@ +package problem18 + +import "testing" + +// Tests +func TestProblem18_Func(t *testing.T) { + tests := []struct { + name string + input []string + deep int + expected int + }{ + { + name: "Test case 1", + input: problem18_test_parsed_string, + deep: 2, + expected: 23, + }, + { + name: "Test case 2", + input: problem18_input_parsed_string, + deep: 2, + expected: 1074, + }, + } + + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + actual := Problem18(test.input, test.deep) + if actual != test.expected { + t.Errorf("Expected %d, but got %d", test.expected, actual) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem18_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem18(problem18_input_parsed_string, 2) + } +} diff --git a/project_euler/problem_18/root.go b/project_euler/problem_18/root.go new file mode 100644 index 000000000..4ee018629 --- /dev/null +++ b/project_euler/problem_18/root.go @@ -0,0 +1,62 @@ +package problem18 + +type Root struct { + ID int + NodeValue NodeValue + NodeLeft *Edge + NodeRight *Edge +} + +func (n *Root) Value() NodeValue { + return n.NodeValue +} + +func (n *Root) Left() Node { + return n.NodeLeft +} + +func (n *Root) Right() Node { + return n.NodeRight +} + +func (n *Root) Kind() string { + return "root" +} + +func (n *Root) CreateChild(value NodeValue, id int) Node { + return &Edge{ + ID: id, + NodeValue: value, + Parent: n, + NodeLeft: nil, + NodeRight: nil, + } +} + +func (n *Root) GetID() int { + return n.ID +} + +func (n *Root) Insert(node Node) { + if n.NodeLeft == nil { + n.NodeLeft = node.(*Edge) + } else { + n.NodeRight = node.(*Edge) + } +} + +func (n *Root) HasSpace() bool { + return n.NodeLeft == nil || n.NodeRight == nil +} + +func (n *Root) LeftIsNil() bool { + return n.NodeLeft == nil +} + +func (n *Root) RightIsNil() bool { + return n.NodeRight == nil +} + +func (n *Root) SetParent(node Node) { + panic("Root node cannot have a parent") +} diff --git a/project_euler/problem_18/tree.go b/project_euler/problem_18/tree.go new file mode 100644 index 000000000..6f98f3b1c --- /dev/null +++ b/project_euler/problem_18/tree.go @@ -0,0 +1,229 @@ +package problem18 + +import ( + "fmt" + "strings" +) + +type Tree struct { + Root *Root + Nodes map[int]struct{} + ID int +} + +func (t *Tree) BFSInsert(value NodeValue) { + t.Nodes = make(map[int]struct{}) // Reset the nodes map + + if t.Root == nil { + t.Root = &Root{NodeValue: value, ID: 0} + t.ID = 1 + return + } + + queue := make([]Node, 0) + queue = append(queue, t.Root) + t.isInQueue(t.Root.GetID()) + + head := 0 + + for head < len(queue) { + current := queue[head] + head++ + childNode := current.CreateChild(value, t.ID) + + if current.HasSpace() { + current.Insert(childNode) + t.ID++ + return + } + + if !t.isInQueue(current.Left().GetID()) { // Avoid duplicates + queue = append(queue, current.Left()) + } + if !t.isInQueue(current.Right().GetID()) { + queue = append(queue, current.Right()) + } + } +} + +// MaxPathValueSearch is a method that searches the maximum path value in a tree +// given a certain depth +func (r *Tree) MaxPathValueSearch(deep int) int { + if r.Root == nil { + return 0 + } + + type DFSNode struct { + Node Node + StepsLeft int + Sum int + } + + var pivot Node = r.Root + pivotEnded := false + maxPathValue := int(pivot.Value()) + + stack := make([]DFSNode, 0) + + for !pivotEnded { + stack = append(stack, DFSNode{Node: pivot, StepsLeft: deep, Sum: maxPathValue}) + + for len(stack) > 0 { + current := stack[len(stack)-1] + stack = stack[:len(stack)-1] + + // If we run out of steps, we check the sum of the path, + // update the maxPathValue if necessary and continue + if current.StepsLeft == 0 { + if current.Sum > maxPathValue { + maxPathValue = current.Sum + pivot = current.Node + } + continue + } + + if !current.Node.RightIsNil() { + stack = append(stack, DFSNode{ + Node: current.Node.Right(), + StepsLeft: current.StepsLeft - 1, + Sum: current.Sum + int(current.Node.Right().Value()), + }) + } + + // If the left child is nil, we have reached the end of the path + if !current.Node.LeftIsNil() { + stack = append(stack, DFSNode{ + Node: current.Node.Left(), + StepsLeft: current.StepsLeft - 1, + Sum: current.Sum + int(current.Node.Left().Value()), + }) + } else { + if current.Sum > maxPathValue { + maxPathValue = current.Sum + pivot = current.Node + } + } + } + + // If we don't have reached the end of the left side of the tree, + // we continue with the search using the pivot node + // We use the left child only because how the tree is built + if pivot.LeftIsNil() { + pivotEnded = true + } + } + + return maxPathValue +} + +// PrintReport is a method that prints a report of the tree +// Node by node +func (t *Tree) PrintReport() { + t.Nodes = make(map[int]struct{}) + if t.Root == nil { + return + } + + queue := make([]Node, 0) + queue = append(queue, t.Root) + + head := 0 + + for head < len(queue) { + current := queue[head] + head++ + + print("ID:", current.GetID()) + print(", Current node:", current.Value()) + + if !current.LeftIsNil() { + print(", Left Child:", current.Left().Value()) + + if !t.isInQueue(current.Left().GetID()) { + queue = append(queue, current.Left()) + } + } + + if !current.RightIsNil() { + print(", Right Child:", current.Right().Value()) + + if !t.isInQueue(current.Right().GetID()) { + queue = append(queue, current.Right()) + } + } + + println() + } +} + +// PrintPyramid is a method that prints the tree as a pyramid +func (t *Tree) PrintPyramid() { + t.Nodes = make(map[int]struct{}) + if t.Root == nil { + return + } + + queue := []Node{t.Root} + levels := []int{0} + outputByLevel := []string{} + + head := 0 + currentLevel := 0 + + output := "" + + for head < len(queue) { + current := queue[head] + level := levels[head] + head++ + + // Level change + if level > currentLevel { + currentLevel = level + outputByLevel = append(outputByLevel, output+"\n") + output = "" + } + + // Add current node to the output + if current.Value() < 10 { + output += fmt.Sprintf("0%d ", current.Value()) + } else { + output += fmt.Sprintf("%d ", current.Value()) + } + + // Add children to the queue + if !current.LeftIsNil() { + if !t.isInQueue(current.Left().GetID()) { + queue = append(queue, current.Left()) + levels = append(levels, level+1) + } + } + + if !current.RightIsNil() { + if !t.isInQueue(current.Right().GetID()) { + queue = append(queue, current.Right()) + levels = append(levels, level+1) + } + } + } + // Add the last level + outputByLevel = append(outputByLevel, output+"\n") + + totalLevels := len(outputByLevel) + + // Print the pyramid + for i, level := range outputByLevel { + str := strings.Repeat(" ", 2*(totalLevels-i)) + level + print(str) + } +} + +// isInQueue is a method that avoids duplicates in the tree +func (n *Tree) isInQueue(nv int) bool { + if _, ok := n.Nodes[nv]; ok { + return true + } + + n.Nodes[nv] = struct{}{} + return false +} diff --git a/project_euler/problem_19/problem19.go b/project_euler/problem_19/problem19.go new file mode 100644 index 000000000..9a86f0dea --- /dev/null +++ b/project_euler/problem_19/problem19.go @@ -0,0 +1,63 @@ +package problem19 + +/** +* Problem 19 - Counting Sundays +* @see {@link https://projecteuler.net/problem=19} +* +* You are given the following information, +* but you may prefer to do some research for yourself. +* +* 1 Jan 1900 was a Monday. +* Thirty days has September, +* April, June and November. +* All the rest have thirty-one, +* Saving February alone, +* Which has twenty-eight, rain or shine. +* And on leap years, twenty-nine. +* A leap year occurs on any year evenly divisible by 4, +* but not on a century unless it is divisible by 400. +* +* How many Sundays fell on the first of the month during +* the twentieth century (1 Jan 1901 to 31 Dec 2000)? +* +* @author ddaniel27 + */ + +func Problem19() int { + count := 0 + dayOfWeek := 2 // 1 Jan 1901 was a Tuesday + + for year := 1901; year <= 2000; year++ { + for month := 1; month <= 12; month++ { + if dayOfWeek == 0 { + count++ + } + + daysInMonth := 31 + switch month { + case 4, 6, 9, 11: + daysInMonth = 30 + case 2: + if IsLeapYear(year) { + daysInMonth = 29 + } else { + daysInMonth = 28 + } + } + + dayOfWeek = (dayOfWeek + daysInMonth) % 7 + } + } + + return count +} + +func IsLeapYear(year int) bool { + if year%4 == 0 { + if year%100 == 0 { + return year%400 == 0 + } + return true + } + return false +} diff --git a/project_euler/problem_19/problem19_test.go b/project_euler/problem_19/problem19_test.go new file mode 100644 index 000000000..d26c10938 --- /dev/null +++ b/project_euler/problem_19/problem19_test.go @@ -0,0 +1,29 @@ +package problem19 + +import "testing" + +// Tests +func TestProblem19_Func(t *testing.T) { + tests := []struct { + name string + expected int + }{ + {"Problem 19 - Counting Sundays", 171}, + } + + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + got := Problem19() + if got != test.expected { + t.Errorf("Problem19() = got %v, want %v", got, test.expected) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem19_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem19() + } +} diff --git a/project_euler/problem_2/problem2.go b/project_euler/problem_2/problem2.go new file mode 100644 index 000000000..e8eaeb85e --- /dev/null +++ b/project_euler/problem_2/problem2.go @@ -0,0 +1,30 @@ +/** +* Problem 2 - Even Fibonacci numbers +* @see {@link https://projecteuler.net/problem=2} +* +* Each new term in the Fibonacci sequence is generated by adding the previous two terms. +* By starting with 1 and 2, the first 10 terms will be: +* +* 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... +* +* By considering the terms in the Fibonacci sequence whose values do not exceed four million, +* find the sum of the even-valued terms. +* +* @author ddaniel27 + */ +package problem2 + +func Problem2(n uint) uint { + sum := uint(0) + a, b := uint(1), uint(2) + + for b < n { + if b%2 == 0 { + sum += b + } + + a, b = b, a+b + } + + return sum +} diff --git a/project_euler/problem_2/problem2_test.go b/project_euler/problem_2/problem2_test.go new file mode 100644 index 000000000..32c3834c6 --- /dev/null +++ b/project_euler/problem_2/problem2_test.go @@ -0,0 +1,45 @@ +package problem2 + +import "testing" + +// Tests +func TestProblem2_Func(t *testing.T) { + tests := []struct { + name string + input uint + want uint + }{ + { + name: "Testcase 1 - input 10", + input: 10, + want: 10, + }, + { + name: "Testcase 2 - input 100", + input: 100, + want: 44, + }, + { + name: "Testcase 3 - input 4e6", + input: 4e6, + want: 4613732, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem2(tt.input) + + if n != tt.want { + t.Errorf("Problem2() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem2(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem2(4e6) + } +} diff --git a/project_euler/problem_20/problem20.go b/project_euler/problem_20/problem20.go new file mode 100644 index 000000000..fc731da6b --- /dev/null +++ b/project_euler/problem_20/problem20.go @@ -0,0 +1,37 @@ +/** +* Problem 20 - Factorial digit sum +* @see {@link https://projecteuler.net/problem=20} +* +* n! means n × (n − 1) × ... × 3 × 2 × 1 +* +* For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800, +* and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27. +* +* Find the sum of the digits in the number 100! +* +* @author ddaniel27 + */ +package problem20 + +import "math/big" + +func Problem20(input int) int { + factorial := bigFactorial(input) + sum := 0 + for _, digit := range factorial.String() { + sum += int(digit - '0') + } + return sum +} + +// bigFactorial returns the factorial of n as a big.Int +// Use big package to handle large numbers +func bigFactorial(n int) *big.Int { + if n < 0 { + return big.NewInt(0) + } + if n == 0 { + return big.NewInt(1) + } + return big.NewInt(0).Mul(big.NewInt(int64(n)), bigFactorial(n-1)) +} diff --git a/project_euler/problem_20/problem20_test.go b/project_euler/problem_20/problem20_test.go new file mode 100644 index 000000000..f1ac574c6 --- /dev/null +++ b/project_euler/problem_20/problem20_test.go @@ -0,0 +1,31 @@ +package problem20 + +import "testing" + +// Tests +func TestProblem20_Func(t *testing.T) { + tests := []struct { + name string + input int + expected int + }{ + {"Problem 20 - Factorial digit sum", 10, 27}, + {"Problem 20 - Factorial digit sum", 100, 648}, + } + + for _, test := range tests { + t.Run(test.name, func(t *testing.T) { + got := Problem20(test.input) + if got != test.expected { + t.Errorf("Problem20() = got %v, want %v", got, test.expected) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem20_Func(b *testing.B) { + for i := 0; i < b.N; i++ { + Problem20(100) + } +} diff --git a/project_euler/problem_3/problem3.go b/project_euler/problem_3/problem3.go new file mode 100644 index 000000000..f13525fb6 --- /dev/null +++ b/project_euler/problem_3/problem3.go @@ -0,0 +1,24 @@ +/** +* Problem 3 - Largest prime factor +* @see {@link https://projecteuler.net/problem=3} +* +* The prime factors of 13195 are 5, 7, 13 and 29. +* What is the largest prime factor of the number 600851475143 ? +* +* @author ddaniel27 + */ +package problem3 + +func Problem3(n uint) uint { + i := uint(2) + + for n > 1 { + if n%i == 0 { + n /= i + } else { + i++ + } + } + + return i +} diff --git a/project_euler/problem_3/problem3_test.go b/project_euler/problem_3/problem3_test.go new file mode 100644 index 000000000..d00379f8e --- /dev/null +++ b/project_euler/problem_3/problem3_test.go @@ -0,0 +1,40 @@ +package problem3 + +import "testing" + +// Tests +func TestProblem3_Func(t *testing.T) { + tests := []struct { + name string + input uint + want uint + }{ + { + name: "Testcase 1 - input 13195", + input: 13195, + want: 29, + }, + { + name: "Testcase 2 - input 600851475143", + input: 600851475143, + want: 6857, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem3(tt.input) + + if n != tt.want { + t.Errorf("Problem3() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem3(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem3(600851475143) + } +} diff --git a/project_euler/problem_4/problem4.go b/project_euler/problem_4/problem4.go new file mode 100644 index 000000000..b48d81e41 --- /dev/null +++ b/project_euler/problem_4/problem4.go @@ -0,0 +1,33 @@ +/** +* Problem 4 - Largest palindrome product +* @see {@link https://projecteuler.net/problem=4} +* +* A palindromic number reads the same both ways. +* The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. +* Find the largest palindrome made from the product of two 3-digit numbers. +* +* @author ddaniel27 + */ +package problem4 + +import ( + "fmt" + + "github.com/TheAlgorithms/Go/strings/palindrome" +) + +func Problem4() uint { + max := uint(0) + + for i := 999; i >= 100; i-- { + for j := 999; j >= 100; j-- { + n := uint(i * j) + + if palindrome.IsPalindrome(fmt.Sprintf("%d", n)) && n > max { + max = n + } + } + } + + return max +} diff --git a/project_euler/problem_4/problem4_test.go b/project_euler/problem_4/problem4_test.go new file mode 100644 index 000000000..6b91fd2b0 --- /dev/null +++ b/project_euler/problem_4/problem4_test.go @@ -0,0 +1,33 @@ +package problem4 + +import "testing" + +// Tests +func TestProblem4_Func(t *testing.T) { + tests := []struct { + name string + want uint + }{ + { + name: "Testcase 1", + want: 906609, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem4() + + if n != tt.want { + t.Errorf("Problem4() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem4(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem4() + } +} diff --git a/project_euler/problem_5/problem5.go b/project_euler/problem_5/problem5.go new file mode 100644 index 000000000..dad415738 --- /dev/null +++ b/project_euler/problem_5/problem5.go @@ -0,0 +1,33 @@ +/** +* Problem 5 - Smallest multiple +* @see {@link https://projecteuler.net/problem=5} +* +* 2520 is the smallest number that can be divided by +* each of the numbers from 1 to 10 without any remainder. +* What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20? +* +* @author ddaniel27 + */ +package problem5 + +func Problem5(limit uint) uint { + n := limit * limit + + for { + if isDivisible(n, limit) { + return n + } + + n++ + } +} + +func isDivisible(n, limit uint) bool { + for i := uint(1); i <= limit; i++ { + if n%i != 0 { + return false + } + } + + return true +} diff --git a/project_euler/problem_5/problem5_test.go b/project_euler/problem_5/problem5_test.go new file mode 100644 index 000000000..43e7d8ec9 --- /dev/null +++ b/project_euler/problem_5/problem5_test.go @@ -0,0 +1,45 @@ +package problem5 + +import "testing" + +// Tests +func TestProblem5_Func(t *testing.T) { + tests := []struct { + name string + input uint + want uint + }{ + { + name: "Testcase 1 - input 10", + input: 10, + want: 2520, + }, + { + name: "Testcase 2 - input 20", + input: 20, + want: 232792560, + }, + { + name: "Testcase 3 - input 5", + input: 5, + want: 60, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem5(tt.input) + + if n != tt.want { + t.Errorf("Problem5() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem5(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem5(20) + } +} diff --git a/project_euler/problem_6/problem6.go b/project_euler/problem_6/problem6.go new file mode 100644 index 000000000..83287b87d --- /dev/null +++ b/project_euler/problem_6/problem6.go @@ -0,0 +1,33 @@ +/** +* Problem 6 - Sum square difference +* @see {@link https://projecteuler.net/problem=6} +* +* The sum of the squares of the first ten natural numbers is, +* 1^2 + 2^2 + ... + 10^2 = 385 +* +* The square of the sum of the first ten natural numbers is, +* (1 + 2 + ... + 10)^2 = 55^2 = 3025 +* +* Hence the difference between the sum of the squares of the first ten natural numbers +* and the square of the sum is 3025 − 385 = 2640. +* +* Find the difference between the sum of the squares of the first one hundred natural numbers +* and the square of the sum. +* +* @author ddaniel27 + */ +package problem6 + +func Problem6(n uint) uint { + sumOfSquares := uint(0) + squareOfSum := uint(0) + + for i := uint(1); i <= n; i++ { + sumOfSquares += i * i + squareOfSum += i + } + + squareOfSum *= squareOfSum + + return squareOfSum - sumOfSquares +} diff --git a/project_euler/problem_6/problem6_test.go b/project_euler/problem_6/problem6_test.go new file mode 100644 index 000000000..afa4e5fb7 --- /dev/null +++ b/project_euler/problem_6/problem6_test.go @@ -0,0 +1,40 @@ +package problem6 + +import "testing" + +// Tests +func TestProblem6_Func(t *testing.T) { + tests := []struct { + name string + input uint + want uint + }{ + { + name: "Testcase 1 - input 10", + input: 10, + want: 2640, + }, + { + name: "Testcase 2 - input 100", + input: 100, + want: 25164150, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem6(tt.input) + + if n != tt.want { + t.Errorf("Problem6() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem6(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem6(100) + } +} diff --git a/project_euler/problem_7/problem7.go b/project_euler/problem_7/problem7.go new file mode 100644 index 000000000..481844fed --- /dev/null +++ b/project_euler/problem_7/problem7.go @@ -0,0 +1,27 @@ +/** +* Problem 7 - 10001st prime +* @see {@link https://projecteuler.net/problem=7} +* +* By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, +* we can see that the 6th prime is 13. +* +* What is the 10 001st prime number? +* +* @author ddaniel27 + */ +package problem7 + +import "github.com/TheAlgorithms/Go/math/prime" + +func Problem7(n uint) int64 { + count, i := uint(0), int64(1) + + for count < n { + i++ + if prime.OptimizedTrialDivision(i) { + count++ + } + } + + return i +} diff --git a/project_euler/problem_7/problem7_test.go b/project_euler/problem_7/problem7_test.go new file mode 100644 index 000000000..d2ab03e74 --- /dev/null +++ b/project_euler/problem_7/problem7_test.go @@ -0,0 +1,40 @@ +package problem7 + +import "testing" + +// Tests +func TestProblem7_Func(t *testing.T) { + tests := []struct { + name string + input uint + want int64 + }{ + { + name: "Testcase 1 - input 6", + input: 6, + want: 13, + }, + { + name: "Testcase 2 - input 10001", + input: 10001, + want: 104743, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem7(tt.input) + + if n != tt.want { + t.Errorf("Problem7() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem7(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem7(10001) + } +} diff --git a/project_euler/problem_8/problem8.go b/project_euler/problem_8/problem8.go new file mode 100644 index 000000000..0c800dcdb --- /dev/null +++ b/project_euler/problem_8/problem8.go @@ -0,0 +1,33 @@ +/** +* Problem 8 - Largest product in a series +* @see {@link https://projecteuler.net/problem=8} +* +* The four adjacent digits in the 1000-digit number that +* have the greatest product are 9 × 9 × 8 × 9 = 5832. +* Find the thirteen adjacent digits in the 1000-digit number +* that have the greatest product. What is the value of this product? +* +* @author ddaniel27 + */ +package problem8 + +const number = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450" + +func Problem8(window int) uint { + max := uint(0) + + for i := 0; i < len(number)-window; i++ { + product := uint(1) + + for j := 0; j < window; j++ { + n := uint(number[i+j] - '0') + product *= n + } + + if product > max { + max = product + } + } + + return max +} diff --git a/project_euler/problem_8/problem8_test.go b/project_euler/problem_8/problem8_test.go new file mode 100644 index 000000000..eecde4bc6 --- /dev/null +++ b/project_euler/problem_8/problem8_test.go @@ -0,0 +1,40 @@ +package problem8 + +import "testing" + +// Tests +func TestProblem8_Func(t *testing.T) { + tests := []struct { + name string + input int + want uint + }{ + { + name: "Testcase 1 - input 4", + input: 4, + want: 5832, + }, + { + name: "Testcase 2 - input 13", + input: 13, + want: 23514624000, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem8(tt.input) + + if n != tt.want { + t.Errorf("Problem8() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem8(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem8(13) + } +} diff --git a/project_euler/problem_9/problem9.go b/project_euler/problem_9/problem9.go new file mode 100644 index 000000000..0f784c022 --- /dev/null +++ b/project_euler/problem_9/problem9.go @@ -0,0 +1,29 @@ +/** +* Problem 9 - Special Pythagorean triplet +* @see {@link https://projecteuler.net/problem=9} +* +* A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, +* a^2 + b^2 = c^2 +* +* For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. +* +* There exists exactly one Pythagorean triplet for which a + b + c = 1000. +* Find the product abc. +* +* @author ddaniel27 + */ +package problem9 + +func Problem9() uint { + for a := uint(1); a < 1000; a++ { + for b := a + 1; b < 1000; b++ { + c := 1000 - a - b + + if a*a+b*b == c*c { + return a * b * c + } + } + } + + return 0 +} diff --git a/project_euler/problem_9/problem9_test.go b/project_euler/problem_9/problem9_test.go new file mode 100644 index 000000000..d75226103 --- /dev/null +++ b/project_euler/problem_9/problem9_test.go @@ -0,0 +1,33 @@ +package problem9 + +import "testing" + +// Tests +func TestProblem9_Func(t *testing.T) { + tests := []struct { + name string + want uint + }{ + { + name: "Testcase 1", + want: 31875000, + }, + } + + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + n := Problem9() + + if n != tt.want { + t.Errorf("Problem9() = %v, want %v", n, tt.want) + } + }) + } +} + +// Benchmarks +func BenchmarkProblem9(b *testing.B) { + for i := 0; i < b.N; i++ { + _ = Problem9() + } +} diff --git a/search/binary.go b/search/binary.go new file mode 100644 index 000000000..604341edb --- /dev/null +++ b/search/binary.go @@ -0,0 +1,82 @@ +package search + +// Binary search for target within a sorted array by repeatedly dividing the array in half and comparing the midpoint with the target. +// This function uses recursive call to itself. +// If a target is found, the index of the target is returned. Else the function return -1 and ErrNotFound. +func Binary(array []int, target int, lowIndex int, highIndex int) (int, error) { + if highIndex < lowIndex || len(array) == 0 { + return -1, ErrNotFound + } + mid := int(lowIndex + (highIndex-lowIndex)/2) + if array[mid] > target { + return Binary(array, target, lowIndex, mid-1) + } else if array[mid] < target { + return Binary(array, target, mid+1, highIndex) + } else { + return mid, nil + } +} + +// BinaryIterative search for target within a sorted array by repeatedly dividing the array in half and comparing the midpoint with the target. +// Unlike Binary, this function uses iterative method and not recursive. +// If a target is found, the index of the target is returned. Else the function return -1 and ErrNotFound. +func BinaryIterative(array []int, target int) (int, error) { + startIndex := 0 + endIndex := len(array) - 1 + var mid int + for startIndex <= endIndex { + mid = int(startIndex + (endIndex-startIndex)/2) + if array[mid] > target { + endIndex = mid - 1 + } else if array[mid] < target { + startIndex = mid + 1 + } else { + return mid, nil + } + } + return -1, ErrNotFound +} + +// LowerBound returns index to the first element in the range [0, len(array)-1] that is not less than (i.e. greater or equal to) target. +// return -1 and ErrNotFound if no such element is found. +func LowerBound(array []int, target int) (int, error) { + startIndex := 0 + endIndex := len(array) - 1 + var mid int + for startIndex <= endIndex { + mid = int(startIndex + (endIndex-startIndex)/2) + if array[mid] < target { + startIndex = mid + 1 + } else { + endIndex = mid - 1 + } + } + + //when target greater than every element in array, startIndex will out of bounds + if startIndex >= len(array) { + return -1, ErrNotFound + } + return startIndex, nil +} + +// UpperBound returns index to the first element in the range [lowIndex, len(array)-1] that is greater than target. +// return -1 and ErrNotFound if no such element is found. +func UpperBound(array []int, target int) (int, error) { + startIndex := 0 + endIndex := len(array) - 1 + var mid int + for startIndex <= endIndex { + mid = int(startIndex + (endIndex-startIndex)/2) + if array[mid] > target { + endIndex = mid - 1 + } else { + startIndex = mid + 1 + } + } + + //when target greater or equal than every element in array, startIndex will out of bounds + if startIndex >= len(array) { + return -1, ErrNotFound + } + return startIndex, nil +} diff --git a/search/binary_test.go b/search/binary_test.go new file mode 100644 index 000000000..99f907797 --- /dev/null +++ b/search/binary_test.go @@ -0,0 +1,86 @@ +package search + +import ( + "errors" + "testing" +) + +func TestBinary(t *testing.T) { + for _, test := range searchTests { + actualValue, actualError := Binary(test.data, test.key, 0, len(test.data)-1) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if !errors.Is(test.expectedError, actualError) { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func TestBinaryIterative(t *testing.T) { + for _, test := range searchTests { + actualValue, actualError := BinaryIterative(test.data, test.key) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if !errors.Is(test.expectedError, actualError) { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func TestLowerBound(t *testing.T) { + for _, test := range lowerBoundTests { + actualValue, actualError := LowerBound(test.data, test.key) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if !errors.Is(test.expectedError, actualError) { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func TestUpperBound(t *testing.T) { + for _, test := range upperBoundTests { + actualValue, actualError := UpperBound(test.data, test.key) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if !errors.Is(test.expectedError, actualError) { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func BenchmarkBinary(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // this is important because the generateBenchmarkTestCase() is expensive + for i := 0; i < b.N; i++ { + _, _ = Binary(testCase, i, 0, len(testCase)-1) + } +} + +func BenchmarkBinaryIterative(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // this is important because the generateBenchmarkTestCase() is expensive + for i := 0; i < b.N; i++ { + _, _ = BinaryIterative(testCase, i) + } +} + +func BenchmarkLowerBound(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // this is important because the generateBenchmarkTestCase() is expensive + for i := 0; i < b.N; i++ { + _, _ = LowerBound(testCase, i) + } +} + +func BenchmarkUpperBound(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // this is important because the generateBenchmarkTestCase() is expensive + for i := 0; i < b.N; i++ { + _, _ = UpperBound(testCase, i) + } +} diff --git a/search/doc.go b/search/doc.go new file mode 100644 index 000000000..4c71e36b4 --- /dev/null +++ b/search/doc.go @@ -0,0 +1,2 @@ +// Package search is a subpackage dedicated to all searching algorithms related to slices/arrays. +package search diff --git a/search/errors.go b/search/errors.go new file mode 100644 index 000000000..831073599 --- /dev/null +++ b/search/errors.go @@ -0,0 +1,6 @@ +package search + +import "errors" + +// ErrNotFound is returned by search functions when target is not found +var ErrNotFound = errors.New("target not found in array") diff --git a/search/interpolation.go b/search/interpolation.go new file mode 100644 index 000000000..722d77e2a --- /dev/null +++ b/search/interpolation.go @@ -0,0 +1,51 @@ +package search + +// Interpolation searches for the entity in the given sortedData. +// if the entity is present, it will return the index of the entity, if not -1 will be returned. +// see: https://en.wikipedia.org/wiki/Interpolation_search +// Complexity +// +// Worst: O(N) +// Average: O(log(log(N)) if the elements are uniformly distributed +// Best: O(1) +// +// Example +// +// fmt.Println(InterpolationSearch([]int{1, 2, 9, 20, 31, 45, 63, 70, 100},100)) +func Interpolation(sortedData []int, guess int) (int, error) { + if len(sortedData) == 0 { + return -1, ErrNotFound + } + + var ( + low, high = 0, len(sortedData) - 1 + lowVal, highVal = sortedData[low], sortedData[high] + ) + + for lowVal != highVal && (lowVal <= guess) && (guess <= highVal) { + mid := low + int(float64(float64((guess-lowVal)*(high-low))/float64(highVal-lowVal))) + + // if guess is found, array can also have duplicate values, so scan backwards and find the first index + if sortedData[mid] == guess { + for mid > 0 && sortedData[mid-1] == guess { + mid-- + } + return mid, nil + + } + + // adjust our guess and continue + if sortedData[mid] > guess { + high, highVal = mid-1, sortedData[high] + + } else { + low, lowVal = mid+1, sortedData[low] + } + + } + + if guess == lowVal { + return low, nil + } + return -1, ErrNotFound +} diff --git a/search/interpolation_test.go b/search/interpolation_test.go new file mode 100644 index 000000000..b59cf1847 --- /dev/null +++ b/search/interpolation_test.go @@ -0,0 +1,23 @@ +package search + +import "testing" + +func TestInterpolation(t *testing.T) { + for _, test := range searchTests { + actualValue, actualError := Interpolation(test.data, test.key) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if actualError != test.expectedError { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func BenchmarkInterpolation(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // exclude time taken to generate test case + for i := 0; i < b.N; i++ { + _, _ = Interpolation(testCase, i) + } +} diff --git a/search/jump.go b/search/jump.go new file mode 100644 index 000000000..169620d9a --- /dev/null +++ b/search/jump.go @@ -0,0 +1,57 @@ +// jump.go +// description: Implementation of jump search +// details: +// A search algorithm for ordered list that jump through the list to narrow down the range +// before performing a linear search +// reference: https://en.wikipedia.org/wiki/Jump_search +// see jump_test.go for a test implementation, test function TestJump +// time complexity: O(sqrt(n)) +// space complexity: O(1) + +package search + +import "math" + +// Jump search works by jumping multiple steps ahead in sorted list until it find an item larger than target, +// then create a sublist of item from the last searched item up to the current item and perform a linear search. +func Jump(array []int, target int) (int, error) { + n := len(array) + if n == 0 { + return -1, ErrNotFound + } + + // the optimal value of step is square root of the length of list + step := int(math.Round(math.Sqrt(float64(n)))) + + prev := 0 // previous index + curr := step // current index + for array[curr-1] < target { + prev = curr + if prev >= len(array) { + return -1, ErrNotFound + } + + curr += step + + // prevent jumping over list range + if curr > n { + curr = n + } + } + + // perform linear search from index prev to index curr + for array[prev] < target { + prev++ + + // if reach end of range, indicate target not found + if prev == curr { + return -1, ErrNotFound + } + } + if array[prev] == target { + return prev, nil + } + + return -1, ErrNotFound + +} diff --git a/search/jump2.go b/search/jump2.go new file mode 100644 index 000000000..ca16a94fb --- /dev/null +++ b/search/jump2.go @@ -0,0 +1,24 @@ +package search + +import "math" + +func Jump2(arr []int, target int) (int, error) { + step := int(math.Round(math.Sqrt(float64(len(arr))))) + rbound := len(arr) + for i := step; i < len(arr); i += step { + if arr[i] > target { + rbound = i + break + } + } + + for i := rbound - step; i < rbound; i++ { + if arr[i] == target { + return i, nil + } + if arr[i] > target { + break + } + } + return -1, ErrNotFound +} diff --git a/search/jump2_test.go b/search/jump2_test.go new file mode 100644 index 000000000..fc2cdb4af --- /dev/null +++ b/search/jump2_test.go @@ -0,0 +1,23 @@ +package search + +import "testing" + +func TestJump2(t *testing.T) { + for _, test := range searchTests { + actualValue, actualError := Jump2(test.data, test.key) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if actualError != test.expectedError { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func BenchmarkJump2(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // exclude time taken to generate test case + for i := 0; i < b.N; i++ { + _, _ = Jump2(testCase, i) + } +} diff --git a/search/jump_test.go b/search/jump_test.go new file mode 100644 index 000000000..4c27df4f6 --- /dev/null +++ b/search/jump_test.go @@ -0,0 +1,23 @@ +package search + +import "testing" + +func TestJump(t *testing.T) { + for _, test := range searchTests { + actualValue, actualError := Jump(test.data, test.key) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if actualError != test.expectedError { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func BenchmarkJump(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // exclude time taken to generate test case + for i := 0; i < b.N; i++ { + _, _ = Jump(testCase, i) + } +} diff --git a/search/linear.go b/search/linear.go new file mode 100644 index 000000000..4cc360793 --- /dev/null +++ b/search/linear.go @@ -0,0 +1,11 @@ +package search + +// Linear Simple linear search algorithm that iterates over all elements of an array in the worst case scenario +func Linear(array []int, query int) (int, error) { + for i, item := range array { + if item == query { + return i, nil + } + } + return -1, ErrNotFound +} diff --git a/search/linear_test.go b/search/linear_test.go new file mode 100644 index 000000000..36c1f9b49 --- /dev/null +++ b/search/linear_test.go @@ -0,0 +1,25 @@ +package search + +import ( + "testing" +) + +func TestLinear(t *testing.T) { + for _, test := range searchTests { + actualValue, actualError := Linear(test.data, test.key) + if actualValue != test.expected { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected '%d', get '%d'", test.name, test.data, test.key, test.expected, actualValue) + } + if actualError != test.expectedError { + t.Errorf("test '%s' failed: input array '%v' with key '%d', expected error '%s', get error '%s'", test.name, test.data, test.key, test.expectedError, actualError) + } + } +} + +func BenchmarkLinear(b *testing.B) { + testCase := generateBenchmarkTestCase() + b.ResetTimer() // exclude time taken to generate test case + for i := 0; i < b.N; i++ { + _, _ = Linear(testCase, i) + } +} diff --git a/search/selectk.go b/search/selectk.go new file mode 100644 index 000000000..bb81937b4 --- /dev/null +++ b/search/selectk.go @@ -0,0 +1,32 @@ +package search + +func SelectK(array []int, k int) (int, error) { + if k > len(array) { + return -1, ErrNotFound + } + return selectK(array, 0, len(array), len(array)-k), nil +} + +// search the element which index is idx +func selectK(array []int, l, r, idx int) int { + index := partition(array, l, r) + if index == idx { + return array[index] + } + if index < idx { + return selectK(array, index+1, r, idx) + } + return selectK(array, l, index, idx) +} + +func partition(array []int, l, r int) int { + elem, j := array[l], l+1 + for i := l + 1; i < r; i++ { + if array[i] <= elem { + array[i], array[j] = array[j], array[i] + j++ + } + } + array[l], array[j-1] = array[j-1], array[l] + return j - 1 +} diff --git a/search/selectk_test.go b/search/selectk_test.go new file mode 100644 index 000000000..bf81fb9d1 --- /dev/null +++ b/search/selectk_test.go @@ -0,0 +1,41 @@ +package search + +import ( + "testing" +) + +func TestSelectK(t *testing.T) { + tests := []struct { + data []int + k int + expected int + err error + name string + }{ + {[]int{1, 2, 3, 4, 5}, 1, 5, nil, "sorted data"}, + {[]int{5, 4, 3, 2, 1}, 2, 4, nil, "reversed data"}, + {[]int{3, 1, 2, 5, 4}, 3, 3, nil, "random data"}, + {[]int{3, 2, 1, 5, 4}, 10, -1, ErrNotFound, " absent data"}, + } + for _, tc := range tests { + t.Run(tc.name, func(t *testing.T) { + elem, err := SelectK(tc.data, tc.k) + if err != tc.err { + t.Errorf("name:%v SelectK() = _, %v, want err: %v", tc.name, err, tc.err) + } + if elem != tc.expected { + t.Errorf("name:%v SelectK() = %v,_ , want: %v", tc.name, elem, tc.expected) + } + }) + } +} + +func BenchmarkSelectK(b *testing.B) { + testCase := generateBenchmarkTestCase() + testCase = append(testCase, 1) // make sure len(testCase)/2+1 is valid + b.ResetTimer() + + for i := 0; i < b.N; i++ { + _, _ = SelectK(testCase, len(testCase)/2) + } +} diff --git a/search/ternary.go b/search/ternary.go new file mode 100644 index 000000000..1e594f8d7 --- /dev/null +++ b/search/ternary.go @@ -0,0 +1,40 @@ +package search + +import ( + "fmt" + "math" +) + +// TernaryMax is a function to search for maximum value of a uni-modal function `f` +// in the interval [a, b]. a and b should be finit numbers +func TernaryMax(a, b, epsilon float64, f func(x float64) float64) (float64, error) { + if a == math.Inf(-1) || b == math.Inf(1) { + return -1, fmt.Errorf("interval boundaries should be finite numbers") + } + if math.Abs(a-b) <= epsilon { + return f((a + b) / 2), nil + } + left := (2*a + b) / 3 + right := (a + 2*b) / 3 + if f(left) < f(right) { + return TernaryMax(left, b, epsilon, f) + } + return TernaryMax(a, right, epsilon, f) +} + +// TernaryMin is a function to search for minimum value of a uni-modal function `f` +// in the interval [a, b]. a and b should be finit numbers. +func TernaryMin(a, b, epsilon float64, f func(x float64) float64) (float64, error) { + if a == math.Inf(-1) || b == math.Inf(1) { + return -1, fmt.Errorf("interval boundaries should be finite numbers") + } + if math.Abs(a-b) <= epsilon { + return f((a + b) / 2), nil + } + left := (2*a + b) / 3 + right := (a + 2*b) / 3 + if f(left) > f(right) { + return TernaryMin(left, b, epsilon, f) + } + return TernaryMin(a, right, epsilon, f) +} diff --git a/search/ternary_test.go b/search/ternary_test.go new file mode 100644 index 000000000..eb89c161a --- /dev/null +++ b/search/ternary_test.go @@ -0,0 +1,56 @@ +package search + +import ( + "math" + "testing" +) + +const EPS = 1e-6 + +func equal(a, b float64) bool { + return math.Abs(a-b) <= EPS +} + +func TestTernaryMax(t *testing.T) { + + var tests = []struct { + f func(x float64) float64 + a float64 + b float64 + expected float64 + }{ + {f: func(x float64) float64 { return -x * x }, a: 1, b: -1, expected: 0}, + {f: func(x float64) float64 { return -2*x*x - x + 1 }, a: -1, b: 1, expected: 1.125}, + } + for _, test := range tests { + result, err := TernaryMax(test.a, test.b, EPS, test.f) + if err != nil { + t.Errorf("error occurred: %v", err) + } + if !equal(result, test.expected) { + t.Errorf("Wrong result! Expected:%v, returned:%v ", test.expected, result) + } + } +} + +func TestTernaryMin(t *testing.T) { + + var tests = []struct { + f func(x float64) float64 + a float64 + b float64 + expected float64 + }{ + {f: func(x float64) float64 { return x * x }, a: -1, b: 1, expected: 0}, + {f: func(x float64) float64 { return 2*x*x + x + 1 }, a: -1, b: 1, expected: 0.875}, + } + for _, test := range tests { + result, err := TernaryMin(test.a, test.b, EPS, test.f) + if err != nil { + t.Errorf("error occurred: %v", err) + } + if !equal(result, test.expected) { + t.Errorf("Wrong result! Expected:%v, returned:%v ", test.expected, result) + } + } +} diff --git a/search/testcases.go b/search/testcases.go new file mode 100644 index 000000000..0ef2f5cb3 --- /dev/null +++ b/search/testcases.go @@ -0,0 +1,67 @@ +package search + +type searchTest struct { + data []int + key int + expected int + expectedError error + name string +} + +// Note that these are immutable therefore they are shared among all the search tests. +// If your algorithm is mutating these then it is advisable to create separate test cases. +var searchTests = []searchTest{ + //Sanity + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 10, 9, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 9, 8, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 8, 7, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 7, 6, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 6, 5, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 5, 4, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 4, 3, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 3, 2, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 2, 1, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 1, 0, nil, "Sanity"}, + //Absent + {[]int{1, 4, 5, 6, 7, 10}, -25, -1, ErrNotFound, "Absent"}, + {[]int{1, 4, 5, 6, 7, 10}, 25, -1, ErrNotFound, "Absent"}, + //Empty slice + {[]int{}, 2, -1, ErrNotFound, "Empty"}, +} + +var lowerBoundTests = []searchTest{ + //Sanity + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, -25, 0, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 1, 0, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 5, 4, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 10, 9, nil, "Sanity"}, + {[]int{1, 2, 2, 2, 2, 6, 7, 8, 9, 10}, 2, 1, nil, "Sanity"}, + {[]int{2, 2, 2, 2, 2, 2, 2, 2, 2, 2}, 2, 0, nil, "Sanity"}, + //Absent + {[]int{1, 4, 5, 6, 7, 10}, 25, -1, ErrNotFound, "Absent"}, + //Empty slice + {[]int{}, 2, -1, ErrNotFound, "Empty"}, +} + +var upperBoundTests = []searchTest{ + //Sanity + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, -25, 0, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 1, 1, nil, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 5, 5, nil, "Sanity"}, + {[]int{1, 2, 2, 2, 2, 6, 7, 8, 9, 10}, 2, 5, nil, "Sanity"}, + //Absent + {[]int{2, 2, 2, 2, 2, 2, 2, 2, 2, 2}, 2, -1, ErrNotFound, "Sanity"}, + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, 10, -1, ErrNotFound, "Sanity"}, + {[]int{1, 4, 5, 6, 7, 10}, 25, -1, ErrNotFound, "Absent"}, + //Empty slice + {[]int{}, 2, -1, ErrNotFound, "Empty"}, +} + +// This function generate consistent testcase for benchmark test. +func generateBenchmarkTestCase() []int { + var testCase []int + for i := 0; i < 1000; i++ { + testCase = append(testCase, i) + } + return testCase +} diff --git a/searches/binary_search.go b/searches/binary_search.go deleted file mode 100644 index 697b6704b..000000000 --- a/searches/binary_search.go +++ /dev/null @@ -1,35 +0,0 @@ -/* - Binary search implementation in Go -*/ -package main - -func binarySearch(array []int, target int, lowIndex int, highIndex int) int { - if highIndex < lowIndex { - return -1 - } - mid := int((lowIndex + highIndex) / 2) - if array[mid] > target { - return binarySearch(array, target, lowIndex, mid) - } else if array[mid] < target { - return binarySearch(array, target, mid+1, highIndex) - } else { - return mid - } -} - -func iterBinarySearch(array []int, target int, lowIndex int, highIndex int) int { - startIndex := lowIndex - endIndex := highIndex - var mid int - for startIndex < endIndex { - mid = int((startIndex + endIndex) / 2) - if array[mid] > target { - endIndex = mid - } else if array[mid] < target { - startIndex = mid - } else { - return mid - } - } - return -1 -} diff --git a/searches/linear_search.go b/searches/linear_search.go deleted file mode 100644 index d21e79f06..000000000 --- a/searches/linear_search.go +++ /dev/null @@ -1,25 +0,0 @@ -package main - -import "fmt" - -func linearSearch(array []int, query int) int { - for i, item := range array { - if item == query { - return i - } - } - return -1 -} - -func main() { - - fmt.Println("Linear search:") - array := []int{0, 2, 4, 6, 8, 10, 12, 14, 16, 18} - index := linearSearch(array, 10) - if index == -1 { - fmt.Println("Number not found") - } else { - fmt.Println("Index: ", index) - fmt.Println("array[", index, "] = ", array[index]) - } -} diff --git a/sort/binaryinsertionsort.go b/sort/binaryinsertionsort.go new file mode 100644 index 000000000..98b6c5a3d --- /dev/null +++ b/sort/binaryinsertionsort.go @@ -0,0 +1,35 @@ +// Binary Insertion Sort +// description: Implementation of binary insertion sort in Go +// details: Binary Insertion Sort is a variation of +// Insertion sort in which proper location to +// insert the selected element is found using the +// Binary search algorithm. +// ref: https://www.geeksforgeeks.org/binary-insertion-sort + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func BinaryInsertion[T constraints.Ordered](arr []T) []T { + for currentIndex := 1; currentIndex < len(arr); currentIndex++ { + temporary := arr[currentIndex] + low := 0 + high := currentIndex - 1 + + for low <= high { + mid := low + (high-low)/2 + if arr[mid] > temporary { + high = mid - 1 + } else { + low = mid + 1 + } + } + + for itr := currentIndex; itr > low; itr-- { + arr[itr] = arr[itr-1] + } + + arr[low] = temporary + } + return arr +} diff --git a/sort/bogosort.go b/sort/bogosort.go new file mode 100644 index 000000000..165397155 --- /dev/null +++ b/sort/bogosort.go @@ -0,0 +1,39 @@ +// This is a pure Go implementation of the bogosort algorithm, +// also known as permutation sort, stupid sort, slowsort, shotgun sort, or monkey sort. +// Bogosort generates random permutations until it guesses the correct one. +// worst-case time complexity: O((n+1)!) +// best-case time complexity: O(n) +// More info on: https://en.wikipedia.org/wiki/Bogosort + +package sort + +import ( + "math/rand" + + "github.com/TheAlgorithms/Go/constraints" +) + +func isSorted[T constraints.Number](arr []T) bool { + for i := 0; i < len(arr)-1; i++ { + if arr[i] > arr[i+1] { + return false + } + } + + return true +} + +func shuffle[T constraints.Number](arr []T) { + for i := range arr { + j := rand.Intn(i + 1) + arr[i], arr[j] = arr[j], arr[i] + } +} + +func Bogo[T constraints.Number](arr []T) []T { + for !isSorted(arr) { + shuffle(arr) + } + + return arr +} diff --git a/sort/bubblesort.go b/sort/bubblesort.go new file mode 100644 index 000000000..4c40678b7 --- /dev/null +++ b/sort/bubblesort.go @@ -0,0 +1,21 @@ +// Implementation of basic bubble sort algorithm +// Reference: https://en.wikipedia.org/wiki/Bubble_sort + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +// Bubble is a simple generic definition of Bubble sort algorithm. +func Bubble[T constraints.Ordered](arr []T) []T { + swapped := true + for swapped { + swapped = false + for i := 0; i < len(arr)-1; i++ { + if arr[i+1] < arr[i] { + arr[i+1], arr[i] = arr[i], arr[i+1] + swapped = true + } + } + } + return arr +} diff --git a/sort/bucketsort.go b/sort/bucketsort.go new file mode 100644 index 000000000..3f05a41a4 --- /dev/null +++ b/sort/bucketsort.go @@ -0,0 +1,46 @@ +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +// Bucket sorts a slice. It is mainly useful +// when input is uniformly distributed over a range. +func Bucket[T constraints.Number](arr []T) []T { + // early return if the array too small + if len(arr) <= 1 { + return arr + } + + // find the maximum and minimum elements in arr + max := arr[0] + min := arr[0] + for _, v := range arr { + if v > max { + max = v + } + if v < min { + min = v + } + } + + // create an empty bucket for each element in arr + bucket := make([][]T, len(arr)) + + // put each element in the appropriate bucket + for _, v := range arr { + bucketIndex := int((v - min) / (max - min) * T(len(arr)-1)) + bucket[bucketIndex] = append(bucket[bucketIndex], v) + } + + // use insertion sort to sort each bucket + for i := range bucket { + bucket[i] = Insertion(bucket[i]) + } + + // concatenate the sorted buckets + sorted := make([]T, 0, len(arr)) + for _, v := range bucket { + sorted = append(sorted, v...) + } + + return sorted +} diff --git a/sort/circlesort.go b/sort/circlesort.go new file mode 100644 index 000000000..c18b0d408 --- /dev/null +++ b/sort/circlesort.go @@ -0,0 +1,44 @@ +// Package sort implements various sorting algorithms. +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +// Circle sorts an array using the circle sort algorithm. +func Circle[T constraints.Ordered](arr []T) []T { + if len(arr) == 0 { + return arr + } + for doSort(arr, 0, len(arr)-1) { + } + return arr +} + +// doSort is the recursive function that implements the circle sort algorithm. +func doSort[T constraints.Ordered](arr []T, left, right int) bool { + if left == right { + return false + } + swapped := false + low := left + high := right + + for low < high { + if arr[low] > arr[high] { + arr[low], arr[high] = arr[high], arr[low] + swapped = true + } + low++ + high-- + } + + if low == high && arr[low] > arr[high+1] { + arr[low], arr[high+1] = arr[high+1], arr[low] + swapped = true + } + + mid := left + (right-left)/2 + leftHalf := doSort(arr, left, mid) + rightHalf := doSort(arr, mid+1, right) + + return swapped || leftHalf || rightHalf +} diff --git a/sort/cocktailsort.go b/sort/cocktailsort.go new file mode 100644 index 000000000..6aee61681 --- /dev/null +++ b/sort/cocktailsort.go @@ -0,0 +1,54 @@ +// Implementation of Cocktail sorting +// reference: https://en.wikipedia.org/wiki/Cocktail_shaker_sort + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +// Cocktail sort is a variation of bubble sort, operating in two directions (beginning to end, end to beginning) +func Cocktail[T constraints.Ordered](arr []T) []T { + if len(arr) == 0 { // ignore 0 length arrays + return arr + } + + swapped := true // true if swapped two or more elements in the last loop + // if it loops through the array without swapping, the array is sorted + + // start and end indexes, this will be updated excluding already sorted elements + start := 0 + end := len(arr) - 1 + + for swapped { + swapped = false + var new_start int + var new_end int + + for i := start; i < end; i++ { // first loop, from start to end + if arr[i] > arr[i+1] { // if current and next elements are unordered + arr[i], arr[i+1] = arr[i+1], arr[i] // swap two elements + new_end = i + swapped = true + } + } + + end = new_end + + if !swapped { // early exit, skipping the second loop + break + } + + swapped = false + + for i := end; i > start; i-- { // second loop, from end to start + if arr[i] < arr[i-1] { // same process of the first loop, now going 'backwards' + arr[i], arr[i-1] = arr[i-1], arr[i] + new_start = i + swapped = true + } + } + + start = new_start + } + + return arr +} diff --git a/sort/combSort.go b/sort/combSort.go new file mode 100644 index 000000000..15c3e8bab --- /dev/null +++ b/sort/combSort.go @@ -0,0 +1,36 @@ +// Implementation of comb sort algorithm, an improvement of bubble sort +// average time complexity: O(n^2 / 2^p) where p is the number of increments +// worst time complexity: O(n^2) +// space complexity: O(1) +// Reference: https://www.geeksforgeeks.org/comb-sort/ + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func getNextGap(gap int) int { + gap = (gap * 10) / 13 + if gap < 1 { + return 1 + } + return gap +} + +// Comb is a simple sorting algorithm which is an improvement of the bubble sorting algorithm. +func Comb[T constraints.Ordered](data []T) []T { + n := len(data) + gap := n + swapped := true + + for gap != 1 || swapped { + gap = getNextGap(gap) + swapped = false + for i := 0; i < n-gap; i++ { + if data[i] > data[i+gap] { + data[i], data[i+gap] = data[i+gap], data[i] + swapped = true + } + } + } + return data +} diff --git a/sort/countingsort.go b/sort/countingsort.go new file mode 100644 index 000000000..55fbac7c0 --- /dev/null +++ b/sort/countingsort.go @@ -0,0 +1,40 @@ +// countingsort.go +// description: Implementation of counting sort algorithm +// details: A simple counting sort algorithm implementation +// worst-case time complexity: O(n + k) where n is the number of elements in the input array and k is the range of the input +// average-case time complexity: O(n + k) where n is the number of elements in the input array and k is the range of the input +// space complexity: O(n + k) +// author [Phil](https://github.com/pschik) +// see sort_test.go for a test implementation, test function TestQuickSort + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func Count[T constraints.Integer](data []T) []T { + if len(data) == 0 { + return data + } + var aMin, aMax = data[0], data[0] + for _, x := range data { + if x < aMin { + aMin = x + } + if x > aMax { + aMax = x + } + } + count := make([]int, aMax-aMin+1) + for _, x := range data { + count[x-aMin]++ // this is the reason for having only Integer constraint instead of Ordered. + } + z := 0 + for i, c := range count { + for c > 0 { + data[z] = T(i) + aMin + z++ + c-- + } + } + return data +} diff --git a/sort/cyclesort.go b/sort/cyclesort.go new file mode 100644 index 000000000..611fe27c2 --- /dev/null +++ b/sort/cyclesort.go @@ -0,0 +1,58 @@ +package sort + +import ( + "github.com/TheAlgorithms/Go/constraints" +) + +// Cycle sort is an in-place, unstable sorting algorithm that is particularly useful +// when sorting arrays containing elements with a small range of values. It is theoretically +// optimal in terms of the total number of writes to the original array. +func Cycle[T constraints.Number](arr []T) []T { + counter, cycle, len := 0, 0, len(arr) + // Early return if the array too small + if len <= 1 { + return arr + } + + for cycle = 0; cycle < len-1; cycle++ { + elem := arr[cycle] + // Find total smaller elements to right + pos := cycle + for counter = cycle + 1; counter < len; counter++ { + if arr[counter] < elem { + pos++ + } + } + // In case this element is already in correct position, let's skip processing + if pos == cycle { + continue + } + // In case we have same elements, we want to skip to the end of that list as well, ignoring order + // This makes the algorithm unstable for composite elements + for elem == arr[pos] { + pos++ + } + // Now let us put the item to it's right position + arr[pos], elem = elem, arr[pos] + + //We need to rotate the array till we have reached the start of the cycle again + for pos != cycle { + pos = cycle + // Find smaller elements to right again + for counter = cycle + 1; counter < len; counter++ { + if arr[counter] < elem { + pos++ + } + } + for elem == arr[pos] { + pos++ + } + //We can do this unconditionally, but the check helps prevent redundant writes to the array + if elem != arr[pos] { + arr[pos], elem = elem, arr[pos] + } + } + } + + return arr +} diff --git a/sort/doc.go b/sort/doc.go new file mode 100644 index 000000000..aef1ff300 --- /dev/null +++ b/sort/doc.go @@ -0,0 +1,2 @@ +// Package sort a package for demonstrating sorting algorithms in Go +package sort diff --git a/sort/exchangesort.go b/sort/exchangesort.go new file mode 100644 index 000000000..43ada90df --- /dev/null +++ b/sort/exchangesort.go @@ -0,0 +1,21 @@ +// Implementation of exchange sort algorithm, a variant of bubble sort +// average time complexity: O(n^2) +// worst time complexity: O(n^2) +// space complexity: O(1) +// Reference: https://en.wikipedia.org/wiki/Sorting_algorithm#Exchange_sort + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func Exchange[T constraints.Ordered](arr []T) []T { + for i := 0; i < len(arr)-1; i++ { + for j := i + 1; j < len(arr); j++ { + if arr[i] > arr[j] { + arr[i], arr[j] = arr[j], arr[i] + } + } + } + + return arr +} diff --git a/sort/heapsort.go b/sort/heapsort.go new file mode 100644 index 000000000..f4e581306 --- /dev/null +++ b/sort/heapsort.go @@ -0,0 +1,143 @@ +// heapsort.go +// description: Implementation of heap sort algorithm +// worst-case time complexity: O(n log n) +// average-case time complexity: O(n log n) +// space complexity: O(1) + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +type MaxHeap struct { + slice []Comparable + heapSize int + indices map[int]int +} + +func (h *MaxHeap) Init(slice []Comparable) { + if slice == nil { + slice = make([]Comparable, 0) + } + + h.slice = slice + h.heapSize = len(slice) + h.indices = make(map[int]int) + h.Heapify() +} + +func (h MaxHeap) Heapify() { + for i, v := range h.slice { + h.indices[v.Idx()] = i + } + for i := h.heapSize / 2; i >= 0; i-- { + h.heapifyDown(i) + } +} + +func (h *MaxHeap) Pop() Comparable { + if h.heapSize == 0 { + return nil + } + + i := h.slice[0] + h.heapSize-- + + h.slice[0] = h.slice[h.heapSize] + h.updateidx(0) + h.heapifyDown(0) + + h.slice = h.slice[0:h.heapSize] + return i +} + +func (h *MaxHeap) Push(i Comparable) { + h.slice = append(h.slice, i) + h.updateidx(h.heapSize) + h.heapifyUp(h.heapSize) + h.heapSize++ +} + +func (h MaxHeap) Size() int { + return h.heapSize +} + +func (h MaxHeap) Update(i Comparable) { + h.slice[h.indices[i.Idx()]] = i + h.heapifyUp(h.indices[i.Idx()]) + h.heapifyDown(h.indices[i.Idx()]) +} + +func (h MaxHeap) updateidx(i int) { + h.indices[h.slice[i].Idx()] = i +} + +func (h *MaxHeap) swap(i, j int) { + h.slice[i], h.slice[j] = h.slice[j], h.slice[i] + h.updateidx(i) + h.updateidx(j) +} + +func (h MaxHeap) more(i, j int) bool { + return h.slice[i].More(h.slice[j]) +} + +func (h MaxHeap) heapifyUp(i int) { + if i == 0 { + return + } + p := i / 2 + + if h.slice[i].More(h.slice[p]) { + h.swap(i, p) + h.heapifyUp(p) + } +} + +func (h MaxHeap) heapifyDown(i int) { + heapifyDown(h.slice, h.heapSize, i, h.more, h.swap) +} + +func heapifyDown[T any](slice []T, N, i int, moreFunc func(i, j int) bool, swapFunc func(i, j int)) { + l, r := 2*i+1, 2*i+2 + max := i + + if l < N && moreFunc(l, max) { + max = l + } + if r < N && moreFunc(r, max) { + max = r + } + if max != i { + swapFunc(i, max) + + heapifyDown(slice, N, max, moreFunc, swapFunc) + } +} + +type Comparable interface { + Idx() int + More(any) bool +} + +func HeapSort[T constraints.Ordered](slice []T) []T { + N := len(slice) + + moreFunc := func(i, j int) bool { + return slice[i] > slice[j] + } + swapFunc := func(i, j int) { + slice[i], slice[j] = slice[j], slice[i] + } + + // build a maxheap + for i := N/2 - 1; i >= 0; i-- { + heapifyDown(slice, N, i, moreFunc, swapFunc) + } + + for i := N - 1; i > 0; i-- { + slice[i], slice[0] = slice[0], slice[i] + heapifyDown(slice, i, 0, moreFunc, swapFunc) + } + + return slice +} diff --git a/sort/insertionsort.go b/sort/insertionsort.go new file mode 100644 index 000000000..55ac3130f --- /dev/null +++ b/sort/insertionsort.go @@ -0,0 +1,21 @@ +// insertionsort.go +// description: Implementation of insertion sort algorithm +// worst-case time complexity: O(n^2) +// average-case time complexity: O(n^2) +// space complexity: O(1) + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func Insertion[T constraints.Ordered](arr []T) []T { + for currentIndex := 1; currentIndex < len(arr); currentIndex++ { + temporary := arr[currentIndex] + iterator := currentIndex + for ; iterator > 0 && arr[iterator-1] > temporary; iterator-- { + arr[iterator] = arr[iterator-1] + } + arr[iterator] = temporary + } + return arr +} diff --git a/sort/mergesort.go b/sort/mergesort.go new file mode 100644 index 000000000..550b13eea --- /dev/null +++ b/sort/mergesort.go @@ -0,0 +1,94 @@ +// mergesort.go +// description: Implementation of merge sort algorithm +// worst-case time complexity: O(n log n) +// average-case time complexity: O(n log n) +// space complexity: O(n) + +package sort + +import ( + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/math/min" + "sync" +) + +func merge[T constraints.Ordered](a []T, b []T) []T { + + var r = make([]T, len(a)+len(b)) + var i = 0 + var j = 0 + + for i < len(a) && j < len(b) { + + if a[i] <= b[j] { + r[i+j] = a[i] + i++ + } else { + r[i+j] = b[j] + j++ + } + + } + + for i < len(a) { + r[i+j] = a[i] + i++ + } + for j < len(b) { + r[i+j] = b[j] + j++ + } + + return r + +} + +// Merge Perform merge sort on a slice +func Merge[T constraints.Ordered](items []T) []T { + + if len(items) < 2 { + return items + + } + + var middle = len(items) / 2 + var a = Merge(items[:middle]) + var b = Merge(items[middle:]) + return merge(a, b) + +} + +func MergeIter[T constraints.Ordered](items []T) []T { + for step := 1; step < len(items); step += step { + for i := 0; i+step < len(items); i += 2 * step { + tmp := merge(items[i:i+step], items[i+step:min.Int(i+2*step, len(items))]) + copy(items[i:], tmp) + } + } + return items +} + +// ParallelMerge Perform merge sort on a slice using goroutines +func ParallelMerge[T constraints.Ordered](items []T) []T { + if len(items) < 2 { + return items + } + + if len(items) < 2048 { + return Merge(items) + } + + var wg sync.WaitGroup + wg.Add(1) + + var middle = len(items) / 2 + var a []T + go func() { + defer wg.Done() + a = ParallelMerge(items[:middle]) + }() + var b = ParallelMerge(items[middle:]) + + wg.Wait() + return merge(a, b) +} diff --git a/sort/oddevensort.go b/sort/oddevensort.go new file mode 100644 index 000000000..5e98ef409 --- /dev/null +++ b/sort/oddevensort.go @@ -0,0 +1,39 @@ +// oddevensort.go +// Implementation of Odd-Even Sort (Brick Sort) +// Reference: https://en.wikipedia.org/wiki/Odd%E2%80%93even_sort + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +// OddEvenSort performs the odd-even sort algorithm on the given array. +// It is a variation of bubble sort that compares adjacent pairs, alternating +// between odd and even indexed elements in each pass until the array is sorted. +func OddEvenSort[T constraints.Ordered](arr []T) []T { + if len(arr) == 0 { // handle empty array + return arr + } + + swapped := true + for swapped { + swapped = false + + // Perform "odd" indexed pass + for i := 1; i < len(arr)-1; i += 2 { + if arr[i] > arr[i+1] { + arr[i], arr[i+1] = arr[i+1], arr[i] + swapped = true + } + } + + // Perform "even" indexed pass + for i := 0; i < len(arr)-1; i += 2 { + if arr[i] > arr[i+1] { + arr[i], arr[i+1] = arr[i+1], arr[i] + swapped = true + } + } + } + + return arr +} diff --git a/sort/pancakesort.go b/sort/pancakesort.go new file mode 100644 index 000000000..a809ba1c4 --- /dev/null +++ b/sort/pancakesort.go @@ -0,0 +1,44 @@ +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +// Pancake sorts a slice using flip operations, +// where flip refers to the idea of reversing the +// slice from index `0` to `i`. +func Pancake[T constraints.Ordered](arr []T) []T { + // early return if the array too small + if len(arr) <= 1 { + return arr + } + + // start from the end of the array + for i := len(arr) - 1; i > 0; i-- { + // find the index of the maximum element in arr + max := 0 + for j := 1; j <= i; j++ { + if arr[j] > arr[max] { + max = j + } + } + + // if the maximum element is not at the end of the array + if max != i { + // flip the maximum element to the beginning of the array + arr = flip(arr, max) + + // flip the maximum element to the end of the array by flipping the whole array + arr = flip(arr, i) + } + } + + return arr +} + +// flip reverses the input slice from `0` to `i`. +func flip[T constraints.Ordered](arr []T, i int) []T { + for j := 0; j < i; j++ { + arr[j], arr[i] = arr[i], arr[j] + i-- + } + return arr +} diff --git a/sort/patiencesort.go b/sort/patiencesort.go new file mode 100644 index 000000000..f1b2b46f2 --- /dev/null +++ b/sort/patiencesort.go @@ -0,0 +1,70 @@ +// Patience sorting is a sorting algorithm inspired by the card game patience. +// +// For more details check out those links below here: +// GeeksForGeeks article : https://www.geeksforgeeks.org/patience-sorting/ +// Wikipedia article: https://en.wikipedia.org/wiki/Patience_sorting +// authors [guuzaa](https://github.com/guuzaa) +// worst-case time complexity: O(n log n) +// average time complexity: O(n log n) +// space complexity: O(n) +// see patiencesort.go + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func Patience[T constraints.Ordered](arr []T) []T { + if len(arr) <= 1 { + return arr + } + + var piles [][]T + + for _, card := range arr { + left, right := 0, len(piles) + for left < right { + mid := left + (right-left)/2 + if piles[mid][len(piles[mid])-1] >= card { + right = mid + } else { + left = mid + 1 + } + } + + if left == len(piles) { + piles = append(piles, []T{card}) + } else { + piles[left] = append(piles[left], card) + } + } + + return mergePiles(piles) +} + +func mergePiles[T constraints.Ordered](piles [][]T) []T { + var ret []T + + for len(piles) > 0 { + minID := 0 + minValue := piles[minID][len(piles[minID])-1] + + for i := 1; i < len(piles); i++ { + if minValue <= piles[i][len(piles[i])-1] { + continue + } + + minValue = piles[i][len(piles[i])-1] + minID = i + } + + ret = append(ret, minValue) + + piles[minID] = piles[minID][:len(piles[minID])-1] + + if len(piles[minID]) == 0 { + piles = append(piles[:minID], piles[minID+1:]...) + } + } + + return ret +} diff --git a/sort/pigeonholesort.go b/sort/pigeonholesort.go new file mode 100644 index 000000000..5e735c8fd --- /dev/null +++ b/sort/pigeonholesort.go @@ -0,0 +1,44 @@ +// Pigeonhole algorithm's working at wikipedia. +// https://en.wikipedia.org/wiki/Pigeonhole_sort +// time complexity: O(n + N) where n is the number of elements in the array and N is the range of input +// space complexity: O(N) + +package sort + +import ( + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/math/max" + "github.com/TheAlgorithms/Go/math/min" +) + +// Pigeonhole sorts a slice using pigeonhole sorting algorithm. +// NOTE: To maintain time complexity O(n + N), this is the reason for having +// only Integer constraint instead of Ordered. +func Pigeonhole[T constraints.Integer](arr []T) []T { + if len(arr) == 0 { + return arr + } + + max := max.Int(arr...) + min := min.Int(arr...) + + size := max - min + 1 + + holes := make([]T, size) + + for _, element := range arr { + holes[element-min]++ + } + + i := 0 + + for j := T(0); j < size; j++ { + for holes[j] > 0 { + holes[j]-- + arr[i] = j + min + i++ + } + } + + return arr +} diff --git a/sort/quicksort.go b/sort/quicksort.go new file mode 100644 index 000000000..8b05fe786 --- /dev/null +++ b/sort/quicksort.go @@ -0,0 +1,45 @@ +// quicksort.go +// description: Implementation of in-place quicksort algorithm +// details: +// A simple in-place quicksort algorithm implementation. [Wikipedia](https://en.wikipedia.org/wiki/Quicksort) +// worst time complexity: O(n^2) +// average time complexity: O(n log n) +// space complexity: O(log n) +// author(s) [Taj](https://github.com/tjgurwara99) +// see sort_test.go for a test implementation, test function TestQuickSort. + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func Partition[T constraints.Ordered](arr []T, low, high int) int { + index := low - 1 + pivotElement := arr[high] + for i := low; i < high; i++ { + if arr[i] <= pivotElement { + index += 1 + arr[index], arr[i] = arr[i], arr[index] + } + } + arr[index+1], arr[high] = arr[high], arr[index+1] + return index + 1 +} + +// QuicksortRange Sorts the specified range within the array +func QuicksortRange[T constraints.Ordered](arr []T, low, high int) { + if len(arr) <= 1 { + return + } + + if low < high { + pivot := Partition(arr, low, high) + QuicksortRange(arr, low, pivot-1) + QuicksortRange(arr, pivot+1, high) + } +} + +// Quicksort Sorts the entire array +func Quicksort[T constraints.Ordered](arr []T) []T { + QuicksortRange(arr, 0, len(arr)-1) + return arr +} diff --git a/sort/radixsort.go b/sort/radixsort.go new file mode 100644 index 000000000..28ddee8bf --- /dev/null +++ b/sort/radixsort.go @@ -0,0 +1,66 @@ +// radixsort.go +// description: Implementation of in-place radixsort algorithm +// details: +// A simple in-place quicksort algorithm implementation. [Wikipedia](https://en.wikipedia.org/wiki/Radix_sort) +// worst time complexity: O(n * k) where n is the number of elements in the input array and k is the number of digits in the largest number +// average time complexity: O(n * k) where n is the number of elements in the input array and k is the number of digits in the largest number +// space complexity: O(n) + +package sort + +import ( + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/math/max" +) + +func countSort[T constraints.Integer](arr []T, exp T) []T { + var digits [10]int + var output = make([]T, len(arr)) + + for _, item := range arr { + digits[(item/exp)%10]++ + } + for i := 1; i < 10; i++ { + digits[i] += digits[i-1] + } + + for i := len(arr) - 1; i >= 0; i-- { + output[digits[(arr[i]/exp)%10]-1] = arr[i] + digits[(arr[i]/exp)%10]-- + } + + return output +} + +func unsignedRadixSort[T constraints.Integer](arr []T) []T { + if len(arr) == 0 { + return arr + } + maxElement := max.Int(arr...) + for exp := T(1); maxElement/exp > 0; exp *= 10 { + arr = countSort(arr, exp) + } + return arr +} + +func RadixSort[T constraints.Integer](arr []T) []T { + if len(arr) < 1 { + return arr + } + var negatives, nonNegatives []T + + for _, item := range arr { + if item < 0 { + negatives = append(negatives, -item) + } else { + nonNegatives = append(nonNegatives, item) + } + } + negatives = unsignedRadixSort(negatives) + + // Reverse the negative array and restore signs + for i, j := 0, len(negatives)-1; i <= j; i, j = i+1, j-1 { + negatives[i], negatives[j] = -negatives[j], -negatives[i] + } + return append(negatives, unsignedRadixSort(nonNegatives)...) +} diff --git a/sort/selectionsort.go b/sort/selectionsort.go new file mode 100644 index 000000000..b86000a9b --- /dev/null +++ b/sort/selectionsort.go @@ -0,0 +1,17 @@ +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func Selection[T constraints.Ordered](arr []T) []T { + for i := 0; i < len(arr); i++ { + min := i + for j := i + 1; j < len(arr); j++ { + if arr[j] < arr[min] { + min = j + } + } + + arr[i], arr[min] = arr[min], arr[i] + } + return arr +} diff --git a/sorts/shell_sort.go b/sort/shellsort.go similarity index 62% rename from sorts/shell_sort.go rename to sort/shellsort.go index b1a4702aa..fb04f6f7c 100644 --- a/sorts/shell_sort.go +++ b/sort/shellsort.go @@ -1,7 +1,8 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts +package sort -func shellSort(arr []int) []int { +import "github.com/TheAlgorithms/Go/constraints" + +func Shell[T constraints.Ordered](arr []T) []T { for d := int(len(arr) / 2); d > 0; d /= 2 { for i := d; i < len(arr); i++ { for j := i; j >= d && arr[j-d] > arr[j]; j -= d { diff --git a/sort/simplesort.go b/sort/simplesort.go new file mode 100644 index 000000000..fc60f33de --- /dev/null +++ b/sort/simplesort.go @@ -0,0 +1,40 @@ +// simplesort.go +// description: Implementation of a simple sorting algorithm +// details: +// A simple sorting algorithm that look counter intuitive at first glance and very similar to Exchange Sort +// An improved version is included with slight changes to make the sort slightly more efficient +// reference: https://arxiv.org/abs/2110.01111v1 +// see sort_test.go for a test implementation, test function TestSimple and TestImprovedSimple +// worst-case time complexity: O(n^2) +// average-case time complexity: O(n^2) +// space complexity: O(1) + +package sort + +import "github.com/TheAlgorithms/Go/constraints" + +func Simple[T constraints.Ordered](arr []T) []T { + for i := 0; i < len(arr); i++ { + for j := 0; j < len(arr); j++ { + if arr[i] < arr[j] { + // swap arr[i] and arr[j] + arr[i], arr[j] = arr[j], arr[i] + } + } + } + return arr +} + +// ImprovedSimple is a improve SimpleSort by skipping an unnecessary comparison of the first and last. +// This improved version is more similar to implementation of insertion sort +func ImprovedSimple[T constraints.Ordered](arr []T) []T { + for i := 1; i < len(arr); i++ { + for j := 0; j < len(arr)-1; j++ { + if arr[i] < arr[j] { + // swap arr[i] and arr[j] + arr[i], arr[j] = arr[j], arr[i] + } + } + } + return arr +} diff --git a/sort/sorts_test.go b/sort/sorts_test.go new file mode 100644 index 000000000..f2394c334 --- /dev/null +++ b/sort/sorts_test.go @@ -0,0 +1,350 @@ +package sort_test + +import ( + "math/rand" + "reflect" + "testing" + "time" + + "github.com/TheAlgorithms/Go/sort" +) + +func testFramework(t *testing.T, sortingFunction func([]int) []int) { + sortTests := []struct { + input []int + expected []int + name string + }{ + //Sorted slice + { + input: []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + expected: []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + name: "Sorted Unsigned", + }, + //Reversed slice + { + input: []int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, + expected: []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + name: "Reversed Unsigned", + }, + //Sorted slice + { + input: []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + expected: []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + name: "Sorted Signed", + }, + //Reversed slice + { + input: []int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10}, + expected: []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + name: "Reversed Signed", + }, + //Reversed slice, even length + { + input: []int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10}, + expected: []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + name: "Reversed Signed #2", + }, + //Random order with repetitions + { + input: []int{-5, 7, 4, -2, 6, 5, 8, 3, 2, -7, -1, 0, -3, 9, -6, -4, 10, 9, 1, -8, -9, -10}, + expected: []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10}, + name: "Random order Signed", + }, + //Single-entry slice + { + input: []int{1}, + expected: []int{1}, + name: "Singleton", + }, + // Empty slice + { + input: []int{}, + expected: []int{}, + name: "Empty Slice", + }, + } + for _, test := range sortTests { + t.Run(test.name, func(t *testing.T) { + actual := sortingFunction(test.input) + sorted := reflect.DeepEqual(actual, test.expected) + if !sorted { + t.Errorf("test %s failed", test.name) + t.Errorf("actual %v expected %v", actual, test.expected) + } + }) + } +} + +// BEGIN TESTS +func TestBinaryInsertion(t *testing.T) { + testFramework(t, sort.BinaryInsertion[int]) +} + +func TestBubble(t *testing.T) { + testFramework(t, sort.Bubble[int]) +} + +func TestBogo(t *testing.T) { + t.Skip("Skipping test for Bogo Sort, as it uses a lot of resource.") + testFramework(t, sort.Bogo[int]) +} + +func TestBucketSort(t *testing.T) { + testFramework(t, sort.Bucket[int]) +} + +func TestCocktailSort(t *testing.T) { + testFramework(t, sort.Cocktail[int]) +} + +func TestExchange(t *testing.T) { + testFramework(t, sort.Exchange[int]) +} + +func TestInsertion(t *testing.T) { + testFramework(t, sort.Insertion[int]) +} + +func TestMerge(t *testing.T) { + testFramework(t, sort.Merge[int]) +} + +func TestMergeIter(t *testing.T) { + testFramework(t, sort.MergeIter[int]) +} + +func TestMergeParallel(t *testing.T) { + testFramework(t, sort.ParallelMerge[int]) + + // Test parallel merge sort with a large slice + t.Run("ParallelMerge on large slice", func(t *testing.T) { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + size := 100000 + randomLargeSlice := make([]int, size) + for i := range randomLargeSlice { + randomLargeSlice[i] = rnd.Intn(size) + } + sortedSlice := sort.ParallelMerge[int](randomLargeSlice) + for i := 0; i < len(sortedSlice)-1; i++ { + if sortedSlice[i] > sortedSlice[i+1] { + t.Errorf("ParallelMerge failed") + } + } + }) +} + +func TestHeap(t *testing.T) { + testFramework(t, sort.HeapSort[int]) +} + +func TestCount(t *testing.T) { + testFramework(t, sort.Count[int]) +} + +func TestQuick(t *testing.T) { + testFramework(t, sort.Quicksort[int]) +} + +func TestShell(t *testing.T) { + testFramework(t, sort.Shell[int]) +} + +func TestRadix(t *testing.T) { + testFramework(t, sort.RadixSort[int]) +} + +func TestSimple(t *testing.T) { + testFramework(t, sort.Simple[int]) +} + +func TestImprovedSimple(t *testing.T) { + testFramework(t, sort.ImprovedSimple[int]) +} + +func TestSelection(t *testing.T) { + testFramework(t, sort.Selection[int]) +} + +func TestComb(t *testing.T) { + testFramework(t, sort.Comb[int]) +} + +func TestPancakeSort(t *testing.T) { + testFramework(t, sort.Pancake[int]) +} + +func TestPigeonhole(t *testing.T) { + testFramework(t, sort.Pigeonhole[int]) +} + +func TestPatience(t *testing.T) { + testFramework(t, sort.Patience[int]) +} + +func TestCycle(t *testing.T) { + testFramework(t, sort.Cycle[int]) +} + +func TestTimsort(t *testing.T) { + testFramework(t, sort.Timsort[int]) +} + +func TestCircle(t *testing.T) { + testFramework(t, sort.Circle[int]) +} + +func TestOddEvenSort(t *testing.T) { + testFramework(t, sort.OddEvenSort[int]) +} + +func TestStooge(t *testing.T) { + testFramework(t, sort.Stooge[int]) +} + +// END TESTS + +func benchmarkFramework(b *testing.B, f func(arr []int) []int) { + var sortTests = []struct { + input []int + expected []int + name string + }{ + //Sorted slice + {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, "Sorted Unsigned"}, + //Reversed slice + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, + []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, "Reversed Unsigned"}, + //Sorted slice + {[]int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, + []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, "Sorted Signed"}, + //Reversed slice + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10}, + []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, "Reversed Signed"}, + //Reversed slice, even length + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10}, + []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, "Reversed Signed #2"}, + //Random order with repetitions + {[]int{-5, 7, 4, -2, 6, 5, 8, 3, 2, -7, -1, 0, -3, 9, -6, -4, 10, 9, 1, -8, -9, -10}, + []int{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 10}, "Random order Signed"}, + //Empty slice + {[]int{}, []int{}, "Empty"}, + //Single-entry slice + {[]int{1}, []int{1}, "Singleton"}, + } + b.ResetTimer() + for i := 0; i < b.N; i++ { + for _, test := range sortTests { + f(test.input) + } + } +} + +//BEGIN BENCHMARKS + +func BenchmarkBinaryInsertion(b *testing.B) { + benchmarkFramework(b, sort.BinaryInsertion[int]) +} + +func BenchmarkBubble(b *testing.B) { + benchmarkFramework(b, sort.Bubble[int]) +} + +func BenchmarkBogo(b *testing.B) { + b.Skip("Skipping benchmark for Bogo Sort, as it uses a lot of resource.") + benchmarkFramework(b, sort.Bogo[int]) +} + +func BenchmarkBucketSort(b *testing.B) { + benchmarkFramework(b, sort.Bucket[int]) +} + +func BenchmarkCocktailSort(b *testing.B) { + benchmarkFramework(b, sort.Cocktail[int]) +} + +func BenchmarkExchange(b *testing.B) { + benchmarkFramework(b, sort.Exchange[int]) +} + +func BenchmarkInsertion(b *testing.B) { + benchmarkFramework(b, sort.Insertion[int]) +} + +func BenchmarkMerge(b *testing.B) { + benchmarkFramework(b, sort.Merge[int]) +} + +func BenchmarkMergeIter(b *testing.B) { + benchmarkFramework(b, sort.MergeIter[int]) +} + +func BenchmarkMergeParallel(b *testing.B) { + benchmarkFramework(b, sort.ParallelMerge[int]) +} + +func BenchmarkHeap(b *testing.B) { + benchmarkFramework(b, sort.HeapSort[int]) +} + +func BenchmarkCount(b *testing.B) { + benchmarkFramework(b, sort.Count[int]) +} + +func BenchmarkQuick(b *testing.B) { + benchmarkFramework(b, sort.Quicksort[int]) +} + +func BenchmarkShell(b *testing.B) { + benchmarkFramework(b, sort.Shell[int]) +} + +func BenchmarkRadix(b *testing.B) { + benchmarkFramework(b, sort.RadixSort[int]) +} + +func BenchmarkSimple(b *testing.B) { + benchmarkFramework(b, sort.Simple[int]) +} + +func BenchmarkImprovedSimple(b *testing.B) { + benchmarkFramework(b, sort.ImprovedSimple[int]) +} + +// Very Slow, consider commenting +func BenchmarkSelection(b *testing.B) { + benchmarkFramework(b, sort.Selection[int]) +} + +func BenchmarkComb(b *testing.B) { + benchmarkFramework(b, sort.Comb[int]) +} + +func BenchmarkPancakeSort(b *testing.B) { + benchmarkFramework(b, sort.Pancake[int]) +} + +func BenchmarkPigeonhole(b *testing.B) { + benchmarkFramework(b, sort.Pigeonhole[int]) +} + +func BenchmarkPatience(b *testing.B) { + benchmarkFramework(b, sort.Patience[int]) +} + +func BenchmarkCycle(b *testing.B) { + benchmarkFramework(b, sort.Cycle[int]) +} + +func BenchmarkTimsort(b *testing.B) { + benchmarkFramework(b, sort.Timsort[int]) +} + +func BenchmarkCircle(b *testing.B) { + benchmarkFramework(b, sort.Circle[int]) +} + +func BenchmarkStooge(b *testing.B) { + benchmarkFramework(b, sort.Stooge[int]) +} diff --git a/sort/stooge_sort.go b/sort/stooge_sort.go new file mode 100644 index 000000000..45d2206c4 --- /dev/null +++ b/sort/stooge_sort.go @@ -0,0 +1,34 @@ +// implementation of the Stooge sort +// more info at https://en.wikipedia.org/wiki/Stooge_sort +// worst-case time complexity O(n^2.709511) +// worst-case space complexity O(n) + +package sort + +import ( + "github.com/TheAlgorithms/Go/constraints" + + // math imported for floor division + "math" +) + +func innerStooge[T constraints.Ordered](arr []T, i int32, j int32) []T { + if arr[i] > arr[j] { + arr[i], arr[j] = arr[j], arr[i] + } + if (j - i + 1) > 2 { + t := int32(math.Floor(float64(j-i+1) / 3.0)) + arr = innerStooge(arr, i, j-t) + arr = innerStooge(arr, i+t, j) + arr = innerStooge(arr, i, j-t) + } + return arr +} + +func Stooge[T constraints.Ordered](arr []T) []T { + if len(arr) == 0 { + return arr + } + + return innerStooge(arr, 0, int32(len(arr)-1)) +} diff --git a/sort/timsort.go b/sort/timsort.go new file mode 100644 index 000000000..95520219a --- /dev/null +++ b/sort/timsort.go @@ -0,0 +1,71 @@ +// Implementation of Timsort algorithm +// Reference: https://en.wikipedia.org/wiki/Timsort + +package sort + +import ( + "github.com/TheAlgorithms/Go/constraints" +) + +const runSizeThreshold = 8 + +// Timsort is a simple generic implementation of Timsort algorithm. +func Timsort[T constraints.Ordered](data []T) []T { + runSize := calculateRunSize(len(data)) + insertionSortRuns(data, runSize) + mergeRuns(data, runSize) + return data +} + +// calculateRunSize returns a run size parameter that is further used +// to slice the data slice. +func calculateRunSize(dataLength int) int { + remainder := 0 + for dataLength >= runSizeThreshold { + if dataLength%2 == 1 { + remainder = 1 + } + + dataLength = dataLength / 2 + } + + return dataLength + remainder +} + +// insertionSortRuns runs insertion sort on all the data runs one by one. +func insertionSortRuns[T constraints.Ordered](data []T, runSize int) { + for lower := 0; lower < len(data); lower += runSize { + upper := lower + runSize + if upper >= len(data) { + upper = len(data) + } + + Insertion(data[lower:upper]) + } +} + +// mergeRuns merge sorts all the data runs into a single sorted data slice. +func mergeRuns[T constraints.Ordered](data []T, runSize int) { + for size := runSize; size < len(data); size *= 2 { + for lowerBound := 0; lowerBound < len(data); lowerBound += size * 2 { + middleBound := lowerBound + size - 1 + upperBound := lowerBound + 2*size - 1 + if len(data)-1 < upperBound { + upperBound = len(data) - 1 + } + + mergeRun(data, lowerBound, middleBound, upperBound) + } + } +} + +// mergeRun uses merge sort to sort adjacent data runs. +func mergeRun[T constraints.Ordered](data []T, lower, mid, upper int) { + left := data[lower : mid+1] + right := data[mid+1 : upper+1] + merged := merge(left, right) + // rewrite original data slice values with sorted values from merged slice + for i, value := range merged { + data[lower+i] = value + } +} diff --git a/sorts/bubble_sort.go b/sorts/bubble_sort.go deleted file mode 100644 index 77f73d6a9..000000000 --- a/sorts/bubble_sort.go +++ /dev/null @@ -1,24 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -func bubbleSort(arrayzor []int) []int { - - - swapped := true - for swapped { - swapped = false - for i := 0; i < len(arrayzor)-1; i++ { - if arrayzor[i+1] < arrayzor[i] { - swap(arrayzor, i, i+1) - swapped = true - } - } - } - return arrayzor -} - -func swap(arrayzor []int, i, j int) { - tmp := arrayzor[j] - arrayzor[j] = arrayzor[i] - arrayzor[i] = tmp -} diff --git a/sorts/heap_sort.go b/sorts/heap_sort.go deleted file mode 100644 index c5678893c..000000000 --- a/sorts/heap_sort.go +++ /dev/null @@ -1,51 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -type MaxHeap struct { - slice []int - heapSize int -} - -func BuildMaxHeap(slice []int) MaxHeap { - h := MaxHeap{slice: slice, heapSize: len(slice)} - for i := len(slice) / 2; i >= 0; i-- { - h.MaxHeapify(i) - } - return h -} - -func (h MaxHeap) MaxHeapify(i int) { - l, r := 2*i+1, 2*i+2 - max := i - - if l < h.size() && h.slice[l] > h.slice[max] { - max = l - } - if r < h.size() && h.slice[r] > h.slice[max] { - max = r - } - //log.Printf("MaxHeapify(%v): l,r=%v,%v; max=%v\t%v\n", i, l, r, max, h.slice) - if max != i { - h.slice[i], h.slice[max] = h.slice[max], h.slice[i] - h.MaxHeapify(max) - } -} - -func (h MaxHeap) size() int { return h.heapSize } // ??? - -func heapSort(slice []int) []int { - h := BuildMaxHeap(slice) - //log.Println(slice) - for i := len(h.slice) - 1; i >= 1; i-- { - h.slice[0], h.slice[i] = h.slice[i], h.slice[0] - h.heapSize-- - h.MaxHeapify(0) - /*if i == len(h.slice)-1 || i == len(h.slice)-3 || i == len(h.slice)-5 { - element := (i - len(h.slice)) * -1 - fmt.Println("Heap after removing ", element, " elements") - fmt.Println(h.slice) - - }*/ - } - return h.slice -} diff --git a/sorts/insertion_sort.go b/sorts/insertion_sort.go deleted file mode 100644 index 9a95e0a6b..000000000 --- a/sorts/insertion_sort.go +++ /dev/null @@ -1,15 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -func insertionSort(arr []int) []int { - for out := 1; out < len(arr); out++ { - temp := arr[out] - in := out - - for ; in > 0 && arr[in-1] >= temp; in-- { - arr[in] = arr[in-1] - } - arr[in] = temp - } - return arr -} diff --git a/sorts/merge_sort.go b/sorts/merge_sort.go deleted file mode 100644 index ef52e557a..000000000 --- a/sorts/merge_sort.go +++ /dev/null @@ -1,48 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -func merge(a []int, b []int) []int { - - var r = make([]int, len(a)+len(b)) - var i = 0 - var j = 0 - - for i < len(a) && j < len(b) { - - if a[i] <= b[j] { - r[i+j] = a[i] - i++ - } else { - r[i+j] = b[j] - j++ - } - - } - - for i < len(a) { - r[i+j] = a[i] - i++ - } - for j < len(b) { - r[i+j] = b[j] - j++ - } - - return r - -} - -//Mergesort Perform mergesort on a slice of ints -func Mergesort(items []int) []int { - - if len(items) < 2 { - return items - - } - - var middle = len(items) / 2 - var a = Mergesort(items[:middle]) - var b = Mergesort(items[middle:]) - return merge(a, b) - -} diff --git a/sorts/quick_sort.go b/sorts/quick_sort.go deleted file mode 100644 index 2d719a11e..000000000 --- a/sorts/quick_sort.go +++ /dev/null @@ -1,38 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -import ( - "math/rand" -) - -func quickSort(arr []int) []int { - - if len(arr) <= 1 { - return arr - } - - median := arr[rand.Intn(len(arr))] - - low_part := make([]int, 0, len(arr)) - high_part := make([]int, 0, len(arr)) - middle_part := make([]int, 0, len(arr)) - - for _, item := range arr { - switch { - case item < median: - low_part = append(low_part, item) - case item == median: - middle_part = append(middle_part, item) - case item > median: - high_part = append(high_part, item) - } - } - - low_part = quickSort(low_part) - high_part = quickSort(high_part) - - low_part = append(low_part, middle_part...) - low_part = append(low_part, high_part...) - - return low_part -} diff --git a/sorts/selection_sort.go b/sorts/selection_sort.go deleted file mode 100644 index a142f1a45..000000000 --- a/sorts/selection_sort.go +++ /dev/null @@ -1,19 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -func selectionSort(arr []int) []int { - - for i := 0; i < len(arr); i++ { - min := i - for j := i + 1; j < len(arr); j++ { - if arr[j] < arr[min] { - min = j - } - } - - tmp := arr[i] - arr[i] = arr[min] - arr[min] = tmp - } - return arr -} diff --git a/sorts/sorts_case_test.go b/sorts/sorts_case_test.go deleted file mode 100644 index 093abef3a..000000000 --- a/sorts/sorts_case_test.go +++ /dev/null @@ -1,47 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -import ( - "crypto/rand" - "math/big" - "sort" -) - -type sortTest struct { - input []int - expected []int - name string -} - -var arr []int = makeRandArray(500_000) - - -var sortTests = []sortTest{ - //Sorted slice - {[]int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, - []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, "Sorted"}, - //Reversed slice - {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, - []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, "Reversed"}, - //Empty slice - {[]int{}, []int{}, "Empty"}, - //Single-entry slice - {[]int{1}, []int{1}, "Singleton"}, - - //500k values sort - {arr, getSortedVersion(arr), "Large Random"}, -} - -func makeRandArray(size int) []int { - vals := make([]int, size) - for i := 0; i < size; i++ { - temp, _ := rand.Int(rand.Reader, big.NewInt(int64(size))) - vals[i] = int(temp.Int64()) - } - return vals -} - -func getSortedVersion(a []int) []int { - sort.Slice(a, func(i, j int) bool { return a[i] < a[j] }) - return a -} diff --git a/sorts/sorts_test.go b/sorts/sorts_test.go deleted file mode 100644 index 4769397b5..000000000 --- a/sorts/sorts_test.go +++ /dev/null @@ -1,190 +0,0 @@ -package sorts - -import "testing" - -//BEGIN TESTS - -func TestBubble(t *testing.T) { - for _, test := range sortTests { - actual := bubbleSort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -} - -func TestSelection(t *testing.T) { - for _, test := range sortTests { - actual := selectionSort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -} - -func TestInsertion(t *testing.T) { - for _, test := range sortTests { - actual := insertionSort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -} - -func TestMerge(t *testing.T) { - for _, test := range sortTests { - actual := Mergesort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -} - -func TestHeap(t *testing.T) { - for _, test := range sortTests { - actual := heapSort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -} - -func TestQuick(t *testing.T) { - for _, test := range sortTests { - actual := quickSort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -} - -func TestShell(t *testing.T) { - for _, test := range sortTests { - actual := shellSort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -} - -/*func TestTopological(t *testing.T) { - for _, test := range sortTests { - actual := topologicalSort(test.input) - pos, sorted := compareSlices(actual, test.expected) - if !sorted { - if pos == -1 { - t.Errorf("test %s failed due to slice length changing", test.name) - } - t.Errorf("test %s failed at index %d", test.name, pos) - } - } -}*/ - -//END TESTS - -//BEGIN BENCHMARKS -func BenchmarkBubble(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - bubbleSort(test.input) - } - } -} - -func BenchmarkSelection(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - selectionSort(test.input) - } - } -} - -func BenchmarkInsertion(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - insertionSort(test.input) - } - } -} - -func BenchmarkMerge(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - Mergesort(test.input) - } - } -} - -func BenchmarkHeap(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - heapSort(test.input) - } - } -} - -func BenchmarkQuick(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - quickSort(test.input) - } - } -} - -func BenchmarkShell(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - shellSort(test.input) - } - } -} - -/*func BenchmarkTopological(b *testing.B) { - for i := 0; i < b.N; i++ { - for _, test := range sortTests { - topologicalSort(test.input) - } - } -}*/ - -//END BENCHMARKS - -func compareSlices(a []int, b []int) (int, bool) { - if len(a) != len(b) { - return -1, false - } - for pos := range a { - if a[pos] != b[pos] { - return pos, false - } - } - return -1, true -} diff --git a/sorts/topological_sort.go b/sorts/topological_sort.go deleted file mode 100644 index 91ff40d51..000000000 --- a/sorts/topological_sort.go +++ /dev/null @@ -1,112 +0,0 @@ -//Package sorts a package for demonstrating sorting algorithms in Go -package sorts - -/*type Dependency struct { - nodeId int - children []int -} - -// converts dependencies to edges -func dependenciesToEdges(dependencies []Dependency) []Edge { - edges := []Edge{} - for _, node := range dependencies { - for _, child := range node.children { - edges = append(edges, Edge{start: node.nodeId, end: child}) - } - } - return edges -} - -type Edge struct { - start int // start and end are node ids - end int -} - -type Node struct { - id int - children []int - selected bool - incoming int -} - -// takes a list of edges as input with start and end node_ids -// useful for cases like task ordering -func topologicalSort(input []Edge) ([]int, [][]int) { - - // generate a mapping for node_id and number of incoming edges - incoming := make(map[int]int) - for _, edge := range input { - if _, ok := incoming[edge.start]; !ok { - incoming[edge.start] = 0 - } - incoming[edge.end] += 1 - } - - nodes := make([]*Node, 0) - for k, v := range incoming { - chdn := []int{} - for _, edge := range input { - if edge.start == k { - chdn = append(chdn, edge.end) - } - } - nodes = append(nodes, &Node{id: k, children: chdn, selected: false, incoming: v}) - } - - res := []int{} - var levels [][]int - for len(res) < len(nodes) { - level := []int{} - queue := []int{} - for idx, node := range nodes { - // select a node with no incoming dependency - if !node.selected && node.incoming == 0 { - queue = append(queue, idx) - nodes[idx].selected = true - } - } - for _, idx := range queue { - node := nodes[idx] - level = append(level, node.id) - // decrement incoming values for all children - for _, childId := range node.children { - for _, child := range nodes { - if !child.selected && child.id == childId { - child.incoming-- - } - } - } - } - res = append(res, level...) - levels = append(levels, level) - } - return res, levels -}*/ - -/*func main() { - var edges []Edge - edges = append(edges, Edge{1, 2}) - edges = append(edges, Edge{2, 3}) - edges = append(edges, Edge{4, 3}) - edges = append(edges, Edge{4, 5}) - edges = append(edges, Edge{3, 6}) - edges = append(edges, Edge{5, 6}) - - order, levels := topologicalSort(edges) - fmt.Println("result: ", order) - fmt.Println("levels: ", levels) - - // or you can specify dependencies - var deps []Dependency - deps = append(deps, Dependency{nodeId: 1, children: []int{2}}) - deps = append(deps, Dependency{nodeId: 2, children: []int{3}}) - deps = append(deps, Dependency{nodeId: 4, children: []int{3, 5}}) - deps = append(deps, Dependency{nodeId: 5, children: []int{6}}) - deps = append(deps, Dependency{nodeId: 3, children: []int{6}}) - - edges = dependenciesToEdges(deps) - order, levels = topologicalSort(edges) - fmt.Println("result: ", order) - fmt.Println("levels: ", levels) - -}*/ diff --git a/sqrt/sqrtdecomposition.go b/sqrt/sqrtdecomposition.go new file mode 100644 index 000000000..34e26fc4a --- /dev/null +++ b/sqrt/sqrtdecomposition.go @@ -0,0 +1,102 @@ +// Package sqrt contains algorithms and data structures that contains a √n in their complexity +package sqrt + +import "math" + +// Sqrt (or Square Root) Decomposition is a technique used for query an array and perform updates +// Inside this package is described its most simple data structure, you can find more at: https://cp-algorithms.com/data_structures/sqrt_decomposition.html +// +// Formally, You can use SqrtDecomposition only if: +// +// Given a function $Query:E_1,...,E_n\rightarrow Q$ +// +// if $\exist unionQ:Q,Q\rightarrow Q$ +// +// s.t. +// +// - $\forall n\in \N > 1, 1\le i 0, E_1,..., E_n\in E \\ query(E_1,...,E_{new},..., E_n)=updateQ(query(E_1,...,E_{old},...,E_n), indexof(E_{old}), E_{new})$ +type SqrtDecomposition[E any, Q any] struct { + querySingleElement func(element E) Q + unionQ func(q1 Q, q2 Q) Q + updateQ func(oldQ Q, oldE E, newE E) (newQ Q) + + elements []E + blocks []Q + blockSize uint64 +} + +// Create a new SqrtDecomposition instance with the parameters as specified by SqrtDecomposition comment +// Assumptions: +// - len(elements) > 0 +func NewSqrtDecomposition[E any, Q any]( + elements []E, + querySingleElement func(element E) Q, + unionQ func(q1 Q, q2 Q) Q, + updateQ func(oldQ Q, oldE E, newE E) (newQ Q), +) *SqrtDecomposition[E, Q] { + sqrtDec := &SqrtDecomposition[E, Q]{ + querySingleElement: querySingleElement, + unionQ: unionQ, + updateQ: updateQ, + elements: elements, + } + sqrt := math.Sqrt(float64(len(sqrtDec.elements))) + blockSize := uint64(sqrt) + numBlocks := uint64(math.Ceil(float64(len(elements)) / float64(blockSize))) + sqrtDec.blocks = make([]Q, numBlocks) + for i := uint64(0); i < uint64(len(elements)); i++ { + if i%blockSize == 0 { + sqrtDec.blocks[i/blockSize] = sqrtDec.querySingleElement(elements[i]) + } else { + sqrtDec.blocks[i/blockSize] = sqrtDec.unionQ(sqrtDec.blocks[i/blockSize], sqrtDec.querySingleElement(elements[i])) + } + } + sqrtDec.blockSize = blockSize + return sqrtDec +} + +// Performs a query from index start to index end (non included) +// Assumptions: +// - start < end +// - start and end are valid +func (s *SqrtDecomposition[E, Q]) Query(start uint64, end uint64) Q { + firstIndexNextBlock := ((start / s.blockSize) + 1) * s.blockSize + q := s.querySingleElement(s.elements[start]) + if firstIndexNextBlock > end { // if in same block + start++ + for start < end { + q = s.unionQ(q, s.querySingleElement(s.elements[start])) + start++ + } + } else { + // left side + start++ + for start < firstIndexNextBlock { + q = s.unionQ(q, s.querySingleElement(s.elements[start])) + start++ + } + + //middle part + endBlock := end / s.blockSize + for i := firstIndexNextBlock / s.blockSize; i < endBlock; i++ { + q = s.unionQ(q, s.blocks[i]) + } + + // right part + for i := endBlock * s.blockSize; i < end; i++ { + q = s.unionQ(q, s.querySingleElement(s.elements[i])) + } + } + return q +} + +// Assumptions: +// - index is valid +func (s *SqrtDecomposition[E, Q]) Update(index uint64, newElement E) { + i := index / s.blockSize + s.blocks[i] = s.updateQ(s.blocks[i], s.elements[index], newElement) + s.elements[index] = newElement +} diff --git a/sqrt/sqrtdecomposition_test.go b/sqrt/sqrtdecomposition_test.go new file mode 100644 index 000000000..7a293c802 --- /dev/null +++ b/sqrt/sqrtdecomposition_test.go @@ -0,0 +1,80 @@ +package sqrt_test + +import ( + "github.com/TheAlgorithms/Go/sqrt" + "testing" +) + +// Query interval +type query struct { + firstIndex uint64 + lastIndex uint64 +} + +type update struct { + index uint64 + value int +} + +func TestSqrtDecomposition(t *testing.T) { + var sqrtDecompositionTestData = []struct { + description string + array []int + updates []update + queries []query + expected []int + }{ + { + description: "test 1-sized array", + array: []int{1}, + queries: []query{{0, 1}}, + expected: []int{1}, + }, + { + description: "test array with size 5", + array: []int{1, 2, 3, 4, 5}, + queries: []query{{0, 5}, {0, 2}, {2, 4}}, + expected: []int{15, 3, 7}, + }, + { + description: "test array with size 5 and updates", + array: []int{1, 2, 3, 4, 5}, + updates: []update{{index: 1, value: 3}, + {index: 2, value: 4}}, + queries: []query{{0, 5}, {0, 2}, {2, 4}}, + expected: []int{17, 4, 8}, + }, + { + description: "test array with size 11 and updates", + array: []int{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, + updates: []update{{index: 2, value: 2}, + {index: 3, value: 3}, + {index: 6, value: 6}}, + queries: []query{{3, 5}, {7, 8}, {3, 7}, {0, 10}}, + expected: []int{4, 1, 11, 18}, + }, + } + for _, test := range sqrtDecompositionTestData { + t.Run(test.description, func(t *testing.T) { + s := sqrt.NewSqrtDecomposition(test.array, + func(e int) int { return e }, + func(q1, q2 int) int { return q1 + q2 }, + func(q, a, b int) int { return q - a + b }, + ) + + for i := 0; i < len(test.updates); i++ { + s.Update(test.updates[i].index, test.updates[i].value) + } + + for i := 0; i < len(test.queries); i++ { + result := s.Query(test.queries[i].firstIndex, test.queries[i].lastIndex) + + if result != test.expected[i] { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expected result: %d\nFound: %d\n", test.expected[i], result) + } + } + + }) + } +} diff --git a/strings/ahocorasick/advancedahocorasick.go b/strings/ahocorasick/advancedahocorasick.go new file mode 100644 index 000000000..c53939eac --- /dev/null +++ b/strings/ahocorasick/advancedahocorasick.go @@ -0,0 +1,82 @@ +package ahocorasick + +import ( + "fmt" + "time" +) + +// Advanced Function performing the Advanced Aho-Corasick algorithm. +// Finds and prints occurrences of each pattern. +func Advanced(t string, p []string) Result { + startTime := time.Now() + occurrences := make(map[int][]int) + ac, f := BuildExtendedAc(p) + current := 0 + for pos := 0; pos < len(t); pos++ { + if GetTransition(current, t[pos], ac) != -1 { + current = GetTransition(current, t[pos], ac) + } else { + current = 0 + } + _, ok := f[current] + if ok { + for i := range f[current] { + if p[f[current][i]] == GetWord(pos-len(p[f[current][i]])+1, pos, t) { //check for word match + newOccurrences := IntArrayCapUp(occurrences[f[current][i]]) + occurrences[f[current][i]] = newOccurrences + occurrences[f[current][i]][len(newOccurrences)-1] = pos - len(p[f[current][i]]) + 1 + } + } + } + } + elapsed := time.Since(startTime) + fmt.Printf("\n\nElapsed %f secs\n", elapsed.Seconds()) + + var resultOccurrences = make(map[string][]int) + for key, value := range occurrences { + resultOccurrences[p[key]] = value + } + + return Result{ + resultOccurrences, + } +} + +// BuildExtendedAc Functions that builds extended Aho Corasick automaton. +func BuildExtendedAc(p []string) (acToReturn map[int]map[uint8]int, f map[int][]int) { + acTrie, stateIsTerminal, f := ConstructTrie(p) + s := make([]int, len(stateIsTerminal)) //supply function + i := 0 //root of acTrie + acToReturn = acTrie + s[i] = -1 + for current := 1; current < len(stateIsTerminal); current++ { + o, parent := GetParent(current, acTrie) + down := s[parent] + for StateExists(down, acToReturn) && GetTransition(down, o, acToReturn) == -1 { + down = s[down] + } + if StateExists(down, acToReturn) { + s[current] = GetTransition(down, o, acToReturn) + if stateIsTerminal[s[current]] { + stateIsTerminal[current] = true + f[current] = ArrayUnion(f[current], f[s[current]]) //F(Current) <- F(Current) union F(S(Current)) + } + } else { + s[current] = i //initial state? + } + } + a := ComputeAlphabet(p) // concat of all patterns in p + for j := range a { + if GetTransition(i, a[j], acToReturn) == -1 { + CreateTransition(i, a[j], i, acToReturn) + } + } + for current := 1; current < len(stateIsTerminal); current++ { + for j := range a { + if GetTransition(current, a[j], acToReturn) == -1 { + CreateTransition(current, a[j], GetTransition(s[current], a[j], acToReturn), acToReturn) + } + } + } + return acToReturn, f +} diff --git a/strings/ahocorasick/advancedahocorasick_test.go b/strings/ahocorasick/advancedahocorasick_test.go new file mode 100644 index 000000000..996651457 --- /dev/null +++ b/strings/ahocorasick/advancedahocorasick_test.go @@ -0,0 +1,63 @@ +package ahocorasick + +import ( + "reflect" + "testing" +) + +var testCases = []struct { + name string + words []string + text string + expected Result +}{ + + { + "String comparison on all patterns found", + []string{"announce", "annual", "annually"}, + "CPM_annual_conferenceannounce_announce_annually_announce", + Result{ + map[string][]int{ + "annual": {4, 39}, + "announce": {21, 30, 48}, + "annually": {39}, + }, + }, + }, + { + "String comparison on not all patterns found", + []string{"announce", "annual", "annually"}, + "CPM_annual_conference_announce", + Result{ + map[string][]int{ + "annual": {4}, + "announce": {22}, + }, + }, + }, + { + "String comparison on not all patterns found", + []string{"announce", "annual", "annually"}, + "CPM_annual_conference_announce", + Result{ + map[string][]int{ + "annual": {4}, + "announce": {22}, + }, + }, + }, +} + +func TestAdvanced(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := AhoCorasick(tc.text, tc.words) + if !reflect.DeepEqual(actual, tc.expected) { + actualString := convertToString(actual) + expectedString := convertToString(tc.expected) + t.Errorf("Expected matches for patterns %s for string '%s' are: patterns and positions found %v, but actual matches are: patterns and positions found %v", + tc.words, tc.text, actualString, expectedString) + } + }) + } +} diff --git a/strings/ahocorasick/ahocorasick.go b/strings/ahocorasick/ahocorasick.go new file mode 100644 index 000000000..e052e7905 --- /dev/null +++ b/strings/ahocorasick/ahocorasick.go @@ -0,0 +1,77 @@ +package ahocorasick + +import ( + "fmt" + "time" +) + +// Result structure to hold occurrences +type Result struct { + occurrences map[string][]int +} + +// AhoCorasick Function performing the Basic Aho-Corasick algorithm. +// Finds and prints occurrences of each pattern. +func AhoCorasick(t string, p []string) Result { + startTime := time.Now() + occurrences := make(map[int][]int) + ac, f, s := BuildAc(p) + current := 0 + for pos := 0; pos < len(t); pos++ { + for GetTransition(current, t[pos], ac) == -1 && s[current] != -1 { + current = s[current] + } + if GetTransition(current, t[pos], ac) != -1 { + current = GetTransition(current, t[pos], ac) + fmt.Printf(" (Continue) \n") + } else { + current = 0 + } + _, ok := f[current] + if ok { + for i := range f[current] { + if p[f[current][i]] == GetWord(pos-len(p[f[current][i]])+1, pos, t) { //check for word match + newOccurrences := IntArrayCapUp(occurrences[f[current][i]]) + occurrences[f[current][i]] = newOccurrences + occurrences[f[current][i]][len(newOccurrences)-1] = pos - len(p[f[current][i]]) + 1 + } + } + } + } + elapsed := time.Since(startTime) + fmt.Printf("\n\nElapsed %f secs\n", elapsed.Seconds()) + var resultOccurrences = make(map[string][]int) + for key, value := range occurrences { + resultOccurrences[p[key]] = value + } + + return Result{ + resultOccurrences, + } +} + +// Functions that builds Aho Corasick automaton. +func BuildAc(p []string) (acToReturn map[int]map[uint8]int, f map[int][]int, s []int) { + acTrie, stateIsTerminal, f := ConstructTrie(p) + s = make([]int, len(stateIsTerminal)) //supply function + i := 0 //root of acTrie + acToReturn = acTrie + s[i] = -1 + for current := 1; current < len(stateIsTerminal); current++ { + o, parent := GetParent(current, acTrie) + down := s[parent] + for StateExists(down, acToReturn) && GetTransition(down, o, acToReturn) == -1 { + down = s[down] + } + if StateExists(down, acToReturn) { + s[current] = GetTransition(down, o, acToReturn) + if stateIsTerminal[s[current]] { + stateIsTerminal[current] = true + f[current] = ArrayUnion(f[current], f[s[current]]) //F(Current) <- F(Current) union F(S(Current)) + } + } else { + s[current] = i //initial state? + } + } + return acToReturn, f, s +} diff --git a/strings/ahocorasick/ahocorasick_test.go b/strings/ahocorasick/ahocorasick_test.go new file mode 100644 index 000000000..366410fa1 --- /dev/null +++ b/strings/ahocorasick/ahocorasick_test.go @@ -0,0 +1,37 @@ +package ahocorasick + +import ( + "fmt" + "reflect" + "strings" + "testing" +) + +func TestAhoCorasick(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := AhoCorasick(tc.text, tc.words) + if !reflect.DeepEqual(actual, tc.expected) { + actualString := convertToString(actual) + expectedString := convertToString(tc.expected) + t.Errorf("Expected matches for patterns %s for string '%s' are: patterns and positions found %v, but actual matches are: patterns and positions found %v", + tc.words, tc.text, actualString, expectedString) + } + }) + } +} + +func convertToString(res Result) string { + var r strings.Builder + for key, val := range res.occurrences { + r.WriteString(fmt.Sprintf("Word: '%s' at positions: ", key)) + for i := range val { + r.WriteString(fmt.Sprintf("%d", val[i])) + if i != len(val)-1 { + r.WriteString(", ") + } + } + r.WriteString(". ") + } + return r.String() +} diff --git a/strings/ahocorasick/patterns.txt b/strings/ahocorasick/patterns.txt new file mode 100644 index 000000000..2fedb65dc --- /dev/null +++ b/strings/ahocorasick/patterns.txt @@ -0,0 +1 @@ +announce annual annually \ No newline at end of file diff --git a/strings/ahocorasick/shared.go b/strings/ahocorasick/shared.go new file mode 100644 index 000000000..700dbcd0b --- /dev/null +++ b/strings/ahocorasick/shared.go @@ -0,0 +1,139 @@ +package ahocorasick + +// ConstructTrie Function that constructs Trie as an automaton for a set of reversed & trimmed strings. +func ConstructTrie(p []string) (trie map[int]map[uint8]int, stateIsTerminal []bool, f map[int][]int) { + trie = make(map[int]map[uint8]int) + stateIsTerminal = make([]bool, 1) + f = make(map[int][]int) + state := 1 + CreateNewState(0, trie) + for i := 0; i < len(p); i++ { + current := 0 + j := 0 + for j < len(p[i]) && GetTransition(current, p[i][j], trie) != -1 { + current = GetTransition(current, p[i][j], trie) + j++ + } + for j < len(p[i]) { + stateIsTerminal = BoolArrayCapUp(stateIsTerminal) + CreateNewState(state, trie) + stateIsTerminal[state] = false + CreateTransition(current, p[i][j], state, trie) + current = state + j++ + state++ + } + if stateIsTerminal[current] { + newArray := IntArrayCapUp(f[current]) + newArray[len(newArray)-1] = i + f[current] = newArray // F(Current) <- F(Current) union {i} + } else { + stateIsTerminal[current] = true + f[current] = []int{i} // F(Current) <- {i} + } + } + return trie, stateIsTerminal, f +} + +// Contains Returns 'true' if array of int's 's' contains int 'e', 'false' otherwise. +func Contains(s []int, e int) bool { + for _, a := range s { + if a == e { + return true + } + } + return false +} + +// GetWord Function that returns word found in text 't' at position range 'begin' to 'end'. +func GetWord(begin, end int, t string) string { + for end >= len(t) { + return "" + } + d := make([]uint8, end-begin+1) + for j, i := 0, begin; i <= end; i, j = i+1, j+1 { + d[j] = t[i] + } + return string(d) +} + +// ComputeAlphabet Function that returns string of all the possible characters in given patterns. +func ComputeAlphabet(p []string) (s string) { + s = p[0] + for i := 1; i < len(p); i++ { + s = s + p[i] + } + return s +} + +// IntArrayCapUp Dynamically increases an array size of int's by 1. +func IntArrayCapUp(old []int) (new []int) { + new = make([]int, cap(old)+1) + copy(new, old) //copy(dst,src) + // old = new + return new +} + +// BoolArrayCapUp Dynamically increases an array size of bool's by 1. +func BoolArrayCapUp(old []bool) (new []bool) { + new = make([]bool, cap(old)+1) + copy(new, old) + // old = new + return new +} + +// ArrayUnion Concats two arrays of int's into one. +func ArrayUnion(to, from []int) (concat []int) { + concat = to + for i := range from { + if !Contains(concat, from[i]) { + concat = IntArrayCapUp(concat) + concat[len(concat)-1] = from[i] + } + } + return concat +} + +// GetParent Function that finds the first previous state of a state and returns it. +// Used for trie where there is only one parent. +func GetParent(state int, at map[int]map[uint8]int) (uint8, int) { + for beginState, transitions := range at { + for c, endState := range transitions { + if endState == state { + return c, beginState + } + } + } + return 0, 0 //unreachable +} + +// CreateNewState Automaton function for creating a new state 'state'. +func CreateNewState(state int, at map[int]map[uint8]int) { + at[state] = make(map[uint8]int) +} + +// CreateTransition Creates a transition for function σ(state,letter) = end. +func CreateTransition(fromState int, overChar uint8, toState int, at map[int]map[uint8]int) { + at[fromState][overChar] = toState +} + +// GetTransition Returns ending state for transition σ(fromState,overChar), '-1' if there is none. +func GetTransition(fromState int, overChar uint8, at map[int]map[uint8]int) (toState int) { + if !StateExists(fromState, at) { + return -1 + } + toState, ok := at[fromState][overChar] + if !ok { + return -1 + } + return toState +} + +// StateExists Checks if state 'state' exists. Returns 'true' if it does, 'false' otherwise. +func StateExists(state int, at map[int]map[uint8]int) bool { + _, ok := at[state] + if !ok || state == -1 || at[state] == nil { + return false + } + return true +} diff --git a/strings/ahocorasick/text.txt b/strings/ahocorasick/text.txt new file mode 100644 index 000000000..e98cf5c73 --- /dev/null +++ b/strings/ahocorasick/text.txt @@ -0,0 +1 @@ +CPM_annual_conference_announce \ No newline at end of file diff --git a/strings/bom/bom.go b/strings/bom/bom.go new file mode 100644 index 000000000..86112f649 --- /dev/null +++ b/strings/bom/bom.go @@ -0,0 +1,228 @@ +package bom + +// User defined. +// Set to true to print various extra stuff out (slows down the execution) +// Set to false for quick and quiet execution. +// const debugMode bool = false + +// User defined. +// Set to true to read input from two command line arguments +// Set to false to read input from two files "pattern.txt" and "text.txt" +// const commandLineInput bool = false + +// Implementation of Backward Oracle Matching algorithm (Factor based approach). +// Requires either a two command line arguments separated by a single space, +// or two files in the same folder: "pattern.txt" containing the string to +// be searched for, "text.txt" containing the text to be searched in. +// func main() { +// if commandLineInput == true { // case of command line input +// args := os.Args +// if len(args) <= 2 { +// log.Fatal("Not enough arguments. Two string arguments separated by spaces are required!") +// } +// pattern := args[1] +// s := args[2] +// for i := 3; i < len(args); i++ { +// s = s + " " + args[i] +// } +// if len(args[1]) > len(s) { +// log.Fatal("Pattern is longer than text!") +// } +// if debugMode == true { +// fmt.Printf("\nRunning: Backward Oracle Matching algorithm.\n\n") +// fmt.Printf("Search word (%d chars long): %q.\n", len(args[1]), pattern) +// fmt.Printf("Text (%d chars long): %q.\n\n", len(s), s) +// } else { +// fmt.Printf("\nRunning: Backward Oracle Matching algorithm.\n\n") +// } +// bom(s, pattern) +// } else if commandLineInput == false { // case of file line input +// patFile, err := ioutil.ReadFile("pattern.txt") +// if err != nil { +// log.Fatal(err) +// } +// textFile, err := ioutil.ReadFile("text.txt") +// if err != nil { +// log.Fatal(err) +// } +// if len(patFile) > len(textFile) { +// log.Fatal("Pattern is longer than text!") +// } +// if debugMode == true { +// fmt.Printf("\nRunning: Backward Oracle Matching algorithm.\n\n") +// fmt.Printf("Search word (%d chars long): %q.\n", len(patFile), patFile) +// fmt.Printf("Text (%d chars long): %q.\n\n", len(textFile), textFile) +// } else { +// fmt.Printf("\nRunning: Backward Oracle Matching algorithm.\n\n") +// } +// bom(string(textFile), string(patFile)) +// } +// } + +// // Function bom performing the Backward Oracle Matching algorithm. +// // Prints whether the word/pattern was found + positions of possible multiple occurrences +// // or that the word was not found. +// func bom(t, p string) { +// startTime := time.Now() +// n, m := len(t), len(p) +// var current, j, pos int +// oracle := oracleOnLine(reverse(p)) +// occurrences := make([]int, len(t)) +// currentOcc := 0 +// pos = 0 +// if debugMode == true { +// fmt.Printf("\n\nWe are reading backwards in %q, searching for %q\n\nat position %d:\n", t, p, pos+m-1) +// } +// for pos <= n-m { +// current = 0 //initial state of the oracle +// j = m +// for j > 0 && stateExists(current, oracle) { +// if debugMode == true { +// prettyPrint(current, j, n, pos, t, oracle) +// } +// current = getTransition(current, t[pos+j-1], oracle) +// j-- +// } +// if stateExists(current, oracle) { +// if debugMode == true { +// fmt.Printf(" We got an occurrence!") +// } +// occurrences[currentOcc] = pos +// currentOcc++ +// } +// pos = pos + j + 1 +// if pos+m-1 < len(t) { +// if debugMode == true { +// fmt.Printf("\n\nposition %d:\n", pos+m-1) +// } +// } +// } +// elapsed := time.Since(startTime) +// fmt.Printf("\n\nElapsed %f secs\n", elapsed.Seconds()) +// fmt.Printf("\n\n") +// if currentOcc > 0 { +// fmt.Printf("Word %q was found %d times at positions: ", p, currentOcc) +// for k := 0; k < currentOcc-1; k++ { +// fmt.Printf("%d, ", occurrences[k]) +// } +// fmt.Printf("%d", occurrences[currentOcc-1]) +// fmt.Printf(".\n") +// } +// if currentOcc == 0 { +// fmt.Printf("\nWord was not found.\n") +// } +// return +// } + +// // Construction of the factor oracle automaton for a word p. +// func oracleOnLine(p string) (oracle map[int]map[uint8]int) { +// if debugMode == true { +// fmt.Printf("Oracle construction: \n") +// } +// oracle = make(map[int]map[uint8]int) +// supply := make([]int, len(p)+2) // supply function +// createNewState(0, oracle) +// supply[0] = -1 +// var orP string +// for j := 0; j < len(p); j++ { +// oracle, orP = oracleAddLetter(oracle, supply, orP, p[j]) +// } +// return oracle +// } + +// // Adds one letter to the oracle. +// func oracleAddLetter(oracle map[int]map[uint8]int, supply []int, orP string, o uint8) (oracleToReturn map[int]map[uint8]int, orPToReturn string) { +// m := len(orP) +// var s int +// createNewState(m+1, oracle) +// createTransition(m, o, m+1, oracle) +// k := supply[m] +// for k > -1 && getTransition(k, o, oracle) == -1 { +// createTransition(k, o, m+1, oracle) +// k = supply[k] +// } +// if k == -1 { +// s = 0 +// } else { +// s = getTransition(k, o, oracle) +// } +// supply[m+1] = s +// return oracle, orP + string(o) +// } + +// // Function that takes a single string and reverses it. +// // @author 'Walter' http://stackoverflow.com/a/10043083 +// func reverse(s string) string { +// l := len(s) +// m := make([]rune, l) +// for _, c := range s { +// l-- +// m[l] = c +// } +// return string(m) +// } + +// // Automaton function for creating a new state. +// func createNewState(state int, at map[int]map[uint8]int) { +// at[state] = make(map[uint8]int) +// if debugMode == true { +// fmt.Printf("\ncreated state %d", state) +// } +// } + +// // Creates a transition for function σ(state,letter) = end. +// func createTransition(fromState int, overChar uint8, toState int, at map[int]map[uint8]int) { +// at[fromState][overChar] = toState +// if debugMode == true { +// fmt.Printf("\n σ(%d,%c)=%d;", fromState, overChar, toState) +// } +// } + +// // Returns ending state for transition σ(fromState,overChar), -1 if there is none. +// func getTransition(fromState int, overChar uint8, at map[int]map[uint8]int) (toState int) { +// if !stateExists(fromState, at) { +// return -1 +// } +// toState, ok := at[fromState][overChar] +// if ok == false { +// return -1 +// } +// return toState +// } + +// // Checks if state exists. Returns true if it does, false otherwise. +// func stateExists(state int, at map[int]map[uint8]int) bool { +// _, ok := at[state] +// if !ok || state == -1 || at[state] == nil { +// return false +// } +// return true +// } + +// // Just some printing of extra information about what the algorithm does. +// func prettyPrint(current int, j int, n int, pos int, t string, oracle map[int]map[uint8]int) { +// if current == 0 && !(getTransition(current, t[pos+j-1], oracle) == -1) { +// fmt.Printf("\n -->(%d)---(%c)--->(%d)", current, t[pos+j-1], getTransition(current, t[pos+j-1], oracle)) +// } else if getTransition(current, t[pos+j-1], oracle) == -1 && current != 0 { +// fmt.Printf("\n (%d)---(%c) ", current, t[pos+j-1]) +// } else if getTransition(current, t[pos+j-1], oracle) == -1 && current == 0 { +// fmt.Printf("\n -->(%d)---(%c) ", current, t[pos+j-1]) +// } else { +// fmt.Printf("\n (%d)---(%c)--->(%d)", current, t[pos+j-1], getTransition(current, t[pos+j-1], oracle)) +// } +// fmt.Printf(" ") +// for a := 0; a < pos+j-1; a++ { +// fmt.Printf("%c", t[a]) +// } +// if getTransition(current, t[pos+j-1], oracle) == -1 { +// fmt.Printf("[%c]", t[pos+j-1]) +// } else { +// fmt.Printf("[%c]", t[pos+j-1]) +// } +// for a := pos + j; a < n; a++ { +// fmt.Printf("%c", t[a]) +// } +// if getTransition(current, t[pos+j-1], oracle) == -1 { +// fmt.Printf(" FAIL on the character[%c]", t[pos+j-1]) +// } +// } diff --git a/strings/charoccurrence.go b/strings/charoccurrence.go new file mode 100644 index 000000000..71c3056b1 --- /dev/null +++ b/strings/charoccurrence.go @@ -0,0 +1,21 @@ +// charoccurrence.go +// description: An algorithm which counts the number +// of times a character occurred in a string. +// author(s) [Moein](https://github.com/mo1ein) +// see charoccurrence_test.go + +package strings + +// CountChars counts the number of a times a character +// has occurred in the provided string argument and +// returns a map with `rune` as keys and the count as value. +func CountChars(text string) map[rune]int { + charMap := make(map[rune]int, 0) + for _, c := range text { + if _, ok := charMap[c]; !ok { + charMap[c] = 0 + } + charMap[c]++ + } + return charMap +} diff --git a/strings/charoccurrence_test.go b/strings/charoccurrence_test.go new file mode 100644 index 000000000..0f284acda --- /dev/null +++ b/strings/charoccurrence_test.go @@ -0,0 +1,39 @@ +package strings_test + +import ( + "github.com/TheAlgorithms/Go/strings" + "reflect" + "testing" +) + +func TestCountChars(t *testing.T) { + var testCases = []struct { + name string + input string + expected map[rune]int + }{ + { + "english text", + "hello world!", + map[rune]int{32: 1, 33: 1, 100: 1, 101: 1, 104: 1, 108: 3, 111: 2, 114: 1, 119: 1}, + }, + { + "chinese text", + " 世界 ", + map[rune]int{32: 2, 19990: 1, 30028: 1}, + }, + { + "persian text", + "سلام دنیا!", + map[rune]int{32: 1, 33: 1, 1575: 2, 1583: 1, 1587: 1, 1604: 1, 1605: 1, 1606: 1, 1740: 1}, + }, + } + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + funcResult := strings.CountChars(test.input) + if !reflect.DeepEqual(test.expected, funcResult) { + t.Errorf("expected: %v, got %v", test.expected, funcResult) + } + }) + } +} diff --git a/other/string_combinations.go b/strings/combination/combination.go similarity index 74% rename from other/string_combinations.go rename to strings/combination/combination.go index 8d04fc1a8..42bbdee8b 100644 --- a/other/string_combinations.go +++ b/strings/combination/combination.go @@ -1,16 +1,16 @@ -/* - String combinations in Go -*/ -package main +// Package combination ... +package combination import "fmt" +// Combinations structure with in and out rune type Combinations struct { out []rune in []rune } -func startCombinations(input string) { +// Start ... +func Start(input string) { c := &Combinations{ in: []rune(input), } @@ -18,6 +18,7 @@ func startCombinations(input string) { c.Combine(0) } +// Combine ... func (c *Combinations) Combine(seed int) { inLen := len(c.in) for i := seed; i < inLen-1; i++ { diff --git a/strings/doc.go b/strings/doc.go new file mode 100644 index 000000000..786876fec --- /dev/null +++ b/strings/doc.go @@ -0,0 +1,3 @@ +// Package strings is a package that contains all algorithms +// that are used to analyse and manipulate strings. +package strings diff --git a/strings/generateparentheses/generateparentheses.go b/strings/generateparentheses/generateparentheses.go new file mode 100644 index 000000000..3d466761b --- /dev/null +++ b/strings/generateparentheses/generateparentheses.go @@ -0,0 +1,34 @@ +// generateparenthesesgo +// description: Generate Parentheses +// details: +// Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses. +// author(s) [red_byte](https://github.com/i-redbyte) +// see generateparentheses_test.go + +package generateparentheses + +import "strings" + +func GenerateParenthesis(n int) []string { + result := make([]string, 0) + maxLen := 2 * n + var recursiveComputation func(s []string, left int, right int) + recursiveComputation = func(s []string, left int, right int) { + if len(s) == maxLen { + result = append(result, strings.Join(s, "")) + return + } + if left < n { + s = append(s, "(") + recursiveComputation(s, left+1, right) + s = s[:len(s)-1] + } + if right < left { + s = append(s, ")") + recursiveComputation(s, left, right+1) + _ = s[:len(s)-1] + } + } + recursiveComputation(make([]string, 0), 0, 0) + return result +} diff --git a/strings/generateparentheses/generateparentheses_test.go b/strings/generateparentheses/generateparentheses_test.go new file mode 100644 index 000000000..0013b5ba6 --- /dev/null +++ b/strings/generateparentheses/generateparentheses_test.go @@ -0,0 +1,21 @@ +// generateparentheses_test.go +// description: Generate Parentheses +// author(s) [red_byte](https://github.com/i-redbyte) +// see generateparentheses.go + +package generateparentheses + +import "testing" + +func TestGenerateParenthesis(t *testing.T) { + t.Run("GenerateParenthesis", func(t *testing.T) { + result := GenerateParenthesis(3) + t.Log(result) + exp := []string{"((()))", "(()())", "(())()", "()(())", "()()()"} + for i, v := range result { + if v != exp[i] { + t.Errorf("Wrong result! Expected:%s, returned:%s ", result[i], exp[i]) + } + } + }) +} diff --git a/strings/genetic/genetic.go b/strings/genetic/genetic.go new file mode 100644 index 000000000..a91029433 --- /dev/null +++ b/strings/genetic/genetic.go @@ -0,0 +1,197 @@ +// Package genetic provides functions to work with strings +// using genetic algorithm. https://en.wikipedia.org/wiki/Genetic_algorithm +// +// Author: D4rkia +package genetic + +import ( + "errors" + "fmt" + "math/rand" + "sort" + "strconv" + "time" + "unicode/utf8" +) + +// Population item represent a single step in the evolution process. +// One can think of population item as a single species. +// Key stands for the actual data entity of the species, which is a string +// in current implementation. Key can be interpreted as species DNA. +// Value shows how close this species to the desired target, where 1 means, +// that species DNA equals to the targeted one, 0 for no matchings in the DNA. +// +// **Note** In the current implementation species DNA length is suppose to be +// equal to the target length for algorithm to work. +type PopulationItem struct { + Key string + Value float64 +} + +// Conf stands for configurations set provided to GeneticString function. +type Conf struct { + // Maximum size of the population. + // Bigger could be faster but more memory expensive. + PopulationNum int + + // Number of elements selected in every generation for evolution + // the selection takes. Place from the best to the worst of that + // generation must be smaller than PopulationNum. + SelectionNum int + + // Probability that an element of a generation can mutate changing one of + // its genes this guarantees that all genes will be used during evolution. + MutationProb float64 + + // Enables debugging output to the console. + Debug bool +} + +// Result structure contains generation process statistics, as well as the +// best resulted population item. +type Result struct { + // Number of generations steps performed. + Generation int + + // Number of generated population items. + Analyzed int + + // Result of generation with the best Value. + Best PopulationItem +} + +// GeneticString generates PopulationItem based on the imputed target +// string, and a set of possible runes to build a string with. In order +// to optimise string generation additional configurations can be provided +// with Conf instance. Empty instance of Conf (&Conf{}) can be provided, +// then default values would be set. +// +// Link to the same algorithm implemented in python: +// https://github.com/TheAlgorithms/Python/blob/master/genetic_algorithm/basic_string.py +func GeneticString(target string, charmap []rune, conf *Conf) (*Result, error) { + populationNum := conf.PopulationNum + if populationNum == 0 { + populationNum = 200 + } + + selectionNum := conf.SelectionNum + if selectionNum == 0 { + selectionNum = 50 + } + + // Verify if 'populationNum' s bigger than 'selectionNum' + if populationNum < selectionNum { + return nil, errors.New("populationNum must be bigger than selectionNum") + } + + mutationProb := conf.MutationProb + if mutationProb == .0 { + mutationProb = .4 + } + + debug := conf.Debug + + // Just a seed to improve randomness required by the algorithm + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + + // Verify that the target contains no genes besides the ones inside genes variable. + for position, r := range target { + invalid := true + for _, n := range charmap { + if n == r { + invalid = false + } + } + if invalid { + message := fmt.Sprintf("character not available in charmap at position: %v", position) + return nil, errors.New(message) + } + } + + // Generate random starting population + pop := make([]PopulationItem, populationNum) + for i := 0; i < populationNum; i++ { + key := "" + for x := 0; x < utf8.RuneCountInString(target); x++ { + choice := rnd.Intn(len(charmap)) + key += string(charmap[choice]) + } + pop[i] = PopulationItem{key, 0} + } + + // Just some logs to know what the algorithms is doing + gen, generatedPop := 0, 0 + + // This loop will end when we will find a perfect match for our target + for { + gen++ + generatedPop += len(pop) + + // Random population created now it's time to evaluate + for i, item := range pop { + pop[i].Value = 0 + itemKey, targetRune := []rune(item.Key), []rune(target) + for x := 0; x < len(target); x++ { + if itemKey[x] == targetRune[x] { + pop[i].Value++ + } + } + pop[i].Value = pop[i].Value / float64(len(targetRune)) + } + sort.SliceStable(pop, func(i, j int) bool { return pop[i].Value > pop[j].Value }) + + // Check if there is a matching evolution + if pop[0].Key == target { + break + } + + // Print the best resultPrint the Best result every 10 generations + // just to know that the algorithm is working + if debug && gen%10 == 0 { + fmt.Println("Generation:", strconv.Itoa(gen), "Analyzed:", generatedPop, "Best:", pop[0]) + } + + // Generate a new population vector keeping some of the best evolutions + // Keeping this avoid regression of evolution + var popChildren []PopulationItem + popChildren = append(popChildren, pop[0:int(selectionNum/3)]...) + + // This is Selection + for i := 0; i < int(selectionNum); i++ { + parent1 := pop[i] + // Generate more child proportionally to the fitness score + nChild := (parent1.Value * 100) + 1 + if nChild >= 10 { + nChild = 10 + } + for x := 0.0; x < nChild; x++ { + parent2 := pop[rnd.Intn(selectionNum)] + // Crossover + split := rnd.Intn(utf8.RuneCountInString(target)) + child1 := append([]rune(parent1.Key)[:split], []rune(parent2.Key)[split:]...) + child2 := append([]rune(parent2.Key)[:split], []rune(parent1.Key)[split:]...) + // Clean fitness value + // Mutate + if rnd.Float64() < mutationProb { + child1[rnd.Intn(len(child1))] = charmap[rnd.Intn(len(charmap))] + } + if rnd.Float64() < mutationProb { + child2[rnd.Intn(len(child2))] = charmap[rnd.Intn(len(charmap))] + } + // Push into 'popChildren' + popChildren = append(popChildren, PopulationItem{string(child1), 0}) + popChildren = append(popChildren, PopulationItem{string(child2), 0}) + + // Check if the population has already reached the maximum value and if so, + // break the cycle. If this check is disabled the algorithm will take + // forever to compute large strings but will also calculate small string in + // a lot fewer generationsù + if len(popChildren) >= selectionNum { + break + } + } + } + pop = popChildren + } + return &Result{gen, generatedPop, pop[0]}, nil +} diff --git a/strings/genetic/geneticalgorithm_test.go b/strings/genetic/geneticalgorithm_test.go new file mode 100644 index 000000000..0971331fd --- /dev/null +++ b/strings/genetic/geneticalgorithm_test.go @@ -0,0 +1,25 @@ +package genetic + +import ( + "testing" +) + +func TestSimple(t *testing.T) { + target := "This is a genetic algorithm to evaluate, combine, evolve and mutate a string!" + charmap := []rune(" ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz.,;!?+-*#@^'èéòà€ù=)(&%$£/\\") + + res, err := GeneticString(target, charmap, &Conf{}) + if err != nil { + t.Errorf("Unexpected error: %v\n", err) + } + + got := res.Best + + if got.Value != float64(1.0) { + t.Errorf("Target value not reached\nwant: %f\n, got: %f\n", float64(1.0), got.Value) + } + + if got.Key != target { + t.Errorf("Target string not reached\nwant: %s\n, got: %s\n", target, got.Key) + } +} diff --git a/strings/guid/guid.go b/strings/guid/guid.go new file mode 100644 index 000000000..36cc906a7 --- /dev/null +++ b/strings/guid/guid.go @@ -0,0 +1,48 @@ +// guid.go +// description: Generate random globally unique identifiers (GUIDs). +// details: +// A GUID (globally unique identifier) is a 128-bit text string that +// represents an identification (ID). Organizations generate GUIDs when +// a unique reference number is needed to identify information on +// a computer or network. A GUID can be used to ID hardware, software, +// accounts, documents and other items. The term is also often used in +// software created by Microsoft. +// See more information on: https://en.wikipedia.org/wiki/Universally_unique_identifier +// author(s) [cheatsnake](https://github.com/cheatsnake) +// see guid_test.go + +// Package guid provides facilities for generating random globally unique identifiers. +package guid + +import ( + "crypto/rand" + "fmt" + "math/big" + "strings" +) + +const pattern string = "xxxxxxxx-xxxx-4xxx-xxxx-xxxxxxxxxxxx" +const versionIndex int = 14 + +// New returns a randomly generated global unique identifier. +func New() (string, error) { + var guid strings.Builder + + for i, ch := range pattern { + if i == versionIndex { + guid.WriteRune(ch) + continue + } + if ch == '-' { + guid.WriteRune(ch) + continue + } + random, err := rand.Int(rand.Reader, big.NewInt(16)) + if err != nil { + return "", err + } + guid.WriteString(fmt.Sprintf("%x", random.Int64())) + } + + return guid.String(), nil +} diff --git a/strings/guid/guid_test.go b/strings/guid/guid_test.go new file mode 100644 index 000000000..a9e66c95e --- /dev/null +++ b/strings/guid/guid_test.go @@ -0,0 +1,68 @@ +package guid + +import ( + "strings" + "testing" +) + +func TestNew(t *testing.T) { + t.Run("check for allowed characters", func(t *testing.T) { + allowedChars := "0123456789abcdef-" + guid, err := New() + if err != nil { + t.Errorf(`the test failed, an error occurred: %s`, err.Error()) + } + + for _, char := range guid { + if !strings.Contains(allowedChars, string(char)) { + t.Errorf(`allowed only "%s" characters, but got %v`, allowedChars, char) + } + } + }) + + t.Run("check string length", func(t *testing.T) { + guid, err := New() + if err != nil { + t.Errorf(`the test failed, an error occurred: %s`, err.Error()) + } + + if len(guid) != len(pattern) { + t.Errorf(`the length of the string should be "%d", but got %d`, len(pattern), len(guid)) + } + }) + + t.Run("check for version index", func(t *testing.T) { + expected := "4" + versionIndex := strings.Index(pattern, expected) + guid, err := New() + if err != nil { + t.Errorf(`the test failed, an error occurred: %s`, err.Error()) + } + + result := string(guid[versionIndex]) + + if expected != result { + t.Errorf(`at the index %d should be %s, but got %s`, versionIndex, expected, result) + } + }) + + t.Run("check the number of dashes", func(t *testing.T) { + expected := strings.Count(pattern, "-") + guid, err := New() + if err != nil { + t.Errorf(`the test failed, an error occurred: %s`, err.Error()) + } + + result := strings.Count(guid, "-") + + if expected != result { + t.Errorf(`the length of the string should be "%d", but got %d`, len(pattern), len(guid)) + } + }) +} + +func BenchmarkNew(b *testing.B) { + for i := 0; i < b.N; i++ { + _, _ = New() + } +} diff --git a/strings/hamming/hammingdistance.go b/strings/hamming/hammingdistance.go new file mode 100644 index 000000000..a8c41f3fd --- /dev/null +++ b/strings/hamming/hammingdistance.go @@ -0,0 +1,31 @@ +/* +This algorithm calculates the hamming distance between two equal length strings. +The Hamming distance between two equal-length strings of symbols is the number of positions +at which the corresponding symbols are different: +https://en.wikipedia.org/wiki/Hamming_distance + +Note that we didn't consider strings as an array of bytes, therefore, we didn't use the XOR operator. +In this case, we used a simple loop to compare each character of the strings, and if they are different, +we increment the hamming distance by 1. + +Parameters: two strings to compare +Output: distance between both strings */ + +package hamming + +import "errors" + +func Distance(str1, str2 string) (int, error) { + if len(str1) != len(str2) { + return -1, errors.New("strings must have a same length") + } + + hammingDistance := 0 + for i := 0; i < len(str1); i++ { + if str1[i] != str2[i] { + hammingDistance++ + } + } + + return hammingDistance, nil +} diff --git a/strings/hamming/hammingdistance_test.go b/strings/hamming/hammingdistance_test.go new file mode 100644 index 000000000..663c4daee --- /dev/null +++ b/strings/hamming/hammingdistance_test.go @@ -0,0 +1,56 @@ +package hamming + +import "testing" + +var testCases = []struct { + name string + string1 string + string2 string + expected int +}{ + { + "empty strings", + "", + "", + 0, + }, + { + "single character strings", + "A", + "A", + 0, + }, + { + "two different strings with a same length", + "TestString 1", + "TestString 2", + 1, + }, + { + "two different strings with a different length", + "TestString1", + "TestString", + -1, + }, + { + "two same strings with a same length", + "TestString", + "TestString", + 0, + }, +} + +func TestHammingDistance(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual, err := Distance(tc.string1, tc.string2) + if err != nil { + if tc.expected != -1 { + t.Fatalf("Expected no error, but got %v", err) + } + } else if actual != tc.expected { + t.Errorf("Expected Hamming distance between strings: '%s' and '%s' is %v, but got: %v", tc.string1, tc.string2, tc.expected, actual) + } + }) + } +} diff --git a/strings/horspool/horspool.go b/strings/horspool/horspool.go new file mode 100644 index 000000000..1611c0ce8 --- /dev/null +++ b/strings/horspool/horspool.go @@ -0,0 +1,60 @@ +// Implementation of the +// [Boyer–Moore–Horspool algorithm](https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm) + +package horspool + +import "errors" + +var ErrNotFound = errors.New("pattern was not found in the input string") + +func Horspool(t, p string) (int, error) { + // in order to handle multy-byte character properly + // the input is converted into rune arrays + return horspool([]rune(t), []rune(p)) +} + +func horspool(t, p []rune) (int, error) { + shiftMap := computeShiftMap(t, p) + pos := 0 + for pos <= len(t)-len(p) { + if isMatch(pos, t, p) { + return pos, nil + } + if pos+len(p) >= len(t) { + // because the remaining length of the input string + // is the same as the length of the pattern + // and it does not match the pattern + // it is impossible to find the pattern + break + } + + // because of the check above + // t[pos+len(p)] is defined + pos += shiftMap[t[pos+len(p)]] + } + + return -1, ErrNotFound +} + +// Checks if the array p matches the subarray of t starting at pos. +// Note that backward iteration. +// There are [other](https://en.wikipedia.org/wiki/Boyer%E2%80%93Moore%E2%80%93Horspool_algorithm#Tuning_the_comparison_loop) +// approaches possible. +func isMatch(pos int, t, p []rune) bool { + j := len(p) + for j > 0 && t[pos+j-1] == p[j-1] { + j-- + } + return j == 0 +} + +func computeShiftMap(t, p []rune) (res map[rune]int) { + res = make(map[rune]int) + for _, tCode := range t { + res[tCode] = len(p) + } + for i, pCode := range p { + res[pCode] = len(p) - i + } + return res +} diff --git a/strings/horspool/horspool_test.go b/strings/horspool/horspool_test.go new file mode 100644 index 000000000..6c500f3f2 --- /dev/null +++ b/strings/horspool/horspool_test.go @@ -0,0 +1,68 @@ +// horspool_test.go +// description: Tests for horspool +// see horspool.go + +package horspool + +import "testing" +import "fmt" + +func TestLHorspool(t *testing.T) { + testCases := []struct { + input string + pattern string + expected int + }{ + {"aaaaXaaa", "X", 4}, + {"aaaaXXaa", "XX", 4}, + {"Xaaab", "X", 0}, + {"XYaab", "XY", 0}, + {"abcefghXYZ", "XYZ", 7}, + {"abcefgh€YZ⌘", "€YZ", 7}, + {"⌘bcefgh€YZ⌘", "€YZ", 7}, + {"abc", "abc", 0}, + {"", "", 0}, + {"a", "", 0}, + {"a", "a", 0}, + {"aa", "a", 0}, + {"aa", "aa", 0}, + } + for _, tc := range testCases { + t.Run(fmt.Sprint("test with ", tc.input, " ", tc.pattern), func(t *testing.T) { + result, curError := Horspool(tc.input, tc.pattern) + if curError != nil { + t.Fatalf("Got unexpected error") + } + if tc.expected != result { + t.Fatalf("expected %d, got %d", tc.expected, result) + } + }) + } +} + +func TestLHorspoolNotExisintPattern(t *testing.T) { + testCases := []struct { + input string + pattern string + }{ + {"", "X"}, + {"X", "Y"}, + {"X", "XX"}, + {"aaaaaaaXaXaaaa", "XXX"}, + {"aaaaaaaXaX", "XXX"}, + {"XaX", "XXX"}, + {"XaX", "XXX"}, + {"\xe2\x8c\x98", "\x98"}, + } + for _, tc := range testCases { + t.Run(fmt.Sprint("test with ", tc.input, " ", tc.pattern), func(t *testing.T) { + result, curError := Horspool(tc.input, tc.pattern) + if curError != ErrNotFound { + t.Fatalf("Got unexpected error") + } + if result != -1 { + t.Fatalf("expected -1, got %d", result) + } + }) + } +} diff --git a/strings/isisogram.go b/strings/isisogram.go new file mode 100644 index 000000000..1a3c1a55a --- /dev/null +++ b/strings/isisogram.go @@ -0,0 +1,71 @@ +// Checks if a given string is an isogram. +// A first-order isogram is a word in which no letter of the alphabet occurs more than once. +// A second-order isogram is a word in which each letter appears twice. +// A third-order isogram is a word in which each letter appears three times. +// wiki: https://en.wikipedia.org/wiki/Heterogram_(literature)#Isograms +// Author: M3talM0nk3y + +package strings + +import ( + "errors" + "regexp" + "strings" +) + +type IsogramOrder int + +const ( + First IsogramOrder = iota + 1 + Second + Third +) + +func hasDigit(text string) bool { + re := regexp.MustCompile(`\d`) + return re.MatchString(text) +} + +func hasSymbol(text string) bool { + re := regexp.MustCompile(`[-!@#$%^&*()+]`) + return re.MatchString(text) +} + +func IsIsogram(text string, order IsogramOrder) (bool, error) { + if order < First || order > Third { + return false, errors.New("Invalid isogram order provided") + } + + text = strings.ToLower(text) + text = strings.Join(strings.Fields(text), "") + + if hasDigit(text) || hasSymbol(text) { + return false, errors.New("Cannot contain numbers or symbols") + } + + letters := make(map[string]int) + for _, c := range text { + l := string(c) + if _, ok := letters[l]; ok { + letters[l] += 1 + + if letters[l] > 3 { + return false, nil + } + + continue + } + letters[l] = 1 + } + + mapVals := make(map[int]bool) + for _, v := range letters { + mapVals[v] = true + } + + if _, ok := mapVals[int(order)]; ok && len(mapVals) == 1 { + return true, nil + } + + return false, nil +} diff --git a/strings/isisogram_test.go b/strings/isisogram_test.go new file mode 100644 index 000000000..0b54333e6 --- /dev/null +++ b/strings/isisogram_test.go @@ -0,0 +1,131 @@ +package strings_test + +import ( + "errors" + "testing" + + "github.com/TheAlgorithms/Go/strings" +) + +var testCases = []struct { + name string + input string + order strings.IsogramOrder + expectedVal bool + expectedErr error +}{ + { + "Alphanumeric string 1", + "copy1", + 1, + false, + errors.New("Cannot contain numbers or symbols"), + }, + { + "Alphanumeric string 2", + "copy1sentence", + 1, + false, + errors.New("Cannot contain numbers or symbols"), + }, + { + "Alphanumeric string 3", + "copy1 sentence with space", + 1, + false, + errors.New("Cannot contain numbers or symbols"), + }, + { + "Alphabetic string 1", + "allowance", + 1, + false, + nil, + }, + { + "Alphabetic string 2", + "My Doodle", + 1, + false, + nil, + }, + { + "Alphabetic string with symbol", + "Isogram!", + 1, + false, + errors.New("Cannot contain numbers or symbols"), + }, + { + "Isogram string 1", + "Uncopyrightable", + 1, + true, + nil, + }, + { + "Second order isogram 1", + "Caucasus", + 2, + true, + nil, + }, + { + "Second order isogram 2", + "Couscous", + 2, + true, + nil, + }, + { + "Third order isogram 1", + "Deeded", + 3, + true, + nil, + }, + { + "Third order isogram 2", + "Sestettes", + 3, + true, + nil, + }, + { + "Not an isogram", + "Pneumonoultramicroscopicsilicovolcanoconiosis", + 1, + false, + nil, + }, + { + "Not an isogram", + "Randomstring", + 4, + false, + errors.New("Invalid isogram order provided"), + }, + { + "Third order isogram checked as first order", + "Deeded", + 1, + false, + nil, + }, +} + +func TestIsIsogram(t *testing.T) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + actualVal, actualErr := strings.IsIsogram(test.input, test.order) + + if actualErr != nil && test.expectedErr.Error() != actualErr.Error() { + t.Errorf("Expected to be '%v' for string %s but was '%v'.", test.expectedErr, test.input, actualErr) + } + + if test.expectedVal != actualVal { + t.Errorf("Expected to be '%v' for string %s but was '%v'.", test.expectedVal, test.input, actualVal) + } + }) + } +} diff --git a/strings/issubsequence.go b/strings/issubsequence.go new file mode 100644 index 000000000..8d34177e9 --- /dev/null +++ b/strings/issubsequence.go @@ -0,0 +1,35 @@ +// Checks if a given string is a subsequence of another string. +// A subsequence of a given string is a string that can be derived from the given +// string by deleting some or no characters without changing the order of the +// remaining characters. (i.e., "dpr" is a subsequence of "depqr" while "drp" is not). +// Author: sanjibgirics + +package strings + +// Returns true if s is subsequence of t, otherwise return false. +func IsSubsequence(s string, t string) bool { + if len(s) > len(t) { + return false + } + + if s == t { + return true + } + + if len(s) == 0 { + return true + } + + sIndex := 0 + for tIndex := 0; tIndex < len(t); tIndex++ { + if s[sIndex] == t[tIndex] { + sIndex++ + } + + if sIndex == len(s) { + return true + } + } + + return false +} diff --git a/strings/issubsequence_test.go b/strings/issubsequence_test.go new file mode 100644 index 000000000..1b8c4cba4 --- /dev/null +++ b/strings/issubsequence_test.go @@ -0,0 +1,75 @@ +package strings_test + +import ( + "reflect" + "testing" + + "github.com/TheAlgorithms/Go/strings" +) + +func TestIsSubsequence(t *testing.T) { + var testCases = []struct { + name string + s string + t string + expected bool + }{ + { + "Valid case 1 ", + "ace", + "abcde", + true, + }, + { + "Invalid case 1", + "aec", + "abcde", + false, + }, + { + "Empty strings", + "", + "", + true, + }, + { + "s is more then t", + "aeccccc", + "abcde", + false, + }, + { + "s is empty", + "", + "abcde", + true, + }, + { + "Equal strings", + "aec", + "aec", + true, + }, + { + "Valid case 2", + "pyr", + "wpxqyrz", + true, + }, + { + "Invalid case 2", + "prx", + "wpxqyrz", + false, + }, + } + + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + funcResult := strings.IsSubsequence(test.s, test.t) + if !reflect.DeepEqual(test.expected, funcResult) { + t.Errorf("expected: %v, got %v", test.expected, funcResult) + } + }) + } +} diff --git a/strings/kmp/kmp.go b/strings/kmp/kmp.go new file mode 100644 index 000000000..cef57d7d1 --- /dev/null +++ b/strings/kmp/kmp.go @@ -0,0 +1,49 @@ +package kmp + +// Kmp Function kmp performing the Knuth-Morris-Pratt algorithm. +func Kmp(word, text string, patternTable []int) []int { + if len(word) > len(text) { + return nil + } + + var ( + i, j int + matches []int + ) + for i+j < len(text) { + + if word[j] == text[i+j] { + j++ + if j == len(word) { + matches = append(matches, i) + + i = i + j + j = 0 + } + } else { + i = i + j - patternTable[j] + if patternTable[j] > -1 { + j = patternTable[j] + } else { + j = 0 + } + } + } + return matches +} + +// table building for kmp algorithm. +func table(w string) []int { + var ( + t []int = []int{-1} + k int + ) + for j := 1; j < len(w); j++ { + k = j - 1 + for w[0:k] != w[j-k:j] && k > 0 { + k-- + } + t = append(t, k) + } + return t +} diff --git a/strings/kmp/kmp_test.go b/strings/kmp/kmp_test.go new file mode 100644 index 000000000..4d012986a --- /dev/null +++ b/strings/kmp/kmp_test.go @@ -0,0 +1,62 @@ +package kmp + +import ( + "reflect" + "testing" +) + +func TestKmp(t *testing.T) { + type args struct { + word string + text string + patternTable []int + } + tests := []struct { + name string + args args + want []int + }{ + { + name: "test1", + args: args{ + word: "ab", + text: "ababacaab", + patternTable: table("ababacaab"), + }, + want: []int{0, 2, 7}, + }, + } + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := Kmp(tt.args.word, tt.args.text, tt.args.patternTable); !reflect.DeepEqual(got, tt.want) { + t.Errorf("Kmp() = %v, want %v", got, tt.want) + } + }) + } +} + +func TestTable(t *testing.T) { + type args struct { + w string + } + tests := []struct { + name string + args args + want []int + }{ + { + name: "test1", + args: args{ + w: "ababacaab", + }, + want: []int{-1, 0, 0, 1, 2, 3, 0, 1, 1}, + }, + } + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + if got := table(tt.args.w); !reflect.DeepEqual(got, tt.want) { + t.Errorf("Table() = %v, want %v", got, tt.want) + } + }) + } +} diff --git a/strings/levenshtein/levenshteindistance.go b/strings/levenshtein/levenshteindistance.go new file mode 100644 index 000000000..b5cdec547 --- /dev/null +++ b/strings/levenshtein/levenshteindistance.go @@ -0,0 +1,42 @@ +/* +This algorithm calculates the distance between two strings. +Parameters: two strings to compare and weights of insertion, substitution and deletion. +Output: distance between both strings +*/ + +package levenshtein + +// Distance Function that gives Levenshtein Distance +func Distance(str1, str2 string, icost, scost, dcost int) int { + row1 := make([]int, len(str2)+1) + row2 := make([]int, len(str2)+1) + + for i := 1; i <= len(str2); i++ { + row1[i] = i * icost + } + + for i := 1; i <= len(str1); i++ { + row2[0] = i * dcost + + for j := 1; j <= len(str2); j++ { + if str1[i-1] == str2[j-1] { + row2[j] = row1[j-1] + } else { + ins := row2[j-1] + icost + del := row1[j] + dcost + sub := row1[j-1] + scost + + if ins < del && ins < sub { + row2[j] = ins + } else if del < sub { + row2[j] = del + } else { + row2[j] = sub + } + } + } + row1, row2 = row2, row1 + } + + return row1[len(row1)-1] +} diff --git a/strings/levenshtein/levenshteindistance_test.go b/strings/levenshtein/levenshteindistance_test.go new file mode 100644 index 000000000..8e15cd94e --- /dev/null +++ b/strings/levenshtein/levenshteindistance_test.go @@ -0,0 +1,52 @@ +package levenshtein + +import "testing" + +var testCases = []struct { + name string + string1 string + string2 string + insertionCost int + substitutionCost int + deletionCost int + expected int +}{ + { + "strings with equal operation weights.", + "stingy", + "ring", + 1, + 1, + 1, + 3, + }, + { + "strings with different operation weights.", + "stingy", + "ring", + 1, + 1, + 3, + 7, + }, + { + "strings with different operation weights.", + "kitten", + "sitting", + 1, + 1, + 1, + 3, + }, +} + +func TestLevenshteinDistance(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := Distance(tc.string1, tc.string2, tc.insertionCost, tc.substitutionCost, tc.deletionCost) + if actual != tc.expected { + t.Errorf("Expected Levenshtein distance between strings: '%s' and '%s' is %v, but got: %v", tc.string1, tc.string2, tc.expected, actual) + } + }) + } +} diff --git a/strings/manacher/longestpalindrome.go b/strings/manacher/longestpalindrome.go new file mode 100644 index 000000000..e49ae0f94 --- /dev/null +++ b/strings/manacher/longestpalindrome.go @@ -0,0 +1,63 @@ +// longestpalindrome.go +// description: Manacher's algorithm (Longest palindromic substring) +// details: +// An algorithm with linear running time that allows you to get compressed information about all palindromic substrings of a given string. - [Manacher's algorithm](https://en.wikipedia.org/wiki/Longest_palindromic_substring) +// author(s) [red_byte](https://github.com/i-redbyte) +// see longestpalindrome_test.go + +package manacher + +import ( + "github.com/TheAlgorithms/Go/math/min" + "strings" +) + +func makeBoundaries(s string) string { + var result strings.Builder + result.WriteRune('#') + for _, ch := range s { + if ch != ' ' { //ignore space as palindrome character + result.WriteRune(ch) + } + result.WriteRune('#') + } + return result.String() +} + +func nextBoundary(s string) string { + var result strings.Builder + for _, ch := range s { + if ch != '#' { + result.WriteRune(ch) + } + } + return result.String() +} + +func LongestPalindrome(s string) string { + boundaries := makeBoundaries(s) + b := make([]int, len(boundaries)) + k := 0 + index := 0 + maxLen := 0 + maxCenterSize := 0 + for i := range b { + if i < k { + b[i] = min.Int(b[2*index-i], k-i) + } else { + b[i] = 1 + } + for i-b[i] >= 0 && i+b[i] < len(boundaries) && boundaries[i-b[i]] == boundaries[i+b[i]] { + b[i] += 1 + } + if maxLen < b[i]-1 { + maxLen = b[i] - 1 + maxCenterSize = i + } + if b[i]+i-1 > k { + k = b[i] + i - 1 + index = i + } + } + return nextBoundary(boundaries[maxCenterSize-maxLen : maxCenterSize+maxLen]) +} diff --git a/strings/manacher/longestpalindrome_test.go b/strings/manacher/longestpalindrome_test.go new file mode 100644 index 000000000..af08fa0b4 --- /dev/null +++ b/strings/manacher/longestpalindrome_test.go @@ -0,0 +1,38 @@ +// longestpalindrome_test.go +// description: Manacher's algorithm (Longest palindromic substring) +// author(s) [red_byte](https://github.com/i-redbyte) +// see longestpalindrome.go + +package manacher + +import "testing" + +func getTests() []struct { + s string + result string +} { + var tests = []struct { + s string + result string + }{ + {"olokazakabba", "kazak"}, + {"abaacakkkkk", "kkkkk"}, + {"qqqq C++ groovy mom pooop", "pooop"}, + {"CCCPCCC @@@ hello", "CCCPCCC"}, + {"goog gogogogogog -go- gogogogo ", "gogogogogog"}, + } + return tests +} + +func TestLongestPalindrome(t *testing.T) { + tests := getTests() + for _, tv := range tests { + t.Run(tv.s, func(t *testing.T) { + result := LongestPalindrome(tv.s) + t.Log(tv.s, " ", result) + if result != tv.result { + t.Errorf("Wrong result! Expected:%s, returned:%s ", tv.result, result) + } + }) + } +} diff --git a/strings/naiveStringSearch.go b/strings/naiveStringSearch.go deleted file mode 100644 index 0dc2847cb..000000000 --- a/strings/naiveStringSearch.go +++ /dev/null @@ -1,44 +0,0 @@ -/* -This algorithm tries to search the given pattern in the given text. -If pattern is found from index position i in the text, -it is added to positions. - -Time Complexity : O(n*m) - n = length of text - m = length of pattern -*/ - -package main - -import ( - "fmt" -) - -func naivePatternSearch(text string, pattern string) []int { - var positions []int - for i := 0; i < len(text); i++ { - var match bool = true - for j := 0; j < len(pattern); j++ { - if text[i+j] != pattern[j] { - match = false - break - } - } - if match { - positions = append(positions, i) - } - } - return positions -} - -func main() { - text := "ABAAABCDBBABCDDEBCABC" - pattern := "ABC" - var positions []int = naivePatternSearch(text, pattern) - if len(positions) == 0 { - fmt.Printf("Pattern not found in given text!") - } else { - fmt.Printf("Pattern found in following position:\n") - fmt.Printf("%v", positions) - } -} diff --git a/strings/palindrome/ispalindrome.go b/strings/palindrome/ispalindrome.go new file mode 100644 index 000000000..eb3ab289e --- /dev/null +++ b/strings/palindrome/ispalindrome.go @@ -0,0 +1,55 @@ +// ispalindrome.go +// description: Checks if a given string is palindrome or not +// details: +// Palindromes are expressions that read the same way forwards and backwards. +// They can be words/phrases (like "racecar" and "Do geese see God?"), or even +// numbers (like "02/02/2020"). Usually punctuation signs, capitalization +// and spaces are ignored. A regular expression was used to achieve that. +// See more information on: https://en.wikipedia.org/wiki/Palindrome +// author(s) [Fernanda Kawasaki](https://github.com/fernandakawasaki) +// see ispalindrome_test.go + +package palindrome + +import ( + "regexp" + "strings" +) + +func cleanString(text string) string { + clean_text := strings.ToLower(text) + clean_text = strings.Join(strings.Fields(clean_text), "") // Remove spaces + regex, _ := regexp.Compile(`[^\p{L}\p{N} ]+`) // Regular expression for alphanumeric only characters + return regex.ReplaceAllString(clean_text, "") +} + +func IsPalindrome(text string) bool { + clean_text := cleanString(text) + var i, j int + rune := []rune(clean_text) + for i = 0; i < len(rune)/2; i++ { + j = len(rune) - 1 - i + if string(rune[i]) != string(rune[j]) { + return false + } + } + return true +} + +func IsPalindromeRecursive(text string) bool { + clean_text := cleanString(text) + runes := []rune(clean_text) + return isPalindromeRecursiveHelper(runes, 0, int64(len(runes))) +} + +func isPalindromeRecursiveHelper(runes []rune, start int64, end int64) bool { + if start >= end { + return true + } + if runes[start] != runes[end-1] { + return false + } + start = start + 1 + end = end - 1 + return isPalindromeRecursiveHelper(runes, start, end) +} diff --git a/strings/palindrome/ispalindrome_test.go b/strings/palindrome/ispalindrome_test.go new file mode 100644 index 000000000..7b973b1d5 --- /dev/null +++ b/strings/palindrome/ispalindrome_test.go @@ -0,0 +1,64 @@ +package palindrome + +import ( + "testing" +) + +var testCases = []struct { + name string // test description + input string // user input + expected bool // expected return +}{ + { + "non palindrome string", + "According to the laws of aviation bees can't flyã", + false, + }, + { + "non palindrome string", + "Alô?", + false, + }, + { + "palindrome string 1", + "Do geese see God?", + true, + }, + { + "palindrome string 2", + "ΝΙΨΟΝ ΑΝΟΜΗΜΑΤΑ ΜΗ ΜΟΝΑΝ ΟΨΙΝ", + true, + }, + { + "palindrome string 3", + "Was it a car or a cat I saw?", + true, + }, + { + "empty string", + "", + true, + }, +} + +func TestIsPalindrome(t *testing.T) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + func_result := IsPalindrome(test.input) + if test.expected != func_result { + t.Errorf("Expected answer '%t' for string '%s' but answer given was %t", test.expected, test.input, func_result) + } + }) + } +} + +func TestIsPalindromeRecursive(t *testing.T) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + func_result := IsPalindromeRecursive(test.input) + if test.expected != func_result { + t.Errorf("Expected answer '%t' for string '%s' but answer given was %t", test.expected, test.input, func_result) + } + }) + } +} diff --git a/strings/pangram/ispangram.go b/strings/pangram/ispangram.go new file mode 100644 index 000000000..18d9f90b4 --- /dev/null +++ b/strings/pangram/ispangram.go @@ -0,0 +1,31 @@ +// ispangram.go +// description: Checks if a given string is pangram or not +// details: A pangram is a sentence or expression that uses all the letters of the alphabet. +// Reference: https://www.geeksforgeeks.org/pangram-checking/ +// Author : Kavitha J + +package pangram + +import ( + "regexp" + "strings" +) + +func cleanString(text string) string { + cleanText := strings.ToLower(text) // Convert to lowercase + cleanText = strings.Join(strings.Fields(cleanText), "") // Remove spaces + regex, _ := regexp.Compile(`[^\p{L}\p{N} ]+`) // Regular expression for alphanumeric only characters + return regex.ReplaceAllString(cleanText, "") +} + +func IsPangram(text string) bool { + cleanText := cleanString(text) + if len(cleanText) < 26 { + return false + } + var data = make(map[rune]bool) + for _, i := range cleanText { + data[i] = true + } + return len(data) == 26 +} diff --git a/strings/pangram/ispangram_test.go b/strings/pangram/ispangram_test.go new file mode 100644 index 000000000..29e48de21 --- /dev/null +++ b/strings/pangram/ispangram_test.go @@ -0,0 +1,53 @@ +package pangram + +import ( + "testing" +) + +var testCases = []struct { + name string // test description + input string // user input + expected bool // expected return +}{ + { + "empty string", + "", + false, + }, + { + "non pangram string without spaces", + "abc", + false, + }, + { + "non pangram string with spaces", + "Hello World", + false, + }, + { + "Pangram string 1", + " Abcdefghijklmnopqrstuvwxyz", + true, + }, + { + "pangram string 2", + "cdefghijklmnopqrstuvwxABC zyb", + true, + }, + { + "pangram string 3", + "The Quick Brown Fox Jumps Over the Lazy Dog", + true, + }, +} + +func TestIsPangram(t *testing.T) { + for _, test := range testCases { + t.Run(test.name, func(t *testing.T) { + func_result := IsPangram(test.input) + if test.expected != func_result { + t.Errorf("Expected answer '%t' for string '%s' but answer given was %t", test.expected, test.input, func_result) + } + }) + } +} diff --git a/strings/parenthesis/parenthesis.go b/strings/parenthesis/parenthesis.go new file mode 100644 index 000000000..1fb446ff4 --- /dev/null +++ b/strings/parenthesis/parenthesis.go @@ -0,0 +1,23 @@ +package parenthesis + +// Parenthesis algorithm checks if every opened parenthesis +// is closed correctly. When parcounter is less than 0 when a closing +// parenthesis is detected without an opening parenthesis +// that surrounds it and parcounter will be 0 if all open +// parenthesis are closed correctly. +func Parenthesis(text string) bool { + parcounter := 0 + + for _, r := range text { + switch r { + case '(': + parcounter++ + case ')': + parcounter-- + } + if parcounter < 0 { + return false + } + } + return parcounter == 0 +} diff --git a/strings/parenthesis/parenthesis_test.go b/strings/parenthesis/parenthesis_test.go new file mode 100644 index 000000000..685c761c4 --- /dev/null +++ b/strings/parenthesis/parenthesis_test.go @@ -0,0 +1,53 @@ +package parenthesis + +import ( + "testing" +) + +var parenthesisTestCases = []struct { + name string + text string + expected bool +}{ + { + "simple test with one level deep", + "(3*9-2)+(3/7^3)", + true, + }, + { + "three nested parenthesis with three deep level", + "(-1*(5+2^(3-4)*(7.44-12)+6.66/(3.43-(1+2)))*(sqrt(3-4)))", + true, + }, + { + "one opened parenthesis without be closed", + "(2*9-17)*((7+3/3)*2*(-1+4)", + false, + }, + { + "one open parenthesis for each close one but not in pairs", + "(4*(39.22-7.4)/6.77))(", + false, + }, + { + "6 deep level", + "(5+33.2)*((8.04-6.5)*(1 - (1^(2-1.22*5.44+(4.33*7.2^(0.34*(-1.23+2)))))))", + true, + }, + { + "inverted parenthesis", + ")()()()()(", + false, + }, +} + +func TestParenthesis(t *testing.T) { + for _, tc := range parenthesisTestCases { + t.Run(tc.name, func(t *testing.T) { + actual := Parenthesis(tc.text) + if actual != tc.expected { + t.Errorf("Expected %t value from test %s with input %s\n", tc.expected, tc.name, tc.text) + } + }) + } +} diff --git a/strings/search/boyermoore.go b/strings/search/boyermoore.go new file mode 100644 index 000000000..dd8bb6eb2 --- /dev/null +++ b/strings/search/boyermoore.go @@ -0,0 +1,57 @@ +package search + +// Implementation of boyer moore string search +// O(l) where l=len(text) +func BoyerMoore(text string, pattern string) []int { + var positions []int + + l := len(text) + n := len(pattern) + + // using booyer moore horspool modification + // O(n) space instead of O(n**2) + bcr := make(map[byte]int) + for i := 0; i < n-1; i++ { + bcr[pattern[i]] = n - i - 1 + } + + // Apostolico–Giancarlo modification + // allow to skip patterns that we know matches + // let us do O(l) instead of O(ln) + skips := make(map[int]int) + for _, s := range bcr { + i := 0 + for ; i < n-s; i++ { + if pattern[n-1-i] != pattern[n-1-s-i] { + break + } + } + skips[s] = i + } + + skip := 0 + jump := n + for i := 0; i < l-n+1; { + skip = skips[jump] + for k := n - 1; k > -1; k-- { + if text[i+k] != pattern[k] { + jump, ok := bcr[text[i+k]] + if !ok { + jump = n + } + i += jump + break + } + if k == n-jump { + k -= skip + } + if k == 0 { + positions = append(positions, i) + jump = 1 + i += jump + } + } + } + + return positions +} diff --git a/strings/search/naive.go b/strings/search/naive.go new file mode 100644 index 000000000..51f47222f --- /dev/null +++ b/strings/search/naive.go @@ -0,0 +1,21 @@ +package search + +// Implementation of naive string search +// O(n*m) where n=len(txt) and m=len(pattern) +func Naive(text string, pattern string) []int { + var positions []int + for i := 0; i <= len(text)-len(pattern); i++ { + var match bool = true + for j := 0; j < len(pattern); j++ { + if text[i+j] != pattern[j] { + match = false + break + } + + } + if match { + positions = append(positions, i) + } + } + return positions +} diff --git a/strings/search/patternsearch_test.go b/strings/search/patternsearch_test.go new file mode 100644 index 000000000..83dbf1e72 --- /dev/null +++ b/strings/search/patternsearch_test.go @@ -0,0 +1,72 @@ +package search + +import ( + "reflect" + "testing" +) + +var testCases = []struct { + name string + input string + pattern string + expected []int +}{ + { + "string with multiple pattern matches", + "ABAAABCDBBABCDDEBCABC", + "ABC", + []int{4, 10, 18}, + }, + { + "string with single pattern match", + "ABCDEFGHIJKLMN", + "CDE", + []int{2}, + }, + { + "string with no pattern match", + "ABCDEFGHIJKLMN", + "XYZ", + []int(nil), + }, + { + "empty string", + "", + "XYZ", + []int(nil), + }, + { + "worse case 1", + "AAAAAAAAAA", + "AAA", + []int{0, 1, 2, 3, 4, 5, 6, 7}, + }, + { + "worse case 2", + "NANANANANANANANANA", + "NANANA", + []int{0, 2, 4, 6, 8, 10, 12}, + }, +} + +func TestNaive(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := Naive(tc.input, tc.pattern) + if !reflect.DeepEqual(actual, tc.expected) { + t.Errorf("Expected matches for pattern '%s' for string '%s' are: %v, but actual matches are: %v", tc.pattern, tc.input, tc.expected, actual) + } + }) + } +} + +func TestBooyerMoore(t *testing.T) { + for _, tc := range testCases { + t.Run(tc.name, func(t *testing.T) { + actual := BoyerMoore(tc.input, tc.pattern) + if !reflect.DeepEqual(actual, tc.expected) { + t.Errorf("Expected matches for pattern '%s' for string '%s' are: %v, but actual matches are: %v", tc.pattern, tc.input, tc.expected, actual) + } + }) + } +} diff --git a/strings/strings_test.go b/strings/strings_test.go new file mode 100644 index 000000000..aebadd648 --- /dev/null +++ b/strings/strings_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package strings diff --git a/structure/circularqueue/circularqueue_test.go b/structure/circularqueue/circularqueue_test.go new file mode 100644 index 000000000..0820b0470 --- /dev/null +++ b/structure/circularqueue/circularqueue_test.go @@ -0,0 +1,267 @@ +package circularqueue + +import "testing" + +func TestCircularQueue(t *testing.T) { + t.Run("Size Check", func(t *testing.T) { + _, err := NewCircularQueue[int](-3) + if err == nil { + t.Errorf("Expected error, got nil") + } + + queue, _ := NewCircularQueue[int](5) + expectedSize := 5 + gotSize := queue.Size() + if gotSize != expectedSize { + t.Errorf("Expected size: %v, got: %v\n", expectedSize, gotSize) + } + + if err := queue.Enqueue(1); err != nil { + t.Error(err) + } + if err := queue.Enqueue(2); err != nil { + t.Error(err) + } + if err := queue.Enqueue(3); err != nil { + t.Error(err) + } + if err := queue.Enqueue(4); err != nil { + t.Error(err) + } + if err := queue.Enqueue(5); err != nil { + t.Error(err) + } + + err = queue.Enqueue(6) + if err == nil { + t.Errorf("Expected error, got nil") + } + + expectedSize = 5 + gotSize = queue.Size() + if gotSize != expectedSize { + t.Errorf("Expected size: %v, got: %v\n", expectedSize, gotSize) + } + + if _, err := queue.Dequeue(); err != nil { + t.Error(err) + } + if _, err := queue.Dequeue(); err != nil { + t.Error(err) + } + + err = queue.Enqueue(6) + if err != nil { + t.Errorf("Expected nil, got error: %v\n", err.Error()) + } + + expectedSize = 5 + gotSize = queue.Size() + if gotSize != expectedSize { + t.Errorf("Expected size: %v, got: %v\n", expectedSize, gotSize) + } + }) + t.Run("Enqueue", func(t *testing.T) { + queue, _ := NewCircularQueue[int](10) + + if err := queue.Enqueue(1); err != nil { + t.Error(err) + } + if err := queue.Enqueue(2); err != nil { + t.Error(err) + } + if err := queue.Enqueue(3); err != nil { + t.Error(err) + } + + expected := 1 + got, err := queue.Peek() + if err != nil { + t.Error(err.Error()) + } + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + }) + t.Run("Dequeue", func(t *testing.T) { + queue, _ := NewCircularQueue[string](10) + + if err := queue.Enqueue("one"); err != nil { + t.Error(err) + } + if err := queue.Enqueue("two"); err != nil { + t.Error(err) + } + if err := queue.Enqueue("three"); err != nil { + t.Error(err) + } + + expected := "one" + got, err := queue.Dequeue() + if err != nil { + t.Error(err.Error()) + } + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + + expected = "two" + got, err = queue.Peek() + if err != nil { + t.Error(err.Error()) + } + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + }) + t.Run("Circularity", func(t *testing.T) { + queue, _ := NewCircularQueue[int](10) + + if err := queue.Enqueue(1); err != nil { + t.Error(err) + } + if err := queue.Enqueue(2); err != nil { + t.Error(err) + } + if err := queue.Enqueue(3); err != nil { + t.Error(err) + } + if _, err := queue.Dequeue(); err != nil { + t.Error(err) + } + if _, err := queue.Dequeue(); err != nil { + t.Error(err) + } + if err := queue.Enqueue(4); err != nil { + t.Error(err) + } + if err := queue.Enqueue(5); err != nil { + t.Error(err) + } + if _, err := queue.Dequeue(); err != nil { + t.Error(err) + } + + expected := 4 + got, err := queue.Peek() + if err != nil { + t.Error(err.Error()) + } + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + }) + t.Run("IsFull", func(t *testing.T) { + queue, _ := NewCircularQueue[bool](2) + if err := queue.Enqueue(false); err != nil { + t.Error(err) + } + if err := queue.Enqueue(true); err != nil { + t.Error(err) + } + + expected := true + got := queue.IsFull() + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + + if _, err := queue.Dequeue(); err != nil { + t.Error(err) + } + if _, err := queue.Dequeue(); err != nil { + t.Error(err) + } + + expected = false + got = queue.IsFull() + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + }) + t.Run("IsEmpty", func(t *testing.T) { + queue, _ := NewCircularQueue[float64](2) + + expected := true + got := queue.IsEmpty() + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + + if err := queue.Enqueue(1.0); err != nil { + t.Error(err) + } + + expected = false + got = queue.IsEmpty() + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + + }) + t.Run("Peak", func(t *testing.T) { + queue, _ := NewCircularQueue[rune](10) + + if err := queue.Enqueue('a'); err != nil { + t.Error(err) + } + if err := queue.Enqueue('b'); err != nil { + t.Error(err) + } + if err := queue.Enqueue('c'); err != nil { + t.Error(err) + } + + expected := 'a' + got, err := queue.Peek() + if err != nil { + t.Error(err.Error()) + } + + if got != expected { + t.Errorf("Expected: %v got: %v\n", expected, got) + } + }) +} + +// BenchmarkCircularQueue benchmarks the CircularQueue implementation. +func BenchmarkCircularQueue(b *testing.B) { + b.Run("Enqueue", func(b *testing.B) { + queue, _ := NewCircularQueue[int](1000) + for i := 0; i < b.N; i++ { + if err := queue.Enqueue(i); err != nil { + b.Error(err) + } + } + }) + + b.Run("Dequeue", func(b *testing.B) { + queue, _ := NewCircularQueue[int](1000) + for i := 0; i < 1000; i++ { + if err := queue.Enqueue(i); err != nil { + b.Error(err) + } + } + b.ResetTimer() + for i := 0; i < b.N; i++ { + if _, err := queue.Dequeue(); err != nil { + b.Error(err) + } + } + }) + + b.Run("Peek", func(b *testing.B) { + queue, _ := NewCircularQueue[int](1000) + for i := 0; i < 1000; i++ { + if err := queue.Enqueue(i); err != nil { + b.Error(err) + } + } + b.ResetTimer() + for i := 0; i < b.N; i++ { + if _, err := queue.Peek(); err != nil { + b.Error(err) + } + } + }) +} diff --git a/structure/circularqueue/circularqueuearray.go b/structure/circularqueue/circularqueuearray.go new file mode 100644 index 000000000..97447fa4a --- /dev/null +++ b/structure/circularqueue/circularqueuearray.go @@ -0,0 +1,96 @@ +// circularqueuearray.go +// description: Implementation of a circular queue data structure +// details: +// This file contains the implementation of a circular queue data structure +// using generics in Go. The circular queue supports basic operations such as +// enqueue, dequeue, peek, and checks for full and empty states. +// author(s): [Aram Ceballos](https://github.com/aramceballos) +// ref: https://www.programiz.com/dsa/circular-queue +// ref: https://en.wikipedia.org/wiki/Circular_buffer + +// Package queue provides an implementation of a circular queue data structure. +package circularqueue + +// errors package: Provides functions to create and manipulate error values +import ( + "errors" +) + +// CircularQueue represents a circular queue data structure. +type CircularQueue[T any] struct { + items []T + front int + rear int + size int +} + +// NewCircularQueue creates a new CircularQueue with the given size. +// Returns an error if the size is less than or equal to 0. +func NewCircularQueue[T any](size int) (*CircularQueue[T], error) { + if size <= 0 { + return nil, errors.New("size must be greater than 0") + } + return &CircularQueue[T]{ + items: make([]T, size), + front: -1, + rear: -1, + size: size, + }, nil +} + +// Enqueue adds an item to the rear of the queue. +// Returns an error if the queue is full. +func (cq *CircularQueue[T]) Enqueue(item T) error { + if cq.IsFull() { + return errors.New("queue is full") + } + if cq.IsEmpty() { + cq.front = 0 + } + cq.rear = (cq.rear + 1) % cq.size + cq.items[cq.rear] = item + return nil +} + +// Dequeue removes and returns the item from the front of the queue. +// Returns an error if the queue is empty. +func (cq *CircularQueue[T]) Dequeue() (T, error) { + if cq.IsEmpty() { + var zeroValue T + return zeroValue, errors.New("queue is empty") + } + retVal := cq.items[cq.front] + if cq.front == cq.rear { + cq.front = -1 + cq.rear = -1 + } else { + cq.front = (cq.front + 1) % cq.size + } + return retVal, nil +} + +// IsFull checks if the queue is full. +func (cq *CircularQueue[T]) IsFull() bool { + return (cq.front == 0 && cq.rear == cq.size-1) || cq.front == cq.rear+1 +} + +// IsEmpty checks if the queue is empty. +func (cq *CircularQueue[T]) IsEmpty() bool { + return cq.front == -1 && cq.rear == -1 +} + +// Peek returns the item at the front of the queue without removing it. +// Returns an error if the queue is empty. +func (cq *CircularQueue[T]) Peek() (T, error) { + if cq.IsEmpty() { + var zeroValue T + return zeroValue, errors.New("queue is empty") + } + + return cq.items[cq.front], nil +} + +// Size returns the size of the queue. +func (cq *CircularQueue[T]) Size() int { + return cq.size +} diff --git a/structure/deque/deque.go b/structure/deque/deque.go new file mode 100644 index 000000000..538703596 --- /dev/null +++ b/structure/deque/deque.go @@ -0,0 +1,84 @@ +// description: Double Ended Queue is a generalized version of Queue data structure that allows insert and delete at both ends. +// References: +// Wikipedia : https://en.wikipedia.org/wiki/Double-ended_queue +// Github: https://www.geeksforgeeks.org/deque-set-1-introduction-applications/ +// author [Sayan](https://github.com/bose-sayan) + +// Package deque implements a Double Ended Queue data structure. +package deque + +import ( + "errors" +) + +// ErrEmptyDequeue is a custom error for handling cases when some dequeuing operation is performed on an empty deque. +var ErrEmptyDequeue = errors.New("DoublyEnded queue is empty, so can't perform this operation") + +type DoublyEndedQueue[T any] struct { + deque []T +} + +// New returns a new DoublyEndedQueue. +func New[T any]() *DoublyEndedQueue[T] { + return &DoublyEndedQueue[T]{deque: make([]T, 0)} +} + +// EnqueueFront adds an item at the front of Deque. +func (dq *DoublyEndedQueue[T]) EnqueueFront(item T) { + dq.deque = append([]T{item}, dq.deque...) +} + +// EnqueueRear adds an item at the rear of Deque. +func (dq *DoublyEndedQueue[T]) EnqueueRear(item T) { + dq.deque = append(dq.deque, item) +} + +// DequeueFront deletes an item from front of Deque and returns it. +func (dq *DoublyEndedQueue[T]) DequeueFront() (T, error) { + if len(dq.deque) == 0 { + var zeroVal T + return zeroVal, ErrEmptyDequeue + } + frontElement := dq.deque[0] + dq.deque = dq.deque[1:] + return frontElement, nil +} + +// DequeueRear deletes an item from rear of Deque and returns it. +func (dq *DoublyEndedQueue[T]) DequeueRear() (T, error) { + if len(dq.deque) == 0 { + var zeroVal T + return zeroVal, ErrEmptyDequeue + } + rearElement := dq.deque[len(dq.deque)-1] + dq.deque = dq.deque[:len(dq.deque)-1] + return rearElement, nil +} + +// Front gets the front item from queue. +func (dq *DoublyEndedQueue[T]) Front() (T, error) { + if (len(dq.deque)) == 0 { + var zeroVal T + return zeroVal, ErrEmptyDequeue + } + return dq.deque[0], nil +} + +// Rear gets the last item from queue. +func (dq *DoublyEndedQueue[T]) Rear() (T, error) { + if (len(dq.deque)) == 0 { + var zeroVal T + return zeroVal, ErrEmptyDequeue + } + return dq.deque[len(dq.deque)-1], nil +} + +// IsEmpty checks whether Deque is empty or not. +func (dq *DoublyEndedQueue[T]) IsEmpty() bool { + return len(dq.deque) == 0 +} + +// Length gets the length of Deque. +func (dq *DoublyEndedQueue[T]) Length() int { + return len(dq.deque) +} diff --git a/structure/deque/deque_test.go b/structure/deque/deque_test.go new file mode 100644 index 000000000..26439e5be --- /dev/null +++ b/structure/deque/deque_test.go @@ -0,0 +1,406 @@ +// +// This file contains unit tests for the deque package. +// The tests cover the following scenarios: +// - Empty deque +// - Deque with one element +// - Deque with multiple elements +// The tests are parameterized with int and string types. +// Each test case is defined with a description and a list of queries to be executed on the deque. +// The expected results and errors are also defined for each query. +// + +package deque_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/structure/deque" +) + +type QueryStructure[T any] struct { + queryType string + parameter T + expectedResult interface{} + expectedError error +} + +type TestCaseData[T any] struct { + description string + queries []QueryStructure[T] +} + +func TestDeque(t *testing.T) { + + // Test cases with ints as params + testCasesInt := []TestCaseData[int]{ + { + description: "Test empty deque", + queries: []QueryStructure[int]{ + { + queryType: "IsEmpty", + expectedResult: true, + expectedError: nil, + }, + { + queryType: "Front", + expectedError: deque.ErrEmptyDequeue, + }, + { + queryType: "Rear", + expectedError: deque.ErrEmptyDequeue, + }, + { + queryType: "DeQueueFront", + expectedError: deque.ErrEmptyDequeue, + }, + { + queryType: "DeQueueRear", + expectedError: deque.ErrEmptyDequeue, + }, + { + queryType: "Length", + expectedResult: 0, + expectedError: nil, + }, + }, + }, + { + description: "Test deque with one element", + queries: []QueryStructure[int]{ + { + queryType: "EnQueueFront", + parameter: 1, + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: false, + expectedError: nil, + }, + { + queryType: "Front", + expectedResult: 1, + expectedError: nil, + }, + { + queryType: "Rear", + expectedResult: 1, + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 1, + expectedError: nil, + }, + { + queryType: "DeQueueFront", + expectedResult: 1, + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: true, + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 0, + expectedError: nil, + }, + }, + }, + { + description: "Test deque with multiple elements", + queries: []QueryStructure[int]{ + { + queryType: "EnQueueFront", + parameter: 1, + expectedError: nil, + }, + { + queryType: "EnQueueFront", + parameter: 2, + expectedError: nil, + }, + { + queryType: "EnQueueRear", + parameter: 3, + expectedError: nil, + }, + { + queryType: "EnQueueRear", + parameter: 4, + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: false, + expectedError: nil, + }, + { + queryType: "Front", + expectedResult: 2, + expectedError: nil, + }, + { + queryType: "Rear", + expectedResult: 4, + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 4, + expectedError: nil, + }, + { + queryType: "DeQueueFront", + expectedResult: 2, + expectedError: nil, + }, + { + queryType: "DeQueueRear", + expectedResult: 4, + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: false, + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 2, + expectedError: nil, + }, + }, + }, + } + + // Test cases with strings as params + testCasesString := []TestCaseData[string]{ + { + description: "Test one element deque", + queries: []QueryStructure[string]{ + { + queryType: "EnQueueFront", + parameter: "a", + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: false, + expectedError: nil, + }, + { + queryType: "Front", + expectedResult: "a", + expectedError: nil, + }, + { + queryType: "Rear", + expectedResult: "a", + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 1, + expectedError: nil, + }, + { + queryType: "DeQueueFront", + expectedResult: "a", + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: true, + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 0, + expectedError: nil, + }, + }, + }, + { + description: "Test multiple elements deque", + queries: []QueryStructure[string]{ + { + queryType: "EnQueueFront", + parameter: "a", + expectedError: nil, + }, + { + queryType: "EnQueueFront", + parameter: "b", + expectedError: nil, + }, + { + queryType: "EnQueueRear", + parameter: "c", + expectedError: nil, + }, + { + queryType: "EnQueueRear", + parameter: "d", + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: false, + expectedError: nil, + }, + { + queryType: "Front", + expectedResult: "b", + expectedError: nil, + }, + { + queryType: "Rear", + expectedResult: "d", + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 4, + expectedError: nil, + }, + { + queryType: "DeQueueFront", + expectedResult: "b", + expectedError: nil, + }, + { + queryType: "DeQueueRear", + expectedResult: "d", + expectedError: nil, + }, + { + queryType: "IsEmpty", + expectedResult: false, + expectedError: nil, + }, + { + queryType: "Length", + expectedResult: 2, + expectedError: nil, + }, + }, + }, + } + + // Run tests with ints + for _, testCase := range testCasesInt { + t.Run(testCase.description, func(t *testing.T) { + dq := deque.New[int]() + for _, query := range testCase.queries { + switch query.queryType { + case "EnQueueFront": + dq.EnqueueFront(query.parameter) + case "EnQueueRear": + dq.EnqueueRear(query.parameter) + case "DeQueueFront": + result, err := dq.DequeueFront() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v", query.expectedResult, result) + } + case "DeQueueRear": + result, err := dq.DequeueRear() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v", query.expectedResult, result) + } + case "Front": + result, err := dq.Front() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v, %v", query.expectedResult, result, testCase.description) + } + case "Rear": + result, err := dq.Rear() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v", query.expectedResult, result) + } + case "IsEmpty": + result := dq.IsEmpty() + if result != query.expectedResult { + t.Errorf("Expected error: %v, got : %v", query.expectedResult, result) + } + case "Length": + result := dq.Length() + if result != query.expectedResult { + t.Errorf("Expected %v got %v", query.expectedResult, result) + } + } + } + }) + } + + // Run tests with strings + for _, testCase := range testCasesString { + t.Run(testCase.description, func(t *testing.T) { + dq := deque.New[string]() + for _, query := range testCase.queries { + switch query.queryType { + case "EnQueueFront": + dq.EnqueueFront(query.parameter) + case "EnQueueRear": + dq.EnqueueRear(query.parameter) + case "DeQueueFront": + result, err := dq.DequeueFront() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v", query.expectedResult, result) + } + case "DeQueueRear": + result, err := dq.DequeueRear() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v", query.expectedResult, result) + } + case "Front": + result, err := dq.Front() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v, %v", query.expectedResult, result, testCase.description) + } + case "Rear": + result, err := dq.Rear() + if err != query.expectedError { + t.Errorf("Expected error: %v, got : %v", query.expectedError, err) + } + if err == nil && result != query.expectedResult { + t.Errorf("Expected %v, got %v", query.expectedResult, result) + } + case "IsEmpty": + result := dq.IsEmpty() + if result != query.expectedResult { + t.Errorf("Expected %v, got %v", query.expectedResult, result) + } + case "Length": + result := dq.Length() + if result != query.expectedResult { + t.Errorf("Expected %v got %v", query.expectedResult, result) + } + } + } + }) + } +} diff --git a/structure/doc.go b/structure/doc.go new file mode 100644 index 000000000..fc157dcfd --- /dev/null +++ b/structure/doc.go @@ -0,0 +1,4 @@ +// Package structure is a subpackage that is dedicated to +// different implementations of data structures in the +// domain of computer science. +package structure diff --git a/structure/dynamicarray/dynamicarray.go b/structure/dynamicarray/dynamicarray.go new file mode 100644 index 000000000..948cf71fc --- /dev/null +++ b/structure/dynamicarray/dynamicarray.go @@ -0,0 +1,108 @@ +// Package dynamicarray +// A dynamic array is quite similar to a regular array, but its Size is modifiable during program runtime, +// very similar to how a slice in Go works. The implementation is for educational purposes and explains +// how one might go about implementing their own version of slices. +// +// For more details check out those links below here: +// GeeksForGeeks article : https://www.geeksforgeeks.org/how-do-dynamic-arrays-work/ +// Go blog: https://blog.golang.org/slices-intro +// Go blog: https://blog.golang.org/slices +// authors [Wesllhey Holanda](https://github.com/wesllhey), [Milad](https://github.com/miraddo) +// see dynamicarray.go, dynamicarray_test.go +package dynamicarray + +import ( + "errors" +) + +var defaultCapacity = 10 + +// DynamicArray structure +type DynamicArray struct { + Size int + Capacity int + ElementData []any +} + +// Put function is change/update the value in array with the index and new value +func (da *DynamicArray) Put(index int, element any) error { + err := da.CheckRangeFromIndex(index) + + if err != nil { + return err + } + + da.ElementData[index] = element + + return nil +} + +// Add function is add new element to our array +func (da *DynamicArray) Add(element any) { + if da.Size == da.Capacity { + da.NewCapacity() + } + + da.ElementData[da.Size] = element + da.Size++ +} + +// Remove function is remove an element with the index +func (da *DynamicArray) Remove(index int) error { + err := da.CheckRangeFromIndex(index) + + if err != nil { + return err + } + + copy(da.ElementData[index:], da.ElementData[index+1:da.Size]) + da.ElementData[da.Size-1] = nil + + da.Size-- + + return nil +} + +// Get function is return one element with the index of array +func (da *DynamicArray) Get(index int) (any, error) { + err := da.CheckRangeFromIndex(index) + + if err != nil { + return nil, err + } + + return da.ElementData[index], nil +} + +// IsEmpty function is check that the array has value or not +func (da *DynamicArray) IsEmpty() bool { + return da.Size == 0 +} + +// GetData function return all value of array +func (da *DynamicArray) GetData() []any { + return da.ElementData[:da.Size] +} + +// CheckRangeFromIndex function it will check the range from the index +func (da *DynamicArray) CheckRangeFromIndex(index int) error { + if index >= da.Size || index < 0 { + return errors.New("index out of range") + } + return nil +} + +// NewCapacity function increase the Capacity +func (da *DynamicArray) NewCapacity() { + if da.Capacity == 0 { + da.Capacity = defaultCapacity + } else { + da.Capacity = da.Capacity << 1 + } + + newDataElement := make([]any, da.Capacity) + + copy(newDataElement, da.ElementData) + + da.ElementData = newDataElement +} diff --git a/structure/dynamicarray/dynamicarray_test.go b/structure/dynamicarray/dynamicarray_test.go new file mode 100644 index 000000000..e6b30b2b1 --- /dev/null +++ b/structure/dynamicarray/dynamicarray_test.go @@ -0,0 +1,97 @@ +package dynamicarray + +import ( + "reflect" + "testing" +) + +func TestDynamicArray(t *testing.T) { + numbers := DynamicArray{} + + // check numbers is empty or nut + t.Run("Check Empty Dynamic Array", func(t *testing.T) { + if numbers.IsEmpty() != true { + t.Errorf("Expected be true but got %v", numbers.IsEmpty()) + } + }) + + numbers.Add(10) + numbers.Add(20) + numbers.Add(30) + numbers.Add(40) + numbers.Add(50) + + // check numbers added to our dynamic array + t.Run("Add Element into Dynamic Array", func(t *testing.T) { + if numbers.IsEmpty() != false { + t.Errorf("Expected be false but got %v", numbers.IsEmpty()) + } + var res []any + res = append(res, 10) + res = append(res, 20) + res = append(res, 30) + res = append(res, 40) + res = append(res, 50) + + if !reflect.DeepEqual(numbers.GetData(), res) { + t.Errorf("Expected be [10, 20, 30, 40, 50] but got %v", numbers.GetData()) + } + }) + + // Remove an Element inside the dynamic array with the index of array + t.Run("Remove in Dynamic Array", func(t *testing.T) { + if numbers.IsEmpty() != false { + t.Errorf("Expected be false but got %v", numbers.IsEmpty()) + } + var res []any + res = append(res, 10) + res = append(res, 30) + res = append(res, 40) + res = append(res, 50) + + // remove the element by the index + err := numbers.Remove(1) + + if err != nil { + t.Errorf("Expected be [10, 30, 40, 50] but got an Error %v", err) + } + + if !reflect.DeepEqual(numbers.GetData(), res) { + t.Errorf("Expected be [10, 30, 40, 50] but got %v", numbers.GetData()) + } + }) + + // get one element by the index of the dynamic array + t.Run("Get in Dynamic Array", func(t *testing.T) { + if numbers.IsEmpty() != false { + t.Errorf("Expected be false but got %v", numbers.IsEmpty()) + } + + // return one element with the index + getOne, _ := numbers.Get(2) + + if getOne != 40 { + t.Errorf("Expected be 40 but got %v", getOne) + } + + }) + + // Put to add a value to specific index of Dynamic Array + t.Run("Put to Dynamic Array", func(t *testing.T) { + if numbers.IsEmpty() != false { + t.Errorf("Expected be false but got %v", numbers.IsEmpty()) + } + + // change value of specific index + err := numbers.Put(0, 100) + if err != nil { + t.Errorf("Expected be [10, 30, 40, 50] but got an Error %v", err) + } + + getOne, _ := numbers.Get(0) + if getOne != 100 { + t.Errorf("Expected be 100 but got %v", getOne) + } + }) + +} diff --git a/structure/fenwicktree/fenwicktree.go b/structure/fenwicktree/fenwicktree.go new file mode 100644 index 000000000..915d7b085 --- /dev/null +++ b/structure/fenwicktree/fenwicktree.go @@ -0,0 +1,60 @@ +// Fenwick Tree Data Structure for efficient range queries on an array of integers. +// Also known as Binary Indexed Tree. It can query the sum of any range of the array and +// can update the array at a specific position by adding a value to it (point update). +// Build: O(N) +// Query: O(log(N)) +// Update: O(log(N)) +// reference: https://brilliant.org/wiki/fenwick-tree/ +package fenwicktree + +// FenwickTree represents the data structure of the Fenwick Tree +type FenwickTree struct { + n int // n: Size of the input array. + array []int // array: the input array on which queries are made. + bit []int // bit: store the sum of ranges. +} + +// NewFenwickTree creates a new Fenwick tree, initializes bit with +// the values of the array. Note that the queries and updates should have +// one based indexing. +func NewFenwickTree(array []int) *FenwickTree { + newArray := []int{0} // Appending a 0 to the beginning as this implementation uses 1 based indexing + fenwickTree := &FenwickTree{ + n: len(array), + array: append(newArray, array...), + bit: append(newArray, array...), + } + for i := 1; i < fenwickTree.n; i++ { + nextPos := i + (i & -i) + if nextPos <= fenwickTree.n { + fenwickTree.bit[nextPos] += fenwickTree.bit[i] + } + } + return fenwickTree +} + +// PrefixSum returns the sum of the prefix ending at position pos. +func (f *FenwickTree) PrefixSum(pos int) int { + if pos > f.n { + return 0 + } + prefixSum := 0 + for i := pos; i > 0; i -= (i & -i) { + prefixSum += f.bit[i] + } + return prefixSum +} + +// RangeSum returns the sum of the elements in the range l to r +// both inclusive. +func (f *FenwickTree) RangeSum(l int, r int) int { + return f.PrefixSum(r) - f.PrefixSum(l-1) +} + +// Add Adds value to the element at position pos of the array +// and recomputes the range sums. +func (f *FenwickTree) Add(pos int, value int) { + for i := pos; i <= f.n; i += (i & -i) { + f.bit[i] += value + } +} diff --git a/structure/fenwicktree/fenwicktree_test.go b/structure/fenwicktree/fenwicktree_test.go new file mode 100644 index 000000000..99c9f12fc --- /dev/null +++ b/structure/fenwicktree/fenwicktree_test.go @@ -0,0 +1,81 @@ +package fenwicktree_test + +import ( + "github.com/TheAlgorithms/Go/structure/fenwicktree" + "testing" +) + +type query struct { + queryType string + firstIndex int // firstIndex and lastIndex are same for point queries + lastIndex int +} + +type update struct { + pos int + value int +} + +func TestFenwickTree(t *testing.T) { + var fenwickTreeTestData = []struct { + description string + array []int + updates []update + queries []query + expected []int + }{ + { + description: "test empty array", + array: []int{}, + queries: []query{{"point", 1, 1}}, + expected: []int{0}, + }, + { + description: "test array with size 5", + array: []int{1, 2, 3, 4, 5}, + queries: []query{{"range", 1, 5}, {"range", 1, 3}, {"range", 3, 5}}, + expected: []int{15, 6, 12}, + }, + { + description: "test array with size 5, single index updates and range queries", + array: []int{1, 2, 3, 4, 5}, + updates: []update{{pos: 2, value: 2}, {pos: 3, value: 3}}, + queries: []query{{"range", 1, 5}, {"range", 1, 3}, {"range", 3, 5}}, + expected: []int{20, 11, 15}, + }, + { + description: "test array with size 5, single index updates and point queries", + array: []int{1, 2, 3, 4, 5}, + updates: []update{{pos: 2, value: 2}, {pos: 3, value: 3}}, + queries: []query{{"point", 3, 3}, {"point", 1, 1}, {"point", 5, 5}}, + expected: []int{11, 1, 20}, + }, + } + + for _, test := range fenwickTreeTestData { + t.Run(test.description, func(t *testing.T) { + fenwickTree := fenwicktree.NewFenwickTree(test.array) + + for i := 0; i < len(test.updates); i++ { + fenwickTree.Add(test.updates[i].pos, test.updates[i].value) + } + + for i := 0; i < len(test.queries); i++ { + + var result int + + if test.queries[i].queryType == "point" { + result = fenwickTree.PrefixSum(test.queries[i].firstIndex) + } else { + result = fenwickTree.RangeSum(test.queries[i].firstIndex, test.queries[i].lastIndex) + } + + if result != test.expected[i] { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expected result: %d\nFound: %d\n", test.expected[i], result) + } + } + }) + } + +} diff --git a/structure/hashmap/hashmap.go b/structure/hashmap/hashmap.go new file mode 100644 index 000000000..591ac8685 --- /dev/null +++ b/structure/hashmap/hashmap.go @@ -0,0 +1,112 @@ +package hashmap + +import ( + "fmt" + "hash/fnv" +) + +var defaultCapacity uint64 = 1 << 10 + +type node struct { + key any + value any + next *node +} + +// HashMap is a Golang implementation of a hashmap +type HashMap struct { + capacity uint64 + size uint64 + table []*node +} + +// DefaultNew returns a new HashMap instance with default values +func DefaultNew() *HashMap { + return &HashMap{ + capacity: defaultCapacity, + table: make([]*node, defaultCapacity), + } +} + +// New creates a new HashMap instance with the specified size and capacity +func New(size, capacity uint64) *HashMap { + return &HashMap{ + size: size, + capacity: capacity, + table: make([]*node, capacity), + } +} + +// Get returns the value associated with the given key +func (hm *HashMap) Get(key any) any { + node := hm.getNodeByKey(key) + if node != nil { + return node.value + } + return nil +} + +// Put inserts a new key-value pair into the hashmap +func (hm *HashMap) Put(key, value any) { + index := hm.hash(key) + if hm.table[index] == nil { + hm.table[index] = &node{key: key, value: value} + } else { + current := hm.table[index] + for { + if current.key == key { + current.value = value + return + } + if current.next == nil { + break + } + current = current.next + } + current.next = &node{key: key, value: value} + } + hm.size++ + if float64(hm.size)/float64(hm.capacity) > 0.75 { + hm.resize() + } +} + +// Contains checks if the given key is stored in the hashmap +func (hm *HashMap) Contains(key any) bool { + return hm.getNodeByKey(key) != nil +} + +// getNodeByKey finds the node associated with the given key +func (hm *HashMap) getNodeByKey(key any) *node { + index := hm.hash(key) + current := hm.table[index] + for current != nil { + if current.key == key { + return current + } + current = current.next + } + return nil +} + +// resize doubles the capacity of the hashmap and rehashes all existing entries +func (hm *HashMap) resize() { + oldTable := hm.table + hm.capacity <<= 1 + hm.table = make([]*node, hm.capacity) + hm.size = 0 + + for _, head := range oldTable { + for current := head; current != nil; current = current.next { + hm.Put(current.key, current.value) + } + } +} + +// hash generates a hash value for the given key +func (hm *HashMap) hash(key any) uint64 { + h := fnv.New64a() + _, _ = h.Write([]byte(fmt.Sprintf("%v", key))) + hashValue := h.Sum64() + return (hm.capacity - 1) & (hashValue ^ (hashValue >> 16)) +} diff --git a/structure/hashmap/hashmap_test.go b/structure/hashmap/hashmap_test.go new file mode 100644 index 000000000..7b55df0bb --- /dev/null +++ b/structure/hashmap/hashmap_test.go @@ -0,0 +1,80 @@ +package hashmap_test + +import ( + "testing" + + "github.com/TheAlgorithms/Go/structure/hashmap" +) + +func TestHashMap(t *testing.T) { + mp := hashmap.DefaultNew() + + t.Run("Test 1: Put(10) and checking if Get() is correct", func(t *testing.T) { + mp.Put("test", 10) + got := mp.Get("test") + if got != 10 { + t.Errorf("Put: %v, Got: %v", 10, got) + } + }) + + t.Run("Test 2: Reassiging the value and checking if its correct", func(t *testing.T) { + mp.Put("test", 20) + got := mp.Get("test") + if got != 20 { + t.Errorf("Put (reassign): %v, Got: %v", 20, got) + } + }) + + t.Run("Test 3: Adding new key when there is already some data", func(t *testing.T) { + mp.Put("test2", 30) + got := mp.Get("test2") + if got != 30 { + t.Errorf("Put: %v, Got: %v", got, 30) + } + }) + + t.Run("Test 4: Adding numeric key", func(t *testing.T) { + mp.Put(1, 40) + got := mp.Get(1) + if got != 40 { + t.Errorf("Put: %v, Got: %v", got, 40) + } + }) + + t.Run("Test 5: Checking the Contains function", func(t *testing.T) { + want := true + got := mp.Contains(1) + if want != got { + t.Errorf("Key '1' exists but couldn't be retrieved") + } + }) + + t.Run("Test 6: Checking if the key that does not exist returns false", func(t *testing.T) { + want := false + got := mp.Contains(2) + if got != want { + t.Errorf("Key '2' does not exist in the map but it says otherwise") + } + }) + + t.Run("Test 7: Checking if the key does not exist Get func returns nil", func(t *testing.T) { + want := any(nil) + got := mp.Get(2) + if got != want { + t.Errorf("Key '2' does not exists in the map but it says otherwise") + } + }) + + t.Run("Test 8: Resizing a map", func(t *testing.T) { + mp := hashmap.New(4, 4) + + for i := 0; i < 20; i++ { + mp.Put(i, 40) + } + + got := mp.Get(5) + if got != 40 { + t.Errorf("Put: %v, Got: %v", got, 40) + } + }) +} diff --git a/structure/heap/heap.go b/structure/heap/heap.go new file mode 100644 index 000000000..693f1ab88 --- /dev/null +++ b/structure/heap/heap.go @@ -0,0 +1,98 @@ +package heap + +import ( + "errors" + "github.com/TheAlgorithms/Go/constraints" +) + +// Heap heap implementation using generic. +type Heap[T any] struct { + heaps []T + lessFunc func(a, b T) bool +} + +// New gives a new heap object. +func New[T constraints.Ordered]() *Heap[T] { + less := func(a, b T) bool { + return a < b + } + h, _ := NewAny[T](less) + return h +} + +// NewAny gives a new heap object. element can be anything, but must provide less function. +func NewAny[T any](less func(a, b T) bool) (*Heap[T], error) { + if less == nil { + return nil, errors.New("less func is necessary") + } + return &Heap[T]{ + lessFunc: less, + }, nil +} + +// Push pushes the element t onto the heap. +// The complexity is O(log n) where n = h.Len(). +func (h *Heap[T]) Push(t T) { + h.heaps = append(h.heaps, t) + h.up(len(h.heaps) - 1) +} + +// Top returns the minimum element (according to Less) from the heap. +// Top panics if the heap is empty. +func (h *Heap[T]) Top() T { + return h.heaps[0] +} + +// Pop removes the minimum element (according to Less) from the heap. +// The complexity is O(log n) where n = h.Len(). +func (h *Heap[T]) Pop() { + if len(h.heaps) <= 1 { + h.heaps = nil + return + } + h.swap(0, len(h.heaps)-1) + h.heaps = h.heaps[:len(h.heaps)-1] + h.down(0) +} + +// Empty returns the heap is empty or not. +func (h *Heap[T]) Empty() bool { + return len(h.heaps) == 0 +} + +// Size returns the size of the heap +func (h *Heap[T]) Size() int { + return len(h.heaps) +} + +func (h *Heap[T]) swap(i, j int) { + h.heaps[i], h.heaps[j] = h.heaps[j], h.heaps[i] +} + +func (h *Heap[T]) up(child int) { + if child <= 0 { + return + } + parent := (child - 1) >> 1 + if !h.lessFunc(h.heaps[child], h.heaps[parent]) { + return + } + h.swap(child, parent) + h.up(parent) +} + +func (h *Heap[T]) down(parent int) { + lessIdx := parent + lChild, rChild := (parent<<1)+1, (parent<<1)+2 + if lChild < len(h.heaps) && h.lessFunc(h.heaps[lChild], h.heaps[lessIdx]) { + lessIdx = lChild + } + if rChild < len(h.heaps) && h.lessFunc(h.heaps[rChild], h.heaps[lessIdx]) { + lessIdx = rChild + } + if lessIdx == parent { + return + } + h.swap(lessIdx, parent) + h.down(lessIdx) +} diff --git a/structure/heap/heap_test.go b/structure/heap/heap_test.go new file mode 100644 index 000000000..00ba54d7e --- /dev/null +++ b/structure/heap/heap_test.go @@ -0,0 +1,150 @@ +package heap_test + +import ( + "github.com/TheAlgorithms/Go/structure/heap" + "reflect" + "testing" +) + +type testInt int + +func (u testInt) Less(o testInt) bool { + return u < o +} + +type testStudent struct { + Name string + Score int64 +} + +func (u testStudent) Less(o testStudent) bool { + if u.Score == o.Score { + return u.Name < o.Name + } + return u.Score > o.Score +} + +func TestHeap_Empty(t *testing.T) { + tests := []struct { + name string + want bool + }{ + {name: "empty", want: true}, + } + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + h := heap.New[testInt]() + if got := h.Empty(); got != tt.want { + t.Errorf("Empty() = %v, want %v", got, tt.want) + } + }) + } +} + +type testOpType int + +const ( + testPush = 1 + testPop = 2 + testTop = 3 + testEmpty = 4 +) + +type testOp[T any] struct { + typ testOpType + x T + isEmpty bool +} + +type testStruct[T any] struct { + name string + ops []testOp[T] +} + +func TestHeapExample1(t *testing.T) { + tests1 := []testStruct[testInt]{ + { + name: "example 1", + ops: []testOp[testInt]{ + {typ: testEmpty, isEmpty: true}, + {typ: testPush, x: 10}, + {typ: testEmpty, isEmpty: false}, + {typ: testTop, x: 10}, + {typ: testPop}, + {typ: testEmpty, isEmpty: true}, + {typ: testPush, x: 9}, + {typ: testPush, x: 8}, + {typ: testPop}, + {typ: testPush, x: 3}, + {typ: testTop, x: 3}, + {typ: testPush, x: 2}, + {typ: testTop, x: 2}, + {typ: testPush, x: 4}, + {typ: testPush, x: 6}, + {typ: testPush, x: 5}, + {typ: testTop, x: 2}, + {typ: testPop}, + {typ: testTop, x: 3}, + {typ: testPop}, + {typ: testPop}, + {typ: testTop, x: 5}, + {typ: testEmpty, isEmpty: false}, + }, + }, + } + testFunc(t, tests1, testInt.Less) +} + +func TestHeapExample2(t *testing.T) { + tests1 := []testStruct[testStudent]{ + { + name: "example 2", + ops: []testOp[testStudent]{ + {typ: testPush, x: testStudent{Name: "Alan", Score: 87}}, + {typ: testPush, x: testStudent{Name: "Bob", Score: 98}}, + {typ: testTop, x: testStudent{Name: "Bob", Score: 98}}, + {typ: testPop}, + {typ: testPush, x: testStudent{Name: "Carl", Score: 70}}, + {typ: testTop, x: testStudent{Name: "Alan", Score: 87}}, + }, + }, + } + testFunc(t, tests1, testStudent.Less) +} + +func testFunc[T any](t *testing.T, tests []testStruct[T], less func(a, b T) bool) { + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + h, err := heap.NewAny[T](less) + if err != nil { + t.Errorf("New Heap err %v", err) + } + for i, op := range tt.ops { + switch op.typ { + case testPush: + oldSize := h.Size() + h.Push(op.x) + newSize := h.Size() + if oldSize+1 != newSize { + t.Errorf("op %d testPush %v failed", i, op.x) + } + case testPop: + oldSize := h.Size() + h.Pop() + newSize := h.Size() + if oldSize-1 != newSize { + t.Errorf("op %d testPop %v failed", i, op.x) + } + case testTop: + if got := h.Top(); !reflect.DeepEqual(got, op.x) { + t.Errorf("op %d testTop %v, want %v", i, got, op.x) + } + case testEmpty: + if got := h.Empty(); got != op.isEmpty { + t.Errorf("op %d Empty() = %v, want %v", i, got, op.isEmpty) + } + } + } + }) + } +} diff --git a/structure/linkedlist/Linked_Cyclic_List.jpg b/structure/linkedlist/Linked_Cyclic_List.jpg new file mode 100644 index 000000000..84c432516 Binary files /dev/null and b/structure/linkedlist/Linked_Cyclic_List.jpg differ diff --git a/structure/linkedlist/Readme.md b/structure/linkedlist/Readme.md new file mode 100644 index 000000000..cb6c1f6e7 --- /dev/null +++ b/structure/linkedlist/Readme.md @@ -0,0 +1,27 @@ +# Linked List +*** +## What is it? +*** +[Linked list](https://www.scaler.com/topics/linked-list/) is a data structure that is a linear chain of data elements whose order is not given by their phyisical placement in memory. This structure is built up of nodes which point to the element ahead or behind this particular node (depending on the type of Linked List). + +# Types of Linked List implemented within this repository + +## Singly Linked List +Singly Linked List is a linked list in which a node only points to the next element. +Some of the main applications of Singly Linked List are in the construction +of fundamental data structures such as Stacks and Queues. + +## Doubly Linked List +Doubly Linked List is a linked list in which a node points to both the element ahead and behind the node. +Any application which requires us to keep track of forward and backward information uses doubly linked list. +For example, the feature of undo and redo are implemented using these doubly linked lists. + +## Cyclic Linked List AKA Looped Linked List +Looped Linked Lists are singly or doubly-linked that chase their own tail: +A points to B, B points to C, C points to D, and D points to A. +They are better suited for cyclic data such as train schedules. +These lists are missing the first and last items. +Therefore, it is necessary to introduce the concept of the current position. + +This picture shows similar lists: +![Alt text](./Linked_Cyclic_List.jpg?raw=true) diff --git a/structure/linkedlist/cyclic.go b/structure/linkedlist/cyclic.go new file mode 100644 index 000000000..14bc518cc --- /dev/null +++ b/structure/linkedlist/cyclic.go @@ -0,0 +1,129 @@ +package linkedlist + +import "fmt" + +// Cyclic Struct which cycles the linked list in this implementation. +type Cyclic[T any] struct { + Size int + Head *Node[T] +} + +// Create new list. +func NewCyclic[T any]() *Cyclic[T] { + return &Cyclic[T]{} +} + +// Inserting the first node is a special case. It will +// point to itself. For other cases, the node will be added +// to the end of the list. End of the list is Prev field of +// current item. Complexity O(1). +func (cl *Cyclic[T]) Add(val T) { + n := NewNode(val) + cl.Size++ + if cl.Head == nil { + n.Prev = n + n.Next = n + cl.Head = n + } else { + n.Prev = cl.Head.Prev + n.Next = cl.Head + cl.Head.Prev.Next = n + cl.Head.Prev = n + } +} + +// Rotate list by P places. +// This method is interesting for optimization. +// For first optimization we must decrease +// P value so that it ranges from 0 to N-1. +// For this we need to use the operation of +// division modulo. But be careful if P is less than 0. +// if it is - make it positive. This can be done without +// violating the meaning of the number by adding to it +// a multiple of N. Now you can decrease P modulo N to +// rotate the list by the minimum number of places. +// We use the fact that moving forward in a circle by P +// places is the same as moving N - P places back. +// Therefore, if P > N / 2, you can turn the list by N-P places back. +// Complexity O(n). +func (cl *Cyclic[T]) Rotate(places int) { + if cl.Size > 0 { + if places < 0 { + multiple := cl.Size - 1 - places/cl.Size + places += multiple * cl.Size + } + places %= cl.Size + + if places > cl.Size/2 { + places = cl.Size - places + for i := 0; i < places; i++ { + cl.Head = cl.Head.Prev + } + } else if places == 0 { + return + } else { + for i := 0; i < places; i++ { + cl.Head = cl.Head.Next + } + + } + } +} + +// Delete the current item. +func (cl *Cyclic[T]) Delete() bool { + var deleted bool + var prevItem, thisItem, nextItem *Node[T] + + if cl.Size == 0 { + return deleted + } + + deleted = true + thisItem = cl.Head + nextItem = thisItem.Next + prevItem = thisItem.Prev + + if cl.Size == 1 { + cl.Head = nil + } else { + cl.Head = nextItem + nextItem.Prev = prevItem + prevItem.Next = nextItem + } + cl.Size-- + + return deleted +} + +// Destroy all items in the list. +func (cl *Cyclic[T]) Destroy() { + for cl.Delete() { + continue + } +} + +// Show list body. +func (cl *Cyclic[T]) Walk() *Node[T] { + var start *Node[T] + start = cl.Head + + for i := 0; i < cl.Size; i++ { + fmt.Printf("%v \n", start.Val) + start = start.Next + } + return start +} + +// https://en.wikipedia.org/wiki/Josephus_problem +// This is a struct-based solution for Josephus problem. +func JosephusProblem(cl *Cyclic[int], k int) int { + for cl.Size > 1 { + cl.Rotate(k) + cl.Delete() + cl.Rotate(-1) + } + retval := cl.Head.Val + cl.Destroy() + return retval +} diff --git a/structure/linkedlist/cyclic_test.go b/structure/linkedlist/cyclic_test.go new file mode 100644 index 000000000..882dbd8ad --- /dev/null +++ b/structure/linkedlist/cyclic_test.go @@ -0,0 +1,129 @@ +package linkedlist + +import ( + "reflect" + "testing" +) + +func fillList(list *Cyclic[int], n int) { + for i := 1; i <= n; i++ { + list.Add(i) + } +} + +func TestAdd(t *testing.T) { + list := NewCyclic[int]() + fillList(list, 3) + + want := []any{1, 2, 3} + var got []any + var start *Node[int] + start = list.Head + + for i := 0; i < list.Size; i++ { + got = append(got, start.Val) + start = start.Next + } + if !reflect.DeepEqual(got, want) { + t.Errorf("got: %v, want: %v", got, want) + } +} + +func TestWalk(t *testing.T) { + list := NewCyclic[int]() + fillList(list, 3) + + want := 1 + got := list.Walk() + + if got.Val != want { + t.Errorf("got: %v, want: nil", got) + } +} + +func TestRotate(t *testing.T) { + type testCase struct { + param int + wantToReturn int + } + list := NewCyclic[int]() + fillList(list, 3) + + testCases := []testCase{ + {1, 2}, + {3, 2}, + {6, 2}, + {7, 3}, + {-2, 1}, + {5, 3}, + {8, 2}, + {-8, 3}, + } + for idx, tCase := range testCases { + list.Rotate(tCase.param) + got := list.Head.Val + if got != tCase.wantToReturn { + t.Errorf("got: %v, want: %v for test id %v", got, tCase.wantToReturn, idx) + } + } +} + +func TestDelete(t *testing.T) { + list := NewCyclic[int]() + fillList(list, 3) + + want := 2 + wantSize := 2 + list.Delete() + got := list.Head.Val + if want != got { + t.Errorf("got: %v, want: %v", got, want) + } + if wantSize != list.Size { + t.Errorf("got: %v, want: %v", got, want) + } +} + +func TestDestroy(t *testing.T) { + list := NewCyclic[int]() + fillList(list, 3) + wantSize := 0 + list.Destroy() + + got := list.Head + + if got != nil { + t.Errorf("got: %v, want: nil", got) + } + + if wantSize != list.Size { + t.Errorf("got: %v, want: %v", got, wantSize) + } +} + +func TestJosephusProblem(t *testing.T) { + type testCase struct { + param int + wantToReturn int + listCount int + } + + testCases := []testCase{ + {5, 4, 8}, + {3, 8, 8}, + {8, 5, 8}, + {8, 5, 8}, + {2, 14, 14}, + {13, 56, 58}, + {7, 5, 5}, + } + + for _, tCase := range testCases { + list := NewCyclic[int]() + fillList(list, tCase.listCount) + got := JosephusProblem(list, tCase.param) + if got != tCase.wantToReturn { + t.Errorf("got: %v, want: %v", got, tCase.wantToReturn) + } + } +} diff --git a/structure/linkedlist/doc.go b/structure/linkedlist/doc.go new file mode 100644 index 000000000..d4c56c0e1 --- /dev/null +++ b/structure/linkedlist/doc.go @@ -0,0 +1,2 @@ +// Package linkedlist demonstrates different implementations on linkedlists. +package linkedlist diff --git a/structure/linkedlist/doubly.go b/structure/linkedlist/doubly.go new file mode 100644 index 000000000..6864dacf0 --- /dev/null +++ b/structure/linkedlist/doubly.go @@ -0,0 +1,226 @@ +package linkedlist + +import "fmt" + +// Doubly structure with just the Head Node +// We call it `Doubly` to make it easier to +// understand when calling this in peoples +// own local code to understand and experiment +// with this easily. +// For example, we can use gotools `go get` command to get +// this repository cloned inside the +// $GOPATH/src/github.com/TheAlgorithms/Go (you can do this +// manually as well) and use the import statement as follows: +// +// `import "github.com/TheAlgorithms/Go/structure/linkedlist"` +// +// and call linkedlist.Doubly to create a new doubly linked list. +type Doubly[T any] struct { + Head *Node[T] +} + +// Init initializes double linked list +func (ll *Doubly[T]) Init() *Doubly[T] { + ll.Head = &Node[T]{} + ll.Head.Next = ll.Head + ll.Head.Prev = ll.Head + + return ll +} + +func NewDoubly[T any]() *Doubly[T] { + return new(Doubly[T]).Init() +} + +// lazyInit lazily initializes a zero List value. +func (ll *Doubly[T]) lazyInit() { + if ll.Head.Next == nil { + ll.Init() + } +} + +func (ll *Doubly[T]) insert(n, at *Node[T]) *Node[T] { + n.Prev = at + n.Next = at.Next + n.Prev.Next = n + n.Next.Prev = n + + return n +} + +func (ll *Doubly[T]) insertValue(val T, at *Node[T]) *Node[T] { + return ll.insert(NewNode(val), at) +} + +// AddAtBeg Add a node to the beginning of the linkedlist +func (ll *Doubly[T]) AddAtBeg(val T) { + ll.lazyInit() + ll.insertValue(val, ll.Head) +} + +// AddAtEnd Add a node at the end of the linkedlist +func (ll *Doubly[T]) AddAtEnd(val T) { + ll.lazyInit() + ll.insertValue(val, ll.Head.Prev) +} + +func (ll *Doubly[T]) Remove(n *Node[T]) T { + n.Prev.Next = n.Next + n.Next.Prev = n.Prev + n.Next = nil + n.Prev = nil + + return n.Val +} + +// DelAtBeg Delete the node at the beginning of the linkedlist +func (ll *Doubly[T]) DelAtBeg() (T, bool) { + // no item + if ll.Head.Next == nil { + var r T + return r, false + } + + n := ll.Head.Next + val := n.Val + ll.Remove(n) + return val, true +} + +// DetAtEnd Delete a node at the end of the linkedlist +func (ll *Doubly[T]) DelAtEnd() (T, bool) { + // no item + if ll.Head.Prev == nil { + var r T + return r, false + } + + n := ll.Head.Prev + val := n.Val + ll.Remove(n) + return val, true +} + +// DelByPos deletes node at middle based on position in list +// and returns value. If empty or position of node is less than linked list length, returns false +func (ll *Doubly[T]) DelByPos(pos int) (T, bool) { + + switch { + case ll.Head == nil: + var r T + return r, false + case pos-1 == 0: + return ll.DelAtBeg() + case pos-1 == ll.Count(): + return ll.DelAtEnd() + case pos-1 > ll.Count(): + var r T + return r, false + } + var prev *Node[T] + var val T + cur := ll.Head + count := 0 + + for count < pos-1 { + prev = cur + cur = cur.Next + count++ + } + + cur.Next.Prev = prev + val = cur.Val + prev.Next = cur.Next + return val, true +} + +// Count Number of nodes in the linkedlist +func (ll *Doubly[T]) Count() int { + var ctr int = 0 + + if ll.Head.Next == nil { + return 0 + } + + for cur := ll.Head.Next; cur != ll.Head; cur = cur.Next { + ctr += 1 + } + + return ctr +} + +// Reverse Reverse the order of the linkedlist +func (ll *Doubly[T]) Reverse() { + var Prev, Next *Node[T] + cur := ll.Head + + for cur != nil { + Next = cur.Next + cur.Next = Prev + cur.Prev = Next + Prev = cur + cur = Next + } + + ll.Head = Prev +} + +// Display display the linked list +func (ll *Doubly[T]) Display() { + for cur := ll.Head.Next; cur != ll.Head; cur = cur.Next { + fmt.Print(cur.Val, " ") + } + + fmt.Print("\n") +} + +// DisplayReverse Display the linkedlist in reverse order +func (ll *Doubly[T]) DisplayReverse() { + if ll.Head == nil { + return + } + var cur *Node[T] + for cur = ll.Head.Prev; cur != ll.Head; cur = cur.Prev { + fmt.Print(cur.Val, " ") + } + + fmt.Print("\n") +} + +func (ll *Doubly[T]) Front() *Node[T] { + if ll.Count() == 0 { + return nil + } + + return ll.Head.Next +} + +func (ll *Doubly[T]) Back() *Node[T] { + if ll.Count() == 0 { + return nil + } + + return ll.Head.Prev +} + +func (ll *Doubly[T]) MoveToBack(n *Node[T]) { + if ll.Head.Prev == n { + return + } + + ll.move(n, ll.Head.Prev) +} + +func (ll *Doubly[T]) move(n, at *Node[T]) { + if n == at { + return + } + + n.Prev.Next = n.Next + n.Next.Prev = n.Prev + + n.Prev = at + n.Next = at.Next + n.Prev.Next = n + n.Next.Prev = n +} diff --git a/structure/linkedlist/doubly_test.go b/structure/linkedlist/doubly_test.go new file mode 100644 index 000000000..4778be74e --- /dev/null +++ b/structure/linkedlist/doubly_test.go @@ -0,0 +1,112 @@ +package linkedlist + +import ( + "reflect" + "testing" +) + +func TestDoubly(t *testing.T) { + newList := NewDoubly[int]() + + newList.AddAtBeg(1) + newList.AddAtBeg(2) + newList.AddAtBeg(3) + + t.Run("Test AddAtBeg", func(t *testing.T) { + wantNext := []int{3, 2, 1} + wantPrev := []int{1, 2, 3} + got := []int{} + + // check from Next address + current := newList.Head.Next + + got = append(got, current.Val) + + for current.Next != newList.Head { + current = current.Next + got = append(got, current.Val) + } + + if !reflect.DeepEqual(got, wantNext) { + t.Errorf("got: %v, want: %v", got, wantNext) + } + + // check from Prev address + got = []int{} + got = append(got, current.Val) + + for current.Prev != newList.Head { + current = current.Prev + got = append(got, current.Val) + } + + if !reflect.DeepEqual(got, wantPrev) { + t.Errorf("got: %v, want: %v", got, wantPrev) + } + }) + + newList.AddAtEnd(4) + + t.Run("Test AddAtEnd", func(t *testing.T) { + want := []int{3, 2, 1, 4} + got := []int{} + current := newList.Head.Next + got = append(got, current.Val) + for current.Next != newList.Head { + current = current.Next + got = append(got, current.Val) + } + if !reflect.DeepEqual(got, want) { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + t.Run("Test DelAtBeg", func(t *testing.T) { + want := 3 + got, ok := newList.DelAtBeg() + if !ok { + t.Error("unexpected not-ok") + } + if got != want { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + t.Run("Test DelAtEnd", func(t *testing.T) { + want := 4 + got, ok := newList.DelAtEnd() + if !ok { + t.Error("unexpected not-ok") + } + if got != want { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + t.Run("Test Count", func(t *testing.T) { + want := 2 + got := newList.Count() + if got != want { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + newList2 := NewDoubly[int]() + newList2.AddAtBeg(1) + newList2.AddAtBeg(2) + newList2.AddAtBeg(3) + t.Run("Test Reverse", func(t *testing.T) { + want := []int{1, 2, 3} + got := []int{} + newList2.Reverse() + current := newList2.Head.Next + got = append(got, current.Val) + for current.Next != newList2.Head { + current = current.Next + got = append(got, current.Val) + } + if !reflect.DeepEqual(got, want) { + t.Errorf("got: %v, want: %v", got, want) + } + }) +} diff --git a/structure/linkedlist/shared.go b/structure/linkedlist/shared.go new file mode 100644 index 000000000..03e52f7bf --- /dev/null +++ b/structure/linkedlist/shared.go @@ -0,0 +1,14 @@ +package linkedlist + +// Node Structure representing the linkedlist node. +// This node is shared across different implementations. +type Node[T any] struct { + Val T + Prev *Node[T] + Next *Node[T] +} + +// Create new node. +func NewNode[T any](val T) *Node[T] { + return &Node[T]{val, nil, nil} +} diff --git a/structure/linkedlist/singlylinkedlist.go b/structure/linkedlist/singlylinkedlist.go new file mode 100644 index 000000000..57b09b104 --- /dev/null +++ b/structure/linkedlist/singlylinkedlist.go @@ -0,0 +1,181 @@ +package linkedlist + +// demonstration of singly linked list in golang +import ( + "errors" + "fmt" +) + +// Singly structure with length of the list and its head +type Singly[T any] struct { + length int + + // Note that Node here holds both Next and Prev Node + // however only the Next node is used in Singly methods. + Head *Node[T] +} + +// NewSingly returns a new instance of a linked list +func NewSingly[T any]() *Singly[T] { + return &Singly[T]{} +} + +// AddAtBeg adds a new snode with given value at the beginning of the list. +func (ll *Singly[T]) AddAtBeg(val T) { + n := NewNode(val) + n.Next = ll.Head + ll.Head = n + ll.length++ +} + +// AddAtEnd adds a new snode with given value at the end of the list. +func (ll *Singly[T]) AddAtEnd(val T) { + n := NewNode(val) + + if ll.Head == nil { + ll.Head = n + ll.length++ + return + } + + cur := ll.Head + for ; cur.Next != nil; cur = cur.Next { + } + cur.Next = n + ll.length++ +} + +// DelAtBeg deletes the snode at the head(beginning) of the list +// and returns its value. Returns false if the list is empty. +func (ll *Singly[T]) DelAtBeg() (T, bool) { + if ll.Head == nil { + var r T + return r, false + } + + cur := ll.Head + ll.Head = cur.Next + ll.length-- + + return cur.Val, true +} + +// DelAtEnd deletes the snode at the tail(end) of the list +// and returns its value. Returns false if the list is empty. +func (ll *Singly[T]) DelAtEnd() (T, bool) { + if ll.Head == nil { + var r T + return r, false + } + + if ll.Head.Next == nil { + return ll.DelAtBeg() + } + + cur := ll.Head + + for ; cur.Next.Next != nil; cur = cur.Next { + } + + retval := cur.Next.Val + cur.Next = nil + ll.length-- + return retval, true + +} + +// DelByPos deletes the node at the middle based on position in the list +// and returns its value. Returns false if the list is empty or length is not more than given position +func (ll *Singly[T]) DelByPos(pos int) (T, bool) { + switch { + case ll.Head == nil: + var r T + return r, false + case pos-1 > ll.length: + var r T + return r, false + case pos-1 == 0: + return ll.DelAtBeg() + case pos-1 == ll.Count(): + return ll.DelAtEnd() + } + + var prev *Node[T] + var val T + cur := ll.Head + count := 0 + + for count < pos-1 { + prev = cur + cur = cur.Next + count++ + } + + val = cur.Val + prev.Next = cur.Next + ll.length-- + + return val, true +} + +// Count returns the current size of the list. +func (ll *Singly[T]) Count() int { + return ll.length +} + +// Reverse reverses the list. +func (ll *Singly[T]) Reverse() { + var prev, next *Node[T] + cur := ll.Head + + for cur != nil { + next = cur.Next + cur.Next = prev + prev = cur + cur = next + } + + ll.Head = prev +} + +// ReversePartition Reverse the linked list from the ath to the bth node +func (ll *Singly[T]) ReversePartition(left, right int) error { + err := ll.CheckRangeFromIndex(left, right) + if err != nil { + return err + } + tmpNode := &Node[T]{} + tmpNode.Next = ll.Head + pre := tmpNode + for i := 0; i < left-1; i++ { + pre = pre.Next + } + cur := pre.Next + for i := 0; i < right-left; i++ { + next := cur.Next + cur.Next = next.Next + next.Next = pre.Next + pre.Next = next + } + ll.Head = tmpNode.Next + return nil +} +func (ll *Singly[T]) CheckRangeFromIndex(left, right int) error { + if left > right { + return errors.New("left boundary must smaller than right") + } else if left < 1 { + return errors.New("left boundary starts from the first node") + } else if right > ll.length { + return errors.New("right boundary cannot be greater than the length of the linked list") + } + return nil +} + +// Display prints out the elements of the list. +func (ll *Singly[T]) Display() { + for cur := ll.Head; cur != nil; cur = cur.Next { + fmt.Print(cur.Val, " ") + } + + fmt.Print("\n") +} diff --git a/structure/linkedlist/singlylinkedlist_test.go b/structure/linkedlist/singlylinkedlist_test.go new file mode 100644 index 000000000..705770d9c --- /dev/null +++ b/structure/linkedlist/singlylinkedlist_test.go @@ -0,0 +1,115 @@ +package linkedlist + +import ( + "reflect" + "testing" +) + +func TestSingly(t *testing.T) { + list := NewSingly[int]() + list.AddAtBeg(1) + list.AddAtBeg(2) + list.AddAtBeg(3) + + t.Run("Test AddAtBeg()", func(t *testing.T) { + want := []any{3, 2, 1} + got := []any{} + current := list.Head + got = append(got, current.Val) + for current.Next != nil { + current = current.Next + got = append(got, current.Val) + } + if !reflect.DeepEqual(got, want) { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + list.AddAtEnd(4) + + t.Run("Test AddAtEnd()", func(t *testing.T) { + want := []any{3, 2, 1, 4} + got := []any{} + current := list.Head + got = append(got, current.Val) + for current.Next != nil { + current = current.Next + got = append(got, current.Val) + } + if !reflect.DeepEqual(got, want) { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + t.Run("Test DelAtBeg()", func(t *testing.T) { + want := any(3) + got, ok := list.DelAtBeg() + if !ok { + t.Error("unexpected not-ok") + } + if got != want { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + t.Run("Test DelAtEnd()", func(t *testing.T) { + want := any(4) + got, ok := list.DelAtEnd() + if !ok { + t.Error("unexpected not-ok") + } + if got != want { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + t.Run("Test Count()", func(t *testing.T) { + want := 2 + got := list.Count() + if got != want { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + list2 := Singly[int]{} + list2.AddAtBeg(1) + list2.AddAtBeg(2) + list2.AddAtBeg(3) + list2.AddAtBeg(4) + list2.AddAtBeg(5) + list2.AddAtBeg(6) + + t.Run("Test Reverse()", func(t *testing.T) { + want := []any{1, 2, 3, 4, 5, 6} + got := []any{} + list2.Reverse() + current := list2.Head + got = append(got, current.Val) + for current.Next != nil { + current = current.Next + got = append(got, current.Val) + } + if !reflect.DeepEqual(got, want) { + t.Errorf("got: %v, want: %v", got, want) + } + }) + + t.Run("Test ReversePartition()", func(t *testing.T) { + want := []any{1, 5, 4, 3, 2, 6} + got := []any{} + err := list2.ReversePartition(2, 5) + + if err != nil { + t.Errorf("Incorrect boundary conditions entered%v", err) + } + current := list2.Head + got = append(got, current.Val) + for current.Next != nil { + current = current.Next + got = append(got, current.Val) + } + if !reflect.DeepEqual(got, want) { + t.Errorf("got: %v, want: %v", got, want) + } + }) +} diff --git a/structure/queue/queue_test.go b/structure/queue/queue_test.go new file mode 100644 index 000000000..11cda8ca6 --- /dev/null +++ b/structure/queue/queue_test.go @@ -0,0 +1,247 @@ +// Queue Test +// description: based on `geeksforgeeks` description A Queue is a linear structure which follows a particular order in which the operations are performed. +// The order is First In First Out (FIFO). +// details: +// Queue Data Structure : https://www.geeksforgeeks.org/queue-data-structure/ +// Queue (abstract data type) : https://en.wikipedia.org/wiki/Queue_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see queuearray.go, queuelinkedlist.go, queuelinkedlistwithlist.go + +package queue + +import ( + "container/list" + "testing" +) + +func TestQueue(t *testing.T) { + + // Handle Queue Linked List + t.Run("Test Queue Linked List", func(t *testing.T) { + + t.Run("Test EnQueue", func(t *testing.T) { + var newQueue Queue + newQueue.enqueue(2) + newQueue.enqueue(3) + newQueue.enqueue(4) + newQueue.enqueue(45) + + if newQueue.frontQueue() != 2 && newQueue.backQueue() != 45 { + t.Errorf("Test EnQueue is wrong the result must be %v and %v but got %v and %v", 2, 45, newQueue.frontQueue(), newQueue.backQueue()) + } + + }) + + t.Run("Test DeQueue", func(t *testing.T) { + var newQueue Queue + newQueue.enqueue(2) + newQueue.enqueue(3) + newQueue.enqueue(4) + + newQueue.dequeue() + if newQueue.dequeue() != 3 { + t.Errorf("Test DeQueue is wrong the result must be %v but got %v", 3, newQueue.dequeue()) + } + + //fmt.Println(newQueue.show()) + }) + + t.Run("Test Queue isEmpty", func(t *testing.T) { + var newQueue Queue + if newQueue.isEmpty() != true { + t.Errorf("Test Queue isEmpty is wrong the result must be %v but got %v", true, newQueue.isEmpty()) + } + + newQueue.enqueue(3) + newQueue.enqueue(4) + + if newQueue.isEmpty() != false { + t.Errorf("Test Queue isEmpty is wrong the result must be %v but got %v", false, newQueue.isEmpty()) + } + }) + + t.Run("Test Queue Length", func(t *testing.T) { + var newQueue Queue + if newQueue.len() != 0 { + t.Errorf("Test Queue Length is wrong the result must be %v but got %v", 0, newQueue.len()) + } + + newQueue.enqueue(3) + newQueue.enqueue(4) + newQueue.dequeue() + newQueue.enqueue(22) + newQueue.enqueue(99) + newQueue.dequeue() + newQueue.dequeue() + + if newQueue.len() != 1 { + t.Errorf("Test Queue Length is wrong the result must be %v but got %v", 1, newQueue.len()) + } + + }) + }) + + // Handle Queue Array + t.Run("Test Queue Array", func(t *testing.T) { + t.Run("Test EnQueue", func(t *testing.T) { + EnQueue(2) + EnQueue(23) + EnQueue(45) + EnQueue(66) + + if FrontQueue() != 2 && BackQueue() != 66 { + t.Errorf("Test EnQueue is wrong the result must be %v and %v but got %v and %v", 2, 66, FrontQueue(), BackQueue()) + } + + }) + + t.Run("Test DeQueue", func(t *testing.T) { + EnQueue(2) + EnQueue(23) + EnQueue(45) + EnQueue(66) + + DeQueue() + DeQueue() + + if DeQueue() != 45 { + t.Errorf("Test DeQueue is wrong the result must be %v but got %v", 45, DeQueue()) + } + }) + + ListQueue = []any{} + + t.Run("Test Queue isEmpty", func(t *testing.T) { + + if IsEmptyQueue() != true { + t.Errorf("Test Queue isEmpty is wrong the result must be %v but got %v", true, IsEmptyQueue()) + } + + EnQueue(3) + EnQueue(4) + + if IsEmptyQueue() != false { + t.Errorf("Test Queue isEmpty is wrong the result must be %v but got %v", false, IsEmptyQueue()) + } + }) + + ListQueue = []any{} + t.Run("Test Queue Length", func(t *testing.T) { + if LenQueue() != 0 { + t.Errorf("Test Queue Length is wrong the result must be %v but got %v", 0, LenQueue()) + } + + EnQueue(3) + EnQueue(4) + DeQueue() + EnQueue(22) + EnQueue(99) + DeQueue() + DeQueue() + + if LenQueue() != 1 { + t.Errorf("Test Queue Length is wrong the result must be %v but got %v", 1, LenQueue()) + } + + }) + + }) + + // Handle Queue Linked-List With Container/List (STL) + t.Run("Test Container/List For Queue", func(t *testing.T) { + listQueue := &LQueue{ + queue: list.New(), + } + + t.Run("List Enqueue", func(t *testing.T) { + listQueue.Enqueue("Snap") + listQueue.Enqueue(123) + listQueue.Enqueue(true) + listQueue.Enqueue(212.545454) + + if listQueue.Len() != 4 { + t.Errorf("List Enqueue is not correct expected %d but got %d", 4, listQueue.Len()) + } + }) + + t.Run("List Dequeue", func(t *testing.T) { + + err := listQueue.Dequeue() + + if err != nil { + t.Error("got an unexpected error ", err) + } + if listQueue.Len() != 3 { + t.Errorf("List Dequeue is not correct expected %d but got %d", 3, listQueue.Len()) + } + }) + + t.Run("List Front", func(t *testing.T) { + + err := listQueue.Dequeue() + + if err != nil { + t.Error("got an unexpected error ", err) + } + + result, err := listQueue.Front() + + if err != nil { + t.Error("got an unexpected error ", err) + } + + if result != true { + t.Errorf("List Front is not correct expected %v but got %v", true, result) + } + }) + + t.Run("List Back", func(t *testing.T) { + + err := listQueue.Dequeue() + + if err != nil { + t.Error("got an unexpected error ", err) + } + + result, err := listQueue.Back() + + if err != nil { + t.Error("got an unexpected error ", err) + } + + if result != 212.545454 { + t.Errorf("List Back is not correct expected %v but got %v", 212.545454, result) + } + }) + + t.Run("List Length", func(t *testing.T) { + + listQueue.Enqueue("Snap") + + err := listQueue.Dequeue() + + if err != nil { + t.Error("got an unexpected error ", err) + } + + if listQueue.Len() != 1 { + t.Errorf("List Length is not correct expected %v but got %v", 1, listQueue.Len()) + } + }) + + t.Run("List Empty", func(t *testing.T) { + + err := listQueue.Dequeue() + + if err != nil { + t.Error("got an unexpected error ", err) + } + + if !listQueue.Empty() { + t.Errorf("List Empty is not correct expected %v but got %v", true, listQueue.Empty()) + } + }) + + }) + +} diff --git a/structure/queue/queuearray.go b/structure/queue/queuearray.go new file mode 100644 index 000000000..f1813c8e6 --- /dev/null +++ b/structure/queue/queuearray.go @@ -0,0 +1,44 @@ +// Queue Array +// description: based on `geeksforgeeks` description A Queue is a linear structure which follows a particular order in which the operations are performed. +// The order is First In First Out (FIFO). +// details: +// Queue Data Structure : https://www.geeksforgeeks.org/queue-data-structure/ +// Queue (abstract data type) : https://en.wikipedia.org/wiki/Queue_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see queuelinkedlist.go, queuelinkedlistwithlist.go, queue_test.go + +package queue + +var ListQueue []any + +// EnQueue it will be added new value into our list +func EnQueue(n any) { + ListQueue = append(ListQueue, n) +} + +// DeQueue it will be removed the first value that added into the list +func DeQueue() any { + data := ListQueue[0] + ListQueue = ListQueue[1:] + return data +} + +// FrontQueue return the Front value +func FrontQueue() any { + return ListQueue[0] +} + +// BackQueue return the Back value +func BackQueue() any { + return ListQueue[len(ListQueue)-1] +} + +// LenQueue will return the length of the queue list +func LenQueue() int { + return len(ListQueue) +} + +// IsEmptyQueue check our list is empty or not +func IsEmptyQueue() bool { + return len(ListQueue) == 0 +} diff --git a/structure/queue/queuelinkedlist.go b/structure/queue/queuelinkedlist.go new file mode 100644 index 000000000..18c04d3f5 --- /dev/null +++ b/structure/queue/queuelinkedlist.go @@ -0,0 +1,77 @@ +// Queue Linked-List +// description: based on `geeksforgeeks` description A Queue is a linear structure which follows a particular order in which the operations are performed. +// The order is First In First Out (FIFO). +// details: +// Queue Data Structure : https://www.geeksforgeeks.org/queue-data-structure/ +// Queue (abstract data type) : https://en.wikipedia.org/wiki/Queue_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see queuearray.go, queuelinkedlistwithlist.go, queue_test.go + +package queue + +// Node will be store the value and the next node as well +type Node struct { + Data any + Next *Node +} + +// Queue structure is tell us what our head is and what tail should be with length of the list +type Queue struct { + head *Node + tail *Node + length int +} + +// enqueue it will be added new value into queue +func (ll *Queue) enqueue(n any) { + var newNode Node // create new Node + newNode.Data = n // set the data + + if ll.tail != nil { + ll.tail.Next = &newNode + } + + ll.tail = &newNode + + if ll.head == nil { + ll.head = &newNode + } + ll.length++ +} + +// dequeue it will be removed the first value into queue (First In First Out) +func (ll *Queue) dequeue() any { + if ll.isEmpty() { + return -1 // if is empty return -1 + } + data := ll.head.Data + + ll.head = ll.head.Next + + if ll.head == nil { + ll.tail = nil + } + + ll.length-- + return data +} + +// isEmpty it will check our list is empty or not +func (ll *Queue) isEmpty() bool { + return ll.length == 0 +} + +// len is return the length of queue +func (ll *Queue) len() int { + return ll.length +} + +// frontQueue it will return the front data +func (ll *Queue) frontQueue() any { + return ll.head.Data +} + +// backQueue it will return the back data +func (ll *Queue) backQueue() any { + return ll.tail.Data +} diff --git a/structure/queue/queuelinklistwithlist.go b/structure/queue/queuelinklistwithlist.go new file mode 100644 index 000000000..c27bb8bef --- /dev/null +++ b/structure/queue/queuelinklistwithlist.go @@ -0,0 +1,70 @@ +// Queue Linked-List with standard library (Container/List) +// description: based on `geeksforgeeks` description A Queue is a linear structure which follows a particular order in which the operations are performed. +// The order is First In First Out (FIFO). +// details: +// Queue Data Structure : https://www.geeksforgeeks.org/queue-data-structure/ +// Queue (abstract data type) : https://en.wikipedia.org/wiki/Queue_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see queuearray.go, queuelinkedlist.go, queue_test.go + +package queue + +// container/list: is used as linked-list +// fmt: used to return fmt.Errorf for the error part +import ( + "container/list" + "fmt" +) + +// LQueue will be store the value into the list +type LQueue struct { + queue *list.List +} + +// Enqueue will be added new value +func (lq *LQueue) Enqueue(value any) { + lq.queue.PushBack(value) +} + +// Dequeue will be removed the first value that input (First In First Out - FIFO) +func (lq *LQueue) Dequeue() error { + + if !lq.Empty() { + element := lq.queue.Front() + lq.queue.Remove(element) + + return nil + } + + return fmt.Errorf("dequeue is empty we got an error") +} + +// Front it will return the front value +func (lq *LQueue) Front() (any, error) { + if !lq.Empty() { + val := lq.queue.Front().Value + return val, nil + } + + return "", fmt.Errorf("error queue is empty") +} + +// Back it will return the back value +func (lq *LQueue) Back() (any, error) { + if !lq.Empty() { + val := lq.queue.Back().Value + return val, nil + } + + return "", fmt.Errorf("error queue is empty") +} + +// Len it will return the length of list +func (lq *LQueue) Len() int { + return lq.queue.Len() +} + +// Empty is check our list is empty or not +func (lq *LQueue) Empty() bool { + return lq.queue.Len() == 0 +} diff --git a/structure/segmenttree/segmenttree.go b/structure/segmenttree/segmenttree.go new file mode 100644 index 000000000..bf70f4522 --- /dev/null +++ b/structure/segmenttree/segmenttree.go @@ -0,0 +1,137 @@ +// Segment Tree Data Structure for efficient range queries on an array of integers. +// It can query the sum and update the elements to a new value of any range of the array. +// Build: O(n*log(n)) +// Query: O(log(n)) +// Update: O(log(n)) +// reference: https://cp-algorithms.com/data_structures/segment_tree.html +package segmenttree + +import ( + "github.com/TheAlgorithms/Go/math/max" + "github.com/TheAlgorithms/Go/math/min" +) + +const emptyLazyNode = 0 + +// SegmentTree represents the data structure of a segment tree with lazy propagation +type SegmentTree struct { + Array []int // The original array + SegmentTree []int // Stores the sum of different ranges + LazyTree []int // Stores the values of lazy propagation +} + +// Propagate propagates the lazy updates to the child nodes +func (s *SegmentTree) Propagate(node int, leftNode int, rightNode int) { + if s.LazyTree[node] != emptyLazyNode { + //add lazy node value multiplied by (right-left+1), which represents all interval + //this is the same of adding a value on each node + s.SegmentTree[node] += (rightNode - leftNode + 1) * s.LazyTree[node] + + if leftNode == rightNode { + //leaf node + s.Array[leftNode] += s.LazyTree[node] + } else { + //propagate lazy node value for children nodes + //may propagate multiple times, children nodes should accumulate lazy node value + s.LazyTree[2*node] += s.LazyTree[node] + s.LazyTree[2*node+1] += s.LazyTree[node] + } + + //clear lazy node + s.LazyTree[node] = emptyLazyNode + } +} + +// Query returns the sum of elements of the array in the interval [firstIndex, leftIndex]. +// node, leftNode and rightNode should always start with 1, 0 and len(Array)-1, respectively. +func (s *SegmentTree) Query(node int, leftNode int, rightNode int, firstIndex int, lastIndex int) int { + if (firstIndex > lastIndex) || (leftNode > rightNode) { + //outside the interval + return 0 + } + + //propagate lazy tree + s.Propagate(node, leftNode, rightNode) + + if (leftNode >= firstIndex) && (rightNode <= lastIndex) { + //inside the interval + return s.SegmentTree[node] + } + + //get sum of left and right nodes + mid := (leftNode + rightNode) / 2 + + leftNodeSum := s.Query(2*node, leftNode, mid, firstIndex, min.Int(mid, lastIndex)) + rightNodeSum := s.Query(2*node+1, mid+1, rightNode, max.Int(firstIndex, mid+1), lastIndex) + + return leftNodeSum + rightNodeSum +} + +// Update updates the elements of the array in the range [firstIndex, lastIndex] +// with the new value provided and recomputes the sum of different ranges. +// node, leftNode and rightNode should always start with 1, 0 and len(Array)-1, respectively. +func (s *SegmentTree) Update(node int, leftNode int, rightNode int, firstIndex int, lastIndex int, value int) { + //propagate lazy tree + s.Propagate(node, leftNode, rightNode) + + if (firstIndex > lastIndex) || (leftNode > rightNode) { + //outside the interval + return + } + + if (leftNode >= firstIndex) && (rightNode <= lastIndex) { + //inside the interval + //accumulate the lazy node value + s.LazyTree[node] += value + s.Propagate(node, leftNode, rightNode) + } else { + //update left and right nodes + mid := (leftNode + rightNode) / 2 + + s.Update(2*node, leftNode, mid, firstIndex, min.Int(mid, lastIndex), value) + s.Update(2*node+1, mid+1, rightNode, max.Int(firstIndex, mid+1), lastIndex, value) + + s.SegmentTree[node] = s.SegmentTree[2*node] + s.SegmentTree[2*node+1] + } +} + +// Build builds the SegmentTree by computing the sum of different ranges. +// node, leftNode and rightNode should always start with 1, 0 and len(Array)-1, respectively. +func (s *SegmentTree) Build(node int, left int, right int) { + if left == right { + //leaf node + s.SegmentTree[node] = s.Array[left] + } else { + //get sum of left and right nodes + mid := (left + right) / 2 + + s.Build(2*node, left, mid) + s.Build(2*node+1, mid+1, right) + + s.SegmentTree[node] = s.SegmentTree[2*node] + s.SegmentTree[2*node+1] + } +} + +// NewSegmentTree returns a new instance of a SegmentTree. It takes an input +// array of integers representing Array, initializes and builds the SegmentTree. +func NewSegmentTree(Array []int) *SegmentTree { + if len(Array) == 0 { + return nil + } + + segTree := SegmentTree{ + Array: Array, + SegmentTree: make([]int, 4*len(Array)), + LazyTree: make([]int, 4*len(Array)), + } + + for i := range segTree.LazyTree { + //fill LazyTree with empty lazy nodes + segTree.LazyTree[i] = emptyLazyNode + } + + //starts with node 1 and interval [0, len(arr)-1] inclusive + segTree.Build(1, 0, len(Array)-1) + + return &segTree +} diff --git a/structure/segmenttree/segmenttree_test.go b/structure/segmenttree/segmenttree_test.go new file mode 100644 index 000000000..33bfef546 --- /dev/null +++ b/structure/segmenttree/segmenttree_test.go @@ -0,0 +1,91 @@ +package segmenttree + +import ( + "testing" +) + +// Query interval +type query struct { + firstIndex int + lastIndex int +} + +type update struct { + firstIndex int + lastIndex int + value int +} + +func TestSegmentTree(t *testing.T) { + var segmentTreeTestData = []struct { + description string + array []int + updates []update + queries []query + expected []int + }{ + { + description: "test empty array", + array: []int{}, + queries: []query{{0, 0}}, + expected: []int{0}, + }, + { + description: "test array with size 5", + array: []int{1, 2, 3, 4, 5}, + queries: []query{{0, 5}, {0, 2}, {2, 4}}, + expected: []int{15, 6, 12}, + }, + { + description: "test array with size 5 and updates", + array: []int{1, 2, 3, 4, 5}, + updates: []update{{firstIndex: 1, lastIndex: 1, value: 2}, + {firstIndex: 2, lastIndex: 2, value: 3}}, + queries: []query{{0, 5}, {0, 2}, {2, 4}}, + expected: []int{20, 11, 15}, + }, + { + description: "test array with size 5 and single index updates", + array: []int{1, 2, 3, 4, 5}, + updates: []update{{firstIndex: 1, lastIndex: 1, value: 2}, + {firstIndex: 2, lastIndex: 2, value: 3}}, + queries: []query{{0, 5}, {0, 2}, {2, 4}}, + expected: []int{20, 11, 15}, + }, + { + description: "test array with size 5 and range updates", + array: []int{1, 2, 3, 4, 5}, + updates: []update{{firstIndex: 0, lastIndex: 4, value: 2}, + {firstIndex: 2, lastIndex: 4, value: 2}}, + queries: []query{{0, 5}, {0, 2}, {2, 4}}, + expected: []int{31, 14, 24}, + }, + { + description: "test array with size 11 and range updates", + array: []int{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, + updates: []update{{firstIndex: 2, lastIndex: 8, value: 2}, + {firstIndex: 2, lastIndex: 8, value: 2}}, + queries: []query{{3, 5}, {7, 8}, {4, 5}, {8, 8}}, + expected: []int{15, 10, 10, 5}, + }, + } + for _, test := range segmentTreeTestData { + t.Run(test.description, func(t *testing.T) { + segmentTree := NewSegmentTree(test.array) + + for i := 0; i < len(test.updates); i++ { + segmentTree.Update(1, 0, len(test.array)-1, test.updates[i].firstIndex, test.updates[i].lastIndex, test.updates[i].value) + } + + for i := 0; i < len(test.queries); i++ { + result := segmentTree.Query(1, 0, len(test.array)-1, test.queries[i].firstIndex, test.queries[i].lastIndex) + + if result != test.expected[i] { + t.Logf("FAIL: %s", test.description) + t.Fatalf("Expected result: %d\nFound: %d\n", test.expected[i], result) + } + } + + }) + } +} diff --git a/structure/set/set.go b/structure/set/set.go new file mode 100644 index 000000000..b8c7b51e1 --- /dev/null +++ b/structure/set/set.go @@ -0,0 +1,170 @@ +// package set implements a Set using a golang map. +// This implies that only the types that are accepted as valid map keys can be used as set elements. +// For instance, do not try to Add a slice, or the program will panic. +package set + +// New gives new set. +func New[T comparable](items ...T) Set[T] { + st := set[T]{ + elements: make(map[T]bool), + } + for _, item := range items { + st.Add(item) + } + return &st +} + +// Set is an interface of possible methods on 'set'. +type Set[T comparable] interface { + // Add: adds new element to the set + Add(item T) + // Delete: deletes the passed element from the set if present + Delete(item T) + // Len: gives the length of the set (total no. of elements in set) + Len() int + // GetItems: gives the array( []T ) of elements of the set. + GetItems() []T + // In: checks whether item is present in set or not. + In(item T) bool + // IsSubsetOf: checks whether set is subset of set2 or not. + IsSubsetOf(set2 Set[T]) bool + // IsProperSubsetOf: checks whether set is proper subset of set2 or not. + // ex: [1,2,3] proper subset of [1,2,3,4] -> true + IsProperSubsetOf(set2 Set[T]) bool + // IsSupersetOf: checks whether set is superset of set2 or not. + IsSupersetOf(set2 Set[T]) bool + // IsProperSupersetOf: checks whether set is proper superset of set2 or not. + // ex: [1,2,3,4] proper superset of [1,2,3] -> true + IsProperSupersetOf(set2 Set[T]) bool + // Union: gives new union set of both sets. + // ex: [1,2,3] union [3,4,5] -> [1,2,3,4,5] + Union(set2 Set[T]) Set[T] + // Intersection: gives new intersection set of both sets. + // ex: [1,2,3] Intersection [3,4,5] -> [3] + Intersection(set2 Set[T]) Set[T] + // Difference: gives new difference set of both sets. + // ex: [1,2,3] Difference [3,4,5] -> [1,2] + Difference(set2 Set[T]) Set[T] + // SymmetricDifference: gives new symmetric difference set of both sets. + // ex: [1,2,3] SymmetricDifference [3,4,5] -> [1,2,4,5] + SymmetricDifference(set2 Set[T]) Set[T] +} + +type set[T comparable] struct { + elements map[T]bool +} + +func (st *set[T]) Add(value T) { + st.elements[value] = true +} + +func (st *set[T]) Delete(value T) { + delete(st.elements, value) +} + +func (st *set[T]) GetItems() []T { + keys := make([]T, 0, len(st.elements)) + for k := range st.elements { + keys = append(keys, k) + } + return keys +} + +func (st *set[T]) Len() int { + return len(st.elements) +} + +func (st *set[T]) In(value T) bool { + if _, in := st.elements[value]; in { + return true + } + return false +} + +func (st *set[T]) IsSubsetOf(superSet Set[T]) bool { + if st.Len() > superSet.Len() { + return false + } + + for _, item := range st.GetItems() { + if !superSet.In(item) { + return false + } + } + return true +} + +func (st *set[T]) IsProperSubsetOf(superSet Set[T]) bool { + if st.Len() == superSet.Len() { + return false + } + return st.IsSubsetOf(superSet) +} + +func (st *set[T]) IsSupersetOf(subSet Set[T]) bool { + return subSet.IsSubsetOf(st) +} + +func (st *set[T]) IsProperSupersetOf(subSet Set[T]) bool { + if st.Len() == subSet.Len() { + return false + } + return st.IsSupersetOf(subSet) +} + +func (st *set[T]) Union(st2 Set[T]) Set[T] { + unionSet := New[T]() + for _, item := range st.GetItems() { + unionSet.Add(item) + } + for _, item := range st2.GetItems() { + unionSet.Add(item) + } + return unionSet +} + +func (st *set[T]) Intersection(st2 Set[T]) Set[T] { + intersectionSet := New[T]() + var minSet, maxSet Set[T] + if st.Len() > st2.Len() { + minSet = st2 + maxSet = st + } else { + minSet = st + maxSet = st2 + } + for _, item := range minSet.GetItems() { + if maxSet.In(item) { + intersectionSet.Add(item) + } + } + return intersectionSet +} + +func (st *set[T]) Difference(st2 Set[T]) Set[T] { + differenceSet := New[T]() + for _, item := range st.GetItems() { + if !st2.In(item) { + differenceSet.Add(item) + } + } + return differenceSet +} + +func (st *set[T]) SymmetricDifference(st2 Set[T]) Set[T] { + symmetricDifferenceSet := New[T]() + dropSet := New[T]() + for _, item := range st.GetItems() { + if st2.In(item) { + dropSet.Add(item) + } else { + symmetricDifferenceSet.Add(item) + } + } + for _, item := range st2.GetItems() { + if !dropSet.In(item) { + symmetricDifferenceSet.Add(item) + } + } + return symmetricDifferenceSet +} diff --git a/structure/set/set_test.go b/structure/set/set_test.go new file mode 100644 index 000000000..2000760ac --- /dev/null +++ b/structure/set/set_test.go @@ -0,0 +1,220 @@ +package set + +import ( + "testing" +) + +func TestNew(t *testing.T) { + set := New(1, 2, 3) + if set.Len() != 3 { + t.Errorf("expecting 3 elements in the set but got %v: %v", set.Len(), set.GetItems()) + } + for _, n := range []int{1, 2, 3} { + if !set.In(n) { + t.Errorf("expecting %d to be present in the set but was not; set is %v", n, set.GetItems()) + } + } + if set.In(5) { + t.Errorf("expecting 5 not to be present in the set but it was; set is %v", set.GetItems()) + } +} + +func TestAdd(t *testing.T) { + td := []struct { + name string + input int + expElems []int + }{ + {"add new element", 5, []int{1, 2, 3, 5}}, + {"add exiting element", 3, []int{1, 2, 3}}, + } + for _, tc := range td { + t.Run(tc.name, func(t *testing.T) { + s := New(1, 2, 3) + s.Add(tc.input) + if s.Len() != len(tc.expElems) { + t.Errorf("expecting %d elements in the set but got %d: set is %v", len(tc.expElems), s.Len(), s.GetItems()) + } + for _, n := range tc.expElems { + if !s.In(n) { + t.Errorf("expecting %d to be present in the set but was not; set is %v", n, s.GetItems()) + } + } + }) + } +} + +func TestDelete(t *testing.T) { + td := []struct { + name string + input int + expElems []int + }{ + {"delete exiting element", 3, []int{1, 2}}, + {"delete not existing element", 5, []int{1, 2, 3}}, + } + for _, tc := range td { + t.Run(tc.name, func(t *testing.T) { + s := New(1, 2, 3) + s.Delete(tc.input) + if s.Len() != len(tc.expElems) { + t.Errorf("expecting %d elements in the set but got %d: set is %v", len(tc.expElems), s.Len(), s.GetItems()) + } + for _, n := range tc.expElems { + if !s.In(n) { + t.Errorf("expecting %d to be present in the set but was not; set is %v", n, s.GetItems()) + } + } + }) + } +} + +func TestIsSubsetOf(t *testing.T) { + s1, s2 := New(1, 2, 3), New(1, 2, 3, 4) + if !s1.IsSubsetOf(s2) { + t.Errorf("expecting %v to be a subset of %v", s1, s2) + } + if s2.IsSubsetOf(s1) { + t.Errorf("expecting %v not to be a subset of %v", s2, s1) + } + if s3 := New(1, 2, 5, 6); s1.IsSubsetOf(s3) { + t.Errorf("expecting %v not to be a subset of %v", s1, s3) + } +} + +func TestIsProperSubsetOf(t *testing.T) { + s1, s2 := New(1, 2, 3), New(1, 2, 3, 4) + if !s1.IsProperSubsetOf(s2) { + t.Errorf("expecting %v to be a proper subset of %v", s1, s2) + } + if s3 := New(3, 2, 1); s1.IsProperSubsetOf(s3) { + t.Errorf("expecting %v not to be a proper subset of %v", s1, s3) + } +} + +func TestIsSupersetOf(t *testing.T) { + s1, s2 := New(1, 2, 3), New(1, 2, 3, 4) + if !s2.IsSupersetOf(s1) { + t.Errorf("expecting %v to be a superset of %v", s2, s1) + } + if s1.IsSupersetOf(s2) { + t.Errorf("expecting %v not to be a superset of %v", s1, s2) + } + if s3 := New(1, 2, 5); s2.IsSupersetOf(s3) { + t.Errorf("expecting %v not to be a superset of %v", s2, s3) + } +} + +func TestIsProperSupersetOf(t *testing.T) { + s1, s2 := New(1, 2, 3), New(1, 2, 3, 4) + if !s2.IsProperSupersetOf(s1) { + t.Errorf("expecting %v to be a proper superset of %v", s2, s1) + } + if s3 := New(3, 2, 1); s1.IsProperSupersetOf(s3) { + t.Errorf("expecting %v not to be a proper superset of %v", s1, s3) + } +} + +func TestUnion(t *testing.T) { + td := []struct { + name string + s1 Set[int] + s2 Set[int] + expSet Set[int] + }{ + {"union of different sets", New(1, 2, 3), New(4, 5, 6), New(1, 2, 3, 4, 5, 6)}, + {"union of sets with elements in common", New(1, 2, 3), New(1, 2, 4), New(1, 2, 3, 4)}, + {"union of same sets", New(1, 2, 3), New(1, 2, 3), New(1, 2, 3)}, + } + for _, tc := range td { + t.Run(tc.name, func(t *testing.T) { + s := tc.s1.Union(tc.s2) + if s.Len() != tc.expSet.Len() { + t.Errorf("expecting %d elements in the set but got %d: set is %v", tc.expSet.Len(), s.Len(), s.GetItems()) + } + for _, n := range tc.expSet.GetItems() { + if !s.In(n) { + t.Errorf("expecting %d to be present in the set but was not; set is %v", n, s.GetItems()) + } + } + }) + } +} + +func TestIntersection(t *testing.T) { + td := []struct { + name string + s1 Set[int] + s2 Set[int] + expSet Set[int] + }{ + {"intersection of different sets", New(0, 1, 2, 3), New(4, 5, 6), New[int]()}, + {"intersection of sets with elements in common", New(1, 2, 3), New(1, 2, 4), New(1, 2)}, + {"intersection of same sets", New(1, 2, 3), New(1, 2, 3), New(1, 2, 3)}, + } + for _, tc := range td { + t.Run(tc.name, func(t *testing.T) { + s := tc.s1.Intersection(tc.s2) + if s.Len() != tc.expSet.Len() { + t.Errorf("expecting %d elements in the set but got %d: set is %v", tc.expSet.Len(), s.Len(), s.GetItems()) + } + for _, n := range tc.expSet.GetItems() { + if !s.In(n) { + t.Errorf("expecting %d to be present in the set but was not; set is %v", n, s.GetItems()) + } + } + }) + } +} + +func TestDifference(t *testing.T) { + td := []struct { + name string + s1 Set[int] + s2 Set[int] + expSet Set[int] + }{ + {"difference of different sets", New(1, 2, 3), New(4, 5, 6), New(1, 2, 3)}, + {"difference of sets with elements in common", New(1, 2, 3), New(1, 2, 4), New(3)}, + {"difference of same sets", New(1, 2, 3), New(1, 2, 3), New[int]()}, + } + for _, tc := range td { + t.Run(tc.name, func(t *testing.T) { + s := tc.s1.Difference(tc.s2) + if s.Len() != tc.expSet.Len() { + t.Errorf("expecting %d elements in the set but got %d: set is %v", tc.expSet.Len(), s.Len(), s.GetItems()) + } + for _, n := range tc.expSet.GetItems() { + if !s.In(n) { + t.Errorf("expecting %d to be present in the set but was not; set is %v", n, s.GetItems()) + } + } + }) + } +} + +func TestSymmetricDifference(t *testing.T) { + td := []struct { + name string + s1 Set[int] + s2 Set[int] + expSet Set[int] + }{ + {"symmetric difference of different sets", New(1, 2, 3), New(4, 5, 6), New(1, 2, 3, 4, 5, 6)}, + {"symmetric difference of sets with elements in common", New(1, 2, 3), New(1, 2, 4), New(3, 4)}, + {"symmetric difference of same sets", New(1, 2, 3), New(1, 2, 3), New[int]()}, + } + for _, tc := range td { + t.Run(tc.name, func(t *testing.T) { + s := tc.s1.SymmetricDifference(tc.s2) + if s.Len() != tc.expSet.Len() { + t.Errorf("expecting %d elements in the set but got %d: set is %v", tc.expSet.Len(), s.Len(), s.GetItems()) + } + for _, n := range tc.expSet.GetItems() { + if !s.In(n) { + t.Errorf("expecting %d to be present in the set but was not; set is %v", n, s.GetItems()) + } + } + }) + } +} diff --git a/structure/set/setexample_test.go b/structure/set/setexample_test.go new file mode 100644 index 000000000..7cd929462 --- /dev/null +++ b/structure/set/setexample_test.go @@ -0,0 +1,20 @@ +package set + +import ( + "fmt" +) + +func ExampleSet() { + + set := New(1, 2, 3) + fmt.Println(set.Len()) // 3 + set.Add(3) + fmt.Println(set.Len()) // 3 + set.Add(4) + fmt.Println(set.Len()) // 4 + + // output: + // 3 + // 3 + // 4 +} diff --git a/structure/stack/stack_test.go b/structure/stack/stack_test.go new file mode 100644 index 000000000..0de3dc0d6 --- /dev/null +++ b/structure/stack/stack_test.go @@ -0,0 +1,188 @@ +// Stack Test +// description: based on `geeksforgeeks` description Stack is a linear data structure which follows a particular order in which the operations are performed. +// The order may be LIFO(Last In First Out) or FILO(First In Last Out). +// details: +// Stack Data Structure : https://www.geeksforgeeks.org/stack-data-structure-introduction-program/ +// Stack (abstract data type) : https://en.wikipedia.org/wiki/Stack_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see stackarray.go, stacklinkedlist.go, stacklinkedlistwithlist.go + +package stack_test + +import ( + "container/list" + "github.com/TheAlgorithms/Go/structure/stack" + "reflect" + "testing" +) + +// TestStackLinkedList for testing Stack with LinkedList +func TestStackLinkedList(t *testing.T) { + var newStack stack.Stack + + newStack.Push(1) + newStack.Push(2) + + t.Run("Stack Push", func(t *testing.T) { + result := newStack.Show() + expected := []any{2, 1} + for x := range result { + if result[x] != expected[x] { + t.Errorf("Stack Push is not work, got %v but expected %v", result, expected) + } + } + }) + + t.Run("Stack isEmpty", func(t *testing.T) { + if newStack.IsEmpty() { + t.Error("Stack isEmpty is returned true but expected false", newStack.IsEmpty()) + } + + }) + + t.Run("Stack Length", func(t *testing.T) { + if newStack.Length() != 2 { + t.Error("Stack Length should be 2 but got", newStack.Length()) + } + }) + + newStack.Pop() + pop := newStack.Pop() + + t.Run("Stack Pop", func(t *testing.T) { + if pop != 1 { + t.Error("Stack Pop should return 1 but is returned", pop) + } + + }) + + newStack.Push(52) + newStack.Push(23) + newStack.Push(99) + t.Run("Stack Peek", func(t *testing.T) { + if newStack.Peek() != 99 { + t.Error("Stack Peak should return 99 but got ", newStack.Peek()) + } + }) +} + +// TestStackArray for testing Stack with Array +func TestStackArray(t *testing.T) { + newStack := stack.NewStack[int]() + t.Run("Stack With Array", func(t *testing.T) { + + newStack.Push(2) + newStack.Push(3) + + t.Run("Stack Push", func(t *testing.T) { + var stackElements []any + for i := 0; i < 2; i++ { + poppedElement := newStack.Pop() + stackElements = append(stackElements, poppedElement) + } + + if !reflect.DeepEqual([]any{3, 2}, stackElements) { + t.Errorf("Stack Push is not work we expected %v but got %v", []any{3, 2}, newStack) + } + + newStack.Push(2) + newStack.Push(3) + }) + + pop := newStack.Pop() + + t.Run("Stack Pop", func(t *testing.T) { + if newStack.Length() == 2 && pop != 3 { + t.Errorf("Stack Pop is not work we expected %v but got %v", 3, pop) + } + }) + + newStack.Push(2) + newStack.Push(83) + + t.Run("Stack Peak", func(t *testing.T) { + if newStack.Peek() != 83 { + t.Errorf("Stack Peek is not work we expected %v but got %v", 83, newStack.Peek()) + } + }) + + t.Run("Stack Length", func(t *testing.T) { + if newStack.Length() != 3 { + t.Errorf("Stack Length is not work we expected %v but got %v", 3, newStack.Length()) + } + }) + + t.Run("Stack Empty", func(t *testing.T) { + if newStack.IsEmpty() == true { + t.Errorf("Stack Empty is not work we expected %v but got %v", false, newStack.IsEmpty()) + } + + newStack.Pop() + newStack.Pop() + newStack.Pop() + + if newStack.IsEmpty() == false { + t.Errorf("Stack Empty is not work we expected %v but got %v", true, newStack.IsEmpty()) + } + }) + }) +} + +// TestStackLinkedListWithList for testing Stack with Container/List Library (STL) +func TestStackLinkedListWithList(t *testing.T) { + stackList := &stack.SList{ + Stack: list.New(), + } + + t.Run("Stack Push", func(t *testing.T) { + + stackList.Push(2) + stackList.Push(3) + + if stackList.Length() != 2 { + t.Errorf("Stack Push is not work we expected %v but got %v", 2, stackList.Length()) + } + }) + + t.Run("Stack Pop", func(t *testing.T) { + pop, _ := stackList.Pop() + + if stackList.Length() == 1 && pop != 3 { + t.Errorf("Stack Pop is not work we expected %v but got %v", 3, pop) + } + }) + + t.Run("Stack Peak", func(t *testing.T) { + + stackList.Push(2) + stackList.Push(83) + peak, _ := stackList.Peek() + if peak != 83 { + t.Errorf("Stack Peak is not work we expected %v but got %v", 83, peak) + } + }) + + t.Run("Stack Length", func(t *testing.T) { + if stackList.Length() != 3 { + t.Errorf("Stack Length is not work we expected %v but got %v", 3, stackList.Length()) + } + }) + + t.Run("Stack Empty", func(t *testing.T) { + if stackList.IsEmpty() == true { + t.Errorf("Stack Empty is not work we expected %v but got %v", false, stackList.IsEmpty()) + } + + d1, err := stackList.Pop() + d2, _ := stackList.Pop() + d3, _ := stackList.Pop() + + if err != nil { + t.Errorf("got an unexpected error %v, pop1: %v, pop2: %v, pop3: %v", err, d1, d2, d3) + } + + if stackList.IsEmpty() == false { + t.Errorf("Stack Empty is not work we expected %v but got %v", true, stackList.IsEmpty()) + } + }) +} diff --git a/structure/stack/stackarray.go b/structure/stack/stackarray.go new file mode 100644 index 000000000..2d0fc05c4 --- /dev/null +++ b/structure/stack/stackarray.go @@ -0,0 +1,55 @@ +// Stack Array +// description: based on `geeksforgeeks` description Stack is a linear data structure which follows a particular order in which the operations are performed. +// The order may be LIFO(Last In First Out) or FILO(First In Last Out). +// details: +// Stack Data Structure : https://www.geeksforgeeks.org/stack-data-structure-introduction-program/ +// Stack (abstract data type) : https://en.wikipedia.org/wiki/Stack_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see stacklinkedlist.go, stacklinkedlistwithlist.go, stack_test.go + +package stack + +type Array[T any] struct { + elements []T +} + +// NewStack creates and returns a new stack. +func NewStack[T any]() *Array[T] { + return &Array[T]{} +} + +// Push adds an element to the top of the stack. +func (s *Array[T]) Push(value T) { + s.elements = append(s.elements, value) +} + +// Size returns the number of elements in the stack. +func (s *Array[T]) Length() int { + return len(s.elements) +} + +// Peek returns the top element of the stack without removing it. +func (s *Array[T]) Peek() T { + if s.IsEmpty() { + var zeroValue T + return zeroValue // Stack is empty + } + return s.elements[len(s.elements)-1] +} + +// IsEmpty returns true if the stack is empty, false otherwise. +func (s *Array[T]) IsEmpty() bool { + return len(s.elements) == 0 +} + +// Pop removes and returns the top element from the stack. +func (s *Array[T]) Pop() T { + if s.IsEmpty() { + var zeroValue T + return zeroValue // Stack is empty + } + index := len(s.elements) - 1 + popped := s.elements[index] + s.elements = s.elements[:index] + return popped +} diff --git a/structure/stack/stacklinkedlist.go b/structure/stack/stacklinkedlist.go new file mode 100644 index 000000000..1328729e6 --- /dev/null +++ b/structure/stack/stacklinkedlist.go @@ -0,0 +1,72 @@ +// Stack Linked-List +// description: based on `geeksforgeeks` description Stack is a linear data structure which follows a particular order in which the operations are performed. +// The order may be LIFO(Last In First Out) or FILO(First In Last Out). +// details: +// Stack Data Structure : https://www.geeksforgeeks.org/stack-data-structure-introduction-program/ +// Stack (abstract data type) : https://en.wikipedia.org/wiki/Stack_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see stacklinkedlistwithlist.go, stackarray.go, stack_test.go + +package stack + +// Node structure +type Node struct { + Val any + Next *Node +} + +// Stack has jost top of node and with length +type Stack struct { + top *Node + length int +} + +// push add value to last index +func (ll *Stack) Push(n any) { + newStack := &Node{} // new node + + newStack.Val = n + newStack.Next = ll.top + + ll.top = newStack + ll.length++ +} + +// pop remove last item as first output +func (ll *Stack) Pop() any { + result := ll.top.Val + if ll.top.Next == nil { + ll.top = nil + } else { + ll.top.Val, ll.top.Next = ll.top.Next.Val, ll.top.Next.Next + } + + ll.length-- + return result +} + +// isEmpty to check our array is empty or not +func (ll *Stack) IsEmpty() bool { + return ll.length == 0 +} + +// len use to return length of our stack +func (ll *Stack) Length() int { + return ll.length +} + +// peak return last input value +func (ll *Stack) Peek() any { + return ll.top.Val +} + +// show all value as an interface array +func (ll *Stack) Show() (in []any) { + current := ll.top + + for current != nil { + in = append(in, current.Val) + current = current.Next + } + return +} diff --git a/structure/stack/stacklinkedlistwithlist.go b/structure/stack/stacklinkedlistwithlist.go new file mode 100644 index 000000000..ae53a499b --- /dev/null +++ b/structure/stack/stacklinkedlistwithlist.go @@ -0,0 +1,60 @@ +// Stack Linked-List with standard library (Container/List) +// description: based on `geeksforgeeks` description Stack is a linear data structure which follows a particular order in which the operations are performed. +// The order may be LIFO(Last In First Out) or FILO(First In Last Out). +// details: +// Stack Data Structure : https://www.geeksforgeeks.org/stack-data-structure-introduction-program/ +// Stack (abstract data type) : https://en.wikipedia.org/wiki/Stack_(abstract_data_type) +// author [Milad](https://github.com/miraddo) +// see stacklinkedlist.go, stackarray.go, stack_test.go + +package stack + +import ( + "container/list" + "fmt" +) + +// SList is our struct that point to stack with container/list.List library +type SList struct { + Stack *list.List +} + +// Push add a value into our stack +func (sl *SList) Push(val any) { + sl.Stack.PushFront(val) +} + +// Peak is return last value that insert into our stack +func (sl *SList) Peek() (any, error) { + if !sl.IsEmpty() { + element := sl.Stack.Front() + return element.Value, nil + } + return "", fmt.Errorf("stack list is empty") +} + +// Pop is return last value that insert into our stack +// also it will remove it in our stack +func (sl *SList) Pop() (any, error) { + if !sl.IsEmpty() { + // get last element that insert into stack + element := sl.Stack.Front() + // remove element in stack + sl.Stack.Remove(element) + // return element value + return element.Value, nil + } + return "", fmt.Errorf("stack list is empty") +} + +// Length return length of our stack +func (sl *SList) Length() int { + return sl.Stack.Len() +} + +// Empty check our stack has value or not +func (sl *SList) IsEmpty() bool { + // check our stack is empty or not + // if is 0 it means our stack is empty otherwise is not empty + return sl.Stack.Len() == 0 +} diff --git a/structure/structure_test.go b/structure/structure_test.go new file mode 100644 index 000000000..29990a834 --- /dev/null +++ b/structure/structure_test.go @@ -0,0 +1,3 @@ +// Empty test file to keep track of all the tests for the algorithms. + +package structure diff --git a/structure/tree/avl.go b/structure/tree/avl.go new file mode 100644 index 000000000..4b0aee7c4 --- /dev/null +++ b/structure/tree/avl.go @@ -0,0 +1,357 @@ +// AVL tree is a self-balancing binary search tree. +// +// For more details check out those link below here: +// Wikipedia article: https://en.wikipedia.org/wiki/AVL_tree +// see avl.go + +package tree + +import ( + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/math/max" +) + +// Verify Interface Compliance +var _ Node[int] = &AVLNode[int]{} + +// AVLNode represents a single node in the AVL. +type AVLNode[T constraints.Ordered] struct { + key T + parent *AVLNode[T] + left *AVLNode[T] + right *AVLNode[T] + height int +} + +func (n *AVLNode[T]) Key() T { + return n.key +} + +func (n *AVLNode[T]) Parent() Node[T] { + return n.parent +} + +func (n *AVLNode[T]) Left() Node[T] { + return n.left +} + +func (n *AVLNode[T]) Right() Node[T] { + return n.right +} + +func (n *AVLNode[T]) Height() int { + return n.height +} + +// AVL represents a AVL tree. +// By default, _NIL = nil. +type AVL[T constraints.Ordered] struct { + Root *AVLNode[T] + _NIL *AVLNode[T] // a sentinel value for nil +} + +// NewAVL creates a novel AVL tree +func NewAVL[T constraints.Ordered]() *AVL[T] { + return &AVL[T]{ + Root: nil, + _NIL: nil, + } +} + +// Empty determines the AVL tree is empty +func (avl *AVL[T]) Empty() bool { + return avl.Root == avl._NIL +} + +// Push a chain of Node's into the AVL Tree +func (avl *AVL[T]) Push(keys ...T) { + for _, k := range keys { + avl.Root = avl.pushHelper(avl.Root, k) + } +} + +// Delete a Node from the AVL Tree +func (avl *AVL[T]) Delete(key T) bool { + if !avl.Has(key) { + return false + } + + avl.Root = avl.deleteHelper(avl.Root, key) + return true +} + +// Get a Node from the AVL Tree +func (avl *AVL[T]) Get(key T) (Node[T], bool) { + return searchTreeHelper[T](avl.Root, avl._NIL, key) +} + +// Has Determines the tree has the node of Key +func (avl *AVL[T]) Has(key T) bool { + _, ok := searchTreeHelper[T](avl.Root, avl._NIL, key) + return ok +} + +// PreOrder Traverses the tree in the following order Root --> Left --> Right +func (avl *AVL[T]) PreOrder() []T { + traversal := make([]T, 0) + preOrderRecursive[T](avl.Root, avl._NIL, &traversal) + return traversal +} + +// InOrder Traverses the tree in the following order Left --> Root --> Right +func (avl *AVL[T]) InOrder() []T { + return inOrderHelper[T](avl.Root, avl._NIL) +} + +// PostOrder traverses the tree in the following order Left --> Right --> Root +func (avl *AVL[T]) PostOrder() []T { + traversal := make([]T, 0) + postOrderRecursive[T](avl.Root, avl._NIL, &traversal) + return traversal +} + +// LevelOrder returns the level order traversal of the tree +func (avl *AVL[T]) LevelOrder() []T { + traversal := make([]T, 0) + levelOrderHelper[T](avl.Root, avl._NIL, &traversal) + return traversal +} + +// AccessNodesByLayer accesses nodes layer by layer (2-D array), instead of printing the results as 1-D array. +func (avl *AVL[T]) AccessNodesByLayer() [][]T { + return accessNodeByLayerHelper[T](avl.Root, avl._NIL) +} + +// Depth returns the calculated depth of the AVL tree +func (avl *AVL[T]) Depth() int { + return calculateDepth[T](avl.Root, avl._NIL, 0) +} + +// Max returns the Max value of the tree +func (avl *AVL[T]) Max() (T, bool) { + ret := maximum[T](avl.Root, avl._NIL) + if ret == avl._NIL { + var dft T + return dft, false + } + return ret.Key(), true +} + +// Min returns the Min value of the tree +func (avl *AVL[T]) Min() (T, bool) { + ret := minimum[T](avl.Root, avl._NIL) + if ret == avl._NIL { + var dft T + return dft, false + } + return ret.Key(), true +} + +// Predecessor returns the Predecessor of the node of Key +// if there is no predecessor, return default value of type T and false +// otherwise return the Key of predecessor and true +func (avl *AVL[T]) Predecessor(key T) (T, bool) { + node, ok := searchTreeHelper[T](avl.Root, avl._NIL, key) + if !ok { + var dft T + return dft, ok + } + return predecessorHelper[T](node, avl._NIL) +} + +// Successor returns the Successor of the node of Key +// if there is no successor, return default value of type T and false +// otherwise return the Key of successor and true +func (avl *AVL[T]) Successor(key T) (T, bool) { + node, ok := searchTreeHelper[T](avl.Root, avl._NIL, key) + if !ok { + var dft T + return dft, ok + } + return successorHelper[T](node, avl._NIL) +} + +func (avl *AVL[T]) pushHelper(root *AVLNode[T], key T) *AVLNode[T] { + if root == avl._NIL { + return &AVLNode[T]{ + key: key, + left: avl._NIL, + right: avl._NIL, + parent: avl._NIL, + height: 1, + } + } + + switch { + case key < root.key: + tmp := avl.pushHelper(root.left, key) + tmp.parent = root + root.left = tmp + case key > root.key: + tmp := avl.pushHelper(root.right, key) + tmp.parent = root + root.right = tmp + default: + return root + } + + // balance the tree + root.height = avl.height(root) + bFactor := avl.balanceFactor(root) + if bFactor > 1 { + switch { + case key < root.left.key: + return avl.rightRotate(root) + case key > root.left.key: + root.left = avl.leftRotate(root.left) + return avl.rightRotate(root) + } + } + + if bFactor < -1 { + switch { + case key > root.right.key: + return avl.leftRotate(root) + case key < root.right.key: + root.right = avl.rightRotate(root.right) + return avl.leftRotate(root) + } + } + + return root +} + +func (avl *AVL[T]) deleteHelper(root *AVLNode[T], key T) *AVLNode[T] { + if root == avl._NIL { + return root + } + + switch { + case key < root.key: + tmp := avl.deleteHelper(root.left, key) + root.left = tmp + if tmp != avl._NIL { + tmp.parent = root + } + case key > root.key: + tmp := avl.deleteHelper(root.right, key) + root.right = tmp + if tmp != avl._NIL { + tmp.parent = root + } + default: + if root.left == avl._NIL || root.right == avl._NIL { + tmp := root.left + if root.right != avl._NIL { + tmp = root.right + } + + if tmp == avl._NIL { + root = avl._NIL + } else { + tmp.parent = root.parent + root = tmp + } + } else { + tmp := minimum[T](root.right, avl._NIL).(*AVLNode[T]) + root.key = tmp.key + del := avl.deleteHelper(root.right, tmp.key) + root.right = del + if del != avl._NIL { + del.parent = root + } + } + } + + if root == avl._NIL { + return root + } + + // balance the tree + root.height = avl.height(root) + bFactor := avl.balanceFactor(root) + switch { + case bFactor > 1: + switch { + case avl.balanceFactor(root.left) >= 0: + return avl.rightRotate(root) + default: + root.left = avl.leftRotate(root.left) + return avl.rightRotate(root) + } + case bFactor < -1: + switch { + case avl.balanceFactor(root.right) <= 0: + return avl.leftRotate(root) + default: + root.right = avl.rightRotate(root.right) + return avl.leftRotate(root) + } + } + + return root +} + +func (avl *AVL[T]) height(root *AVLNode[T]) int { + if root == avl._NIL { + return 1 + } + + var leftHeight, rightHeight int + if root.left != avl._NIL { + leftHeight = root.left.height + } + if root.right != avl._NIL { + rightHeight = root.right.height + } + return 1 + max.Int(leftHeight, rightHeight) +} + +// balanceFactor : negative balance factor means subtree Root is heavy toward Left +// and positive balance factor means subtree Root is heavy toward Right side +func (avl *AVL[T]) balanceFactor(root *AVLNode[T]) int { + var leftHeight, rightHeight int + if root.left != avl._NIL { + leftHeight = root.left.height + } + if root.right != avl._NIL { + rightHeight = root.right.height + } + return leftHeight - rightHeight +} + +func (avl *AVL[T]) leftRotate(x *AVLNode[T]) *AVLNode[T] { + y := x.right + yl := y.left + y.left = x + x.right = yl + + if yl != avl._NIL { + yl.parent = x + } + + y.parent = x.parent + x.parent = y + + x.height = avl.height(x) + y.height = avl.height(y) + return y +} + +func (avl *AVL[T]) rightRotate(x *AVLNode[T]) *AVLNode[T] { + y := x.left + yr := y.right + y.right = x + x.left = yr + + if yr != avl._NIL { + yr.parent = x + } + + y.parent = x.parent + x.parent = y + + x.height = avl.height(x) + y.height = avl.height(y) + return y +} diff --git a/structure/tree/avl_test.go b/structure/tree/avl_test.go new file mode 100644 index 000000000..70913499a --- /dev/null +++ b/structure/tree/avl_test.go @@ -0,0 +1,321 @@ +package tree_test + +import ( + bt "github.com/TheAlgorithms/Go/structure/tree" + "math/rand" + "sort" + "testing" + "time" +) + +func TestAVLPush(t *testing.T) { + t.Run("LLRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + tree.Push(5, 4, 3) + + root := tree.Root + if root.Key() != 4 { + t.Errorf("Root should have value = 4, not %v", root.Key()) + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2, not %d", root.Height()) + } + + if root.Left().Key() != 3 { + t.Errorf("Left child should have value = 3") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 5 { + t.Errorf("Right child should have value = 5") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + }) + + t.Run("LRRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + tree.Push(5, 3, 4) + + root := tree.Root + if root.Key() != 4 { + t.Errorf("Root should have value = 4, not %v", root.Key()) + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2, not %d", root.Height()) + } + + if root.Left().Key() != 3 { + t.Errorf("Left child should have value = 3") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 5 { + t.Errorf("Right child should have value = 5") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + }) + + t.Run("RRRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + tree.Push(3) + tree.Push(4) + tree.Push(5) + + root := tree.Root + if root.Key() != 4 { + t.Errorf("Root should have value = 4, not %v", root.Key()) + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2, not %d", root.Height()) + } + + if root.Left().Key() != 3 { + t.Errorf("Left child should have value = 3") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 5 { + t.Errorf("Right child should have value = 5") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + }) + t.Run("RLRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + tree.Push(3) + tree.Push(5) + tree.Push(4) + + root := tree.Root + if root.Key() != 4 { + t.Errorf("Root should have value = 4") + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2") + } + + if root.Left().Key() != 3 { + t.Errorf("Left child should have value = 3") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 5 { + t.Errorf("Right child should have value = 5") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + }) +} + +func TestAVLDelete(t *testing.T) { + t.Run("LLRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + if tree.Delete(5) { + t.Errorf("There is no node, whose value is 5") + } + + tree.Push(5) + tree.Push(4) + tree.Push(3) + tree.Push(2) + + if !tree.Delete(5) { + t.Errorf("There is a node, whose value is 5") + } + + if tree.Delete(50) { + t.Errorf("There is no node, whose value is 50") + } + + root := tree.Root + if root.Key() != 3 { + t.Errorf("Root should have value = 3") + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2") + } + + if root.Left().Key() != 2 { + t.Errorf("Left child should have value = 2") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 4 { + t.Errorf("Right child should have value = 5") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + }) + + t.Run("LRRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + + tree.Push(10) + tree.Push(8) + tree.Push(8) + tree.Push(6) + tree.Push(7) + + if !tree.Delete(10) { + t.Errorf("There is a node, whose value is 10") + } + + if tree.Delete(5) { + t.Errorf("There is no node, whose value is 5") + } + + root := tree.Root + if root.Key() != 7 { + t.Errorf("Root should have value = 7") + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2") + } + + if root.Left().Key() != 6 { + t.Errorf("Left child should have value = 6") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 8 { + t.Errorf("Right child should have value = 8") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + + }) + + t.Run("RRRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + + tree.Push(2) + tree.Push(3) + tree.Push(3) + tree.Push(4) + tree.Push(5) + + if !tree.Delete(2) { + t.Errorf("There is a node, whose value is 2") + } + + if tree.Delete(15) { + t.Errorf("There is no node, whose value is 15") + } + + root := tree.Root + if root.Key() != 4 { + t.Errorf("Root should have value = 4") + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2") + } + + if root.Left().Key() != 3 { + t.Errorf("Left child should have value = 3") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 5 { + t.Errorf("Right child should have value = 5") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + + }) + + t.Run("RLRotation-Test", func(t *testing.T) { + tree := bt.NewAVL[int]() + + tree.Push(7) + tree.Push(6) + tree.Push(6) + tree.Push(9) + tree.Push(8) + + tree.Delete(6) + + root := tree.Root + if root.Key() != 8 { + t.Errorf("Root should have value = 8") + } + if root.Height() != 2 { + t.Errorf("Height of Root should be = 2") + } + + if root.Left().Key() != 7 { + t.Errorf("Left child should have value = 7") + } + if root.Left().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Left child should be 1") + } + + if root.Right().Key() != 9 { + t.Errorf("Right child should have value = 9") + } + if root.Right().(*bt.AVLNode[int]).Height() != 1 { + t.Errorf("Height of Right should be 1") + } + + }) + + t.Run("Random Test", func(t *testing.T) { + nums := []int{100, 500, 1000, 10_000} + for _, n := range nums { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + tree := bt.NewAVL[int]() + nums := rnd.Perm(n) + tree.Push(nums...) + + rets := tree.InOrder() + if !sort.IntsAreSorted(rets) { + t.Error("Error with Push") + } + + if res, ok := tree.Min(); !ok || res != rets[0] { + t.Errorf("Error with Min, get %d, want: %d", res, rets[0]) + } + + if res, ok := tree.Max(); !ok || res != rets[n-1] { + t.Errorf("Error with Max, get %d, want: %d", res, rets[n-1]) + } + + for i := 0; i < n-1; i++ { + if ret, ok := tree.Successor(rets[0]); ret != rets[1] || !ok { + t.Error("Error with Successor") + } + if ret, ok := tree.Predecessor(rets[1]); ret != rets[0] || !ok { + t.Error("Error with Predecessor") + } + + ok := tree.Delete(nums[i]) + rets = tree.InOrder() + if !ok || !sort.IntsAreSorted(rets) { + t.Errorf("Error With Delete") + } + } + } + }) +} diff --git a/structure/tree/bstree.go b/structure/tree/bstree.go new file mode 100644 index 000000000..b4f6a0a7c --- /dev/null +++ b/structure/tree/bstree.go @@ -0,0 +1,228 @@ +// Binary search tree. +// +// For more details check out those links below here: +// Wikipedia article: https://en.wikipedia.org/wiki/Binary_search_tree +// see bstree.go + +package tree + +import "github.com/TheAlgorithms/Go/constraints" + +// Verify Interface Compliance +var _ Node[int] = &BSNode[int]{} + +// BSNode represents a single node in the BinarySearch. +type BSNode[T constraints.Ordered] struct { + key T + parent *BSNode[T] + left *BSNode[T] + right *BSNode[T] +} + +func (n *BSNode[T]) Key() T { + return n.key +} + +func (n *BSNode[T]) Parent() Node[T] { + return n.parent +} + +func (n *BSNode[T]) Left() Node[T] { + return n.left +} + +func (n *BSNode[T]) Right() Node[T] { + return n.right +} + +// BinarySearch represents a Binary-Search tree. +// By default, _NIL = nil. +type BinarySearch[T constraints.Ordered] struct { + Root *BSNode[T] + _NIL *BSNode[T] // a sentinel value for nil +} + +// NewBinarySearch creates a novel Binary-Search tree +func NewBinarySearch[T constraints.Ordered]() *BinarySearch[T] { + return &BinarySearch[T]{ + Root: nil, + _NIL: nil, + } +} + +// Empty determines the Binary-Search tree is empty +func (t *BinarySearch[T]) Empty() bool { + return t.Root == t._NIL +} + +// Push a chain of Node's into the BinarySearch +func (t *BinarySearch[T]) Push(keys ...T) { + for _, key := range keys { + t.pushHelper(t.Root, key) + } +} + +// Delete removes the node of val +func (t *BinarySearch[T]) Delete(val T) bool { + node, ok := t.Get(val) + if !ok { + return false + } + t.deleteHelper(node.(*BSNode[T])) + return true +} + +// Get a Node from the Binary-Search Tree +func (t *BinarySearch[T]) Get(key T) (Node[T], bool) { + return searchTreeHelper[T](t.Root, t._NIL, key) +} + +// Has Determines the tree has the node of Key +func (t *BinarySearch[T]) Has(key T) bool { + _, ok := searchTreeHelper[T](t.Root, t._NIL, key) + return ok +} + +// PreOrder Traverses the tree in the following order Root --> Left --> Right +func (t *BinarySearch[T]) PreOrder() []T { + traversal := make([]T, 0) + preOrderRecursive[T](t.Root, t._NIL, &traversal) + return traversal +} + +// InOrder Traverses the tree in the following order Left --> Root --> Right +func (t *BinarySearch[T]) InOrder() []T { + return inOrderHelper[T](t.Root, t._NIL) +} + +// PostOrder traverses the tree in the following order Left --> Right --> Root +func (t *BinarySearch[T]) PostOrder() []T { + traversal := make([]T, 0) + postOrderRecursive[T](t.Root, t._NIL, &traversal) + return traversal +} + +// LevelOrder returns the level order traversal of the tree +func (t *BinarySearch[T]) LevelOrder() []T { + traversal := make([]T, 0) + levelOrderHelper[T](t.Root, t._NIL, &traversal) + return traversal +} + +// AccessNodesByLayer accesses nodes layer by layer (2-D array), instead of printing the results as 1-D array. +func (t *BinarySearch[T]) AccessNodesByLayer() [][]T { + return accessNodeByLayerHelper[T](t.Root, t._NIL) +} + +// Depth returns the calculated depth of a binary search tree +func (t *BinarySearch[T]) Depth() int { + return calculateDepth[T](t.Root, t._NIL, 0) +} + +// Max returns the Max value of the tree +func (t *BinarySearch[T]) Max() (T, bool) { + ret := maximum[T](t.Root, t._NIL) + if ret == t._NIL { + var dft T + return dft, false + } + return ret.Key(), true +} + +// Min returns the Min value of the tree +func (t *BinarySearch[T]) Min() (T, bool) { + ret := minimum[T](t.Root, t._NIL) + if ret == t._NIL { + var dft T + return dft, false + } + return ret.Key(), true +} + +// Predecessor returns the Predecessor of the node of Key +// if there is no predecessor, return default value of type T and false +// otherwise return the Key of predecessor and true +func (t *BinarySearch[T]) Predecessor(key T) (T, bool) { + node, ok := searchTreeHelper[T](t.Root, t._NIL, key) + if !ok { + var dft T + return dft, ok + } + return predecessorHelper[T](node, t._NIL) +} + +// Successor returns the Successor of the node of Key +// if there is no successor, return default value of type T and false +// otherwise return the Key of successor and true +func (t *BinarySearch[T]) Successor(key T) (T, bool) { + node, ok := searchTreeHelper[T](t.Root, t._NIL, key) + if !ok { + var dft T + return dft, ok + } + return successorHelper[T](node, t._NIL) +} + +func (t *BinarySearch[T]) pushHelper(x *BSNode[T], val T) { + y := t._NIL + for x != t._NIL { + y = x + switch { + case val < x.Key(): + x = x.left + case val > x.Key(): + x = x.right + default: + return + } + } + + z := &BSNode[T]{ + key: val, + left: t._NIL, + right: t._NIL, + parent: y, + } + if y == t._NIL { + t.Root = z + } else if val < y.key { + y.left = z + } else { + y.right = z + } +} + +func (t *BinarySearch[T]) deleteHelper(z *BSNode[T]) { + switch { + case z.left == t._NIL: + t.transplant(z, z.right) + case z.right == t._NIL: + t.transplant(z, z.left) + default: + y := minimum[T](z.right, t._NIL).(*BSNode[T]) + if y.parent != z { + t.transplant(y, y.right) + y.right = z.right + y.right.parent = y + } + + t.transplant(z, y) + y.left = z.left + y.left.parent = y + } +} + +func (t *BinarySearch[T]) transplant(u, v *BSNode[T]) { + switch { + case u.parent == t._NIL: + t.Root = v + case u == u.parent.left: + u.parent.left = v + default: + u.parent.right = v + } + + if v != t._NIL { + v.parent = u.parent + } +} diff --git a/structure/tree/bstree_test.go b/structure/tree/bstree_test.go new file mode 100644 index 000000000..211daa28a --- /dev/null +++ b/structure/tree/bstree_test.go @@ -0,0 +1,192 @@ +package tree_test + +import ( + "math/rand" + "sort" + "testing" + "time" + + bt "github.com/TheAlgorithms/Go/structure/tree" +) + +func TestPush(t *testing.T) { + bst := bt.NewBinarySearch[int]() + + bst.Push(90) + bst.Push(80) + bst.Push(100) + + if bst.Root.Key() != 90 { + t.Errorf("Root should have value = 90") + } + + if bst.Root.Left().Key() != 80 { + t.Errorf("Left child should have value = 80") + } + + if bst.Root.Right().Key() != 100 { + t.Errorf("Right child should have value = 100") + } + + if bst.Depth() != 2 { + t.Errorf("tree should have depth = 1") + } +} + +func TestDelete(t *testing.T) { + t.Run("Delete a node with no child", func(t *testing.T) { + bst := bt.NewBinarySearch[int]() + + bst.Push(90) + bst.Push(80) + bst.Push(80) + bst.Push(100) + + if !bst.Delete(100) { + t.Errorf("There is a node, whose value is 100") + } + + if bst.Delete(105) { + t.Errorf("There is no node, whose value is 105") + } + + root := bst.Root + if root.Key() != 90 { + t.Errorf("Root should have value = 90") + } + + if root.Left().Key() != 80 { + t.Errorf("Left child should have value = 80") + } + + if root.Right().(*bt.BSNode[int]) != nil { + t.Errorf("Right child should have value = nil") + } + + if bst.Depth() != 2 { + t.Errorf("Depth should have value = 2") + } + + bst.Delete(80) + + if root.Key() != 90 { + t.Errorf("Root should have value = 90") + } + + if root.Left().(*bt.BSNode[int]) != nil { + t.Errorf("Left child should have value = nil") + } + + if bst.Depth() != 1 { + t.Errorf("Depth should have value = 1") + } + }) + + t.Run("Delete a node with one child", func(t *testing.T) { + bst := bt.NewBinarySearch[int]() + + bst.Push(90) + bst.Push(80) + bst.Push(100) + bst.Push(70) + + if bst.Delete(102) { + t.Errorf("There is no node, whose value is 102") + } + + if !bst.Delete(80) { + t.Errorf("There is a node, whose value is 80") + } + + root := bst.Root + if root.Key() != 90 { + t.Errorf("Root should have value = 90") + } + + if root.Right().Key() != 100 { + t.Errorf("Right child should have value = 100") + } + + if root.Left().Key() != 70 { + t.Errorf("Left child should have value = 70") + } + + if bst.Depth() != 2 { + t.Errorf("Depth should have value = 2") + } + }) + + t.Run("Delete a node with two children", func(t *testing.T) { + bst := bt.NewBinarySearch[int]() + + bst.Push(90) + bst.Push(80) + bst.Push(100) + bst.Push(70) + bst.Push(85) + + if !bst.Delete(80) { + t.Errorf("There is a node, whose value is 80") + } + + if bst.Delete(102) { + t.Errorf("There is no node, whose value is 102") + } + + root := bst.Root + if root.Key() != 90 { + t.Errorf("Root should have value = 90") + } + + if root.Left().Key() != 85 { + t.Errorf("Left child should have value = 85") + } + + if root.Right().Key() != 100 { + t.Errorf("Right child should have value = 100") + } + + if bst.Depth() != 3 { + t.Errorf("Depth should have value = 3") + } + }) + + t.Run("Random Test", func(t *testing.T) { + tests := []int{100, 500, 1000, 10_000} + for _, n := range tests { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + tree := bt.NewBinarySearch[int]() + nums := rnd.Perm(n) + tree.Push(nums...) + + rets := tree.InOrder() + if !sort.IntsAreSorted(rets) { + t.Error("Error with Push") + } + + if res, ok := tree.Min(); !ok || res != rets[0] { + t.Errorf("Error with Min, get %d, want: %d", res, rets[0]) + } + + if res, ok := tree.Max(); !ok || res != rets[n-1] { + t.Errorf("Error with Max, get %d, want: %d", res, rets[n-1]) + } + + for i := 0; i < n-1; i++ { + if ret, ok := tree.Successor(rets[0]); ret != rets[1] || !ok { + t.Error("Error with Successor") + } + + if ret, ok := tree.Predecessor(rets[1]); ret != rets[0] || !ok { + t.Error("Error with Predecessor") + } + + ok := tree.Delete(nums[i]) + rets = tree.InOrder() + if !ok || !sort.IntsAreSorted(rets) { + t.Errorf("Error With Delete") + } + } + } + }) +} diff --git a/structure/tree/btree.go b/structure/tree/btree.go new file mode 100644 index 000000000..5b2e55eb7 --- /dev/null +++ b/structure/tree/btree.go @@ -0,0 +1,355 @@ +// B-tree is a self balancing tree that promotes data locality. +// For more details, see https://en.wikipedia.org/wiki/B-tree + +package tree + +import "github.com/TheAlgorithms/Go/constraints" + +type BTreeNode[T constraints.Ordered] struct { + keys []T + children []*BTreeNode[T] + numKeys int + isLeaf bool +} + +type BTree[T constraints.Ordered] struct { + root *BTreeNode[T] + maxKeys int +} + +func minKeys(maxKeys int) int { + return (maxKeys - 1) / 2 +} + +func NewBTreeNode[T constraints.Ordered](maxKeys int, isLeaf bool) *BTreeNode[T] { + if maxKeys <= 0 { + panic("BTree maxKeys cannot be zero") + } + return &BTreeNode[T]{ + keys: make([]T, maxKeys), + children: make([]*BTreeNode[T], maxKeys+1), + isLeaf: isLeaf, + } +} + +func NewBTree[T constraints.Ordered](maxKeys int) *BTree[T] { + if maxKeys <= 2 { + panic("Must be >= 3 keys") + } + return &BTree[T]{ + root: nil, + maxKeys: maxKeys, + } +} + +func (node *BTreeNode[T]) Verify(tree *BTree[T]) { + minKeys := minKeys(tree.maxKeys) + if node != tree.root && node.numKeys < minKeys { + panic("node has too few keys") + } else if node.numKeys > tree.maxKeys { + panic("node has too many keys") + } +} + +func (node *BTreeNode[T]) IsFull(maxKeys int) bool { + return node.numKeys == maxKeys +} + +func (node *BTreeNode[T]) Search(key T) bool { + i := 0 + for ; i < node.numKeys; i++ { + if key == node.keys[i] { + return true + } + if key < node.keys[i] { + break + } + } + if node.isLeaf { + return false + } + return node.children[i].Search(key) +} + +func (tree *BTree[T]) Search(key T) bool { + if tree.root == nil { + return false + } + return tree.root.Search(key) +} + +func (node *BTreeNode[T]) InsertKeyChild(key T, child *BTreeNode[T]) { + i := node.numKeys + node.children[i+1] = node.children[i] + for ; i > 0; i-- { + if key > node.keys[i-1] { + node.keys[i] = key + node.children[i] = child + break + } + node.keys[i] = node.keys[i-1] + node.children[i] = node.children[i-1] + } + if i == 0 { + node.keys[0] = key + node.children[0] = child + } + node.numKeys++ +} + +func (node *BTreeNode[T]) Append(key T, child *BTreeNode[T]) { + node.keys[node.numKeys] = key + node.children[node.numKeys+1] = child + node.numKeys++ +} + +// Add all of other's keys starting from idx and children starting from idx + 1 +func (node *BTreeNode[T]) Concat(other *BTreeNode[T], idx int) { + for i := 0; i < other.numKeys-idx; i++ { + node.keys[node.numKeys+i] = other.keys[i+idx] + node.children[node.numKeys+i+1] = other.children[i+idx+1] + } + node.numKeys += other.numKeys - idx +} + +// Transform: +// +// A B +// | +// +// a b c d +// +// Into: +// +// A c B +// / \ +// +// a b d +func (parent *BTreeNode[T]) Split(idx int, maxKeys int) { + child := parent.children[idx] + midKeyIndex := maxKeys / 2 + rightChild := NewBTreeNode[T](maxKeys, child.isLeaf) + rightChild.Concat(child, midKeyIndex+1) + rightChild.children[0] = child.children[midKeyIndex+1] + + // Reuse child as the left node + child.numKeys = midKeyIndex + + // Insert the child's mid index to the parent + for i := parent.numKeys; i > idx; i-- { + parent.keys[i] = parent.keys[i-1] + parent.children[i+1] = parent.children[i] + } + parent.keys[idx] = child.keys[midKeyIndex] + parent.children[idx] = child + parent.children[idx+1] = rightChild + parent.numKeys += 1 +} + +func (node *BTreeNode[T]) InsertNonFull(tree *BTree[T], key T) { + node.Verify(tree) + if node.IsFull(tree.maxKeys) { + panic("Called InsertNonFull() with a full node") + } + + if node.isLeaf { + // Node is a leaf. Directly insert the key. + node.InsertKeyChild(key, nil) + return + } + + // Find the child node to insert into + i := 0 + for ; i < node.numKeys; i++ { + if key < node.keys[i] { + break + } + } + + if node.children[i].IsFull(tree.maxKeys) { + node.Split(i, tree.maxKeys) + if key > node.keys[i] { + i++ + } + } + node.children[i].InsertNonFull(tree, key) +} + +func (tree *BTree[T]) Insert(key T) { + if tree.root == nil { + tree.root = NewBTreeNode[T](tree.maxKeys, true) + tree.root.keys[0] = key + tree.root.numKeys = 1 + return + } + + if tree.root.IsFull(tree.maxKeys) { + newRoot := NewBTreeNode[T](tree.maxKeys, false) + newRoot.numKeys = 0 + newRoot.children[0] = tree.root + newRoot.Split(0, tree.maxKeys) + tree.root = newRoot + } + tree.root.InsertNonFull(tree, key) +} + +func (node *BTreeNode[T]) DeleteIthKey(i int) { + if i >= node.numKeys { + panic("deleting out of bounds key") + } + for j := i; j < node.numKeys-1; j++ { + node.keys[j] = node.keys[j+1] + node.children[j+1] = node.children[j+2] + } + node.numKeys-- +} + +// Transform: +// +// A B C +// / \ +// a b +// +// Into: +// +// A C +// | +// +// a B c +func (node *BTreeNode[T]) Merge(idx int) { + if node.isLeaf { + panic("cannot merge when leaf node is parent") + } + left := node.children[idx] + right := node.children[idx+1] + left.Append(node.keys[idx], right.children[0]) + left.Concat(right, 0) + node.DeleteIthKey(idx) +} + +func (node *BTreeNode[T]) Min() T { + if node.isLeaf { + return node.keys[0] + } + return node.children[0].Min() +} + +func (node *BTreeNode[T]) Max() T { + if node.isLeaf { + return node.keys[node.numKeys-1] + } + return node.children[node.numKeys].Max() +} + +func (node *BTreeNode[T]) Delete(tree *BTree[T], key T) { + node.Verify(tree) + if node.isLeaf { + // Case 1: Node is a leaf. Directly delete the key. + for i := 0; i < node.numKeys; i++ { + if key == node.keys[i] { + node.DeleteIthKey(i) + return + } + } + return + } + + minKeys := minKeys(tree.maxKeys) + i := 0 + for ; i < node.numKeys; i++ { + if key == node.keys[i] { + // Case 2: key exists in a non-leaf node + left := node.children[i] + right := node.children[i+1] + if left.numKeys > minKeys { + // Replace the key we want to delete with the max key from the left + // subtree. Then delete that key from the left subtree. + // A B C + // / + // a b c + // + // If we want to delete `B`, then replace `B` with `c`, and delete `c` in the subtree. + // A c C + // / + // a b + replacementKey := left.Max() + node.keys[i] = replacementKey + left.Delete(tree, replacementKey) + } else if right.numKeys > minKeys { + // Replace the key we want to delete with the min key from the right + // subtree. Then delete that key in the right subtree. Mirrors the + // transformation above for replacing from the left subtree. + replacementKey := right.Min() + node.keys[i] = replacementKey + right.Delete(tree, replacementKey) + } else { + // Both left and right subtrees have the minimum number of keys. Merge + // the left tree, the deleted key, and the right tree together into the + // left tree. Then recursively delete the key in the left tree. + if left.numKeys != minKeys || right.numKeys != minKeys { + panic("nodes should not have less than the minimum number of keys") + } + node.Merge(i) + left.Delete(tree, key) + } + return + } + + if key < node.keys[i] { + break + } + } + + // Case 3: key may exist in a child node. + child := node.children[i] + if child.numKeys == minKeys { + // Before we recurse into the child node, make sure it has more than + // the minimum number of keys. + if i > 0 && node.children[i-1].numKeys > minKeys { + // Take a key from the left sibling + // Transform: + // A B C + // / \ + // a b c + // + // Into: + // A b C + // / \ + // a B c + left := node.children[i-1] + child.InsertKeyChild(node.keys[i-1], left.children[left.numKeys]) + node.keys[i-1] = left.keys[left.numKeys-1] + left.numKeys-- + } else if i < node.numKeys && node.children[i+1].numKeys > minKeys { + // Take a key from the right sibling. Mirrors the transformation above for taking a key from the left sibling. + right := node.children[i+1] + child.Append(node.keys[i], right.children[0]) + node.keys[i] = right.keys[0] + right.children[0] = right.children[1] + right.DeleteIthKey(0) + } else { + if i == 0 { + // Merge with right sibling + node.Merge(i) + } else { + // Merge with left sibling + node.Merge(i - 1) + child = node.children[i-1] + } + } + } + if child.numKeys == minKeys { + panic("cannot delete key from node with minimum number of keys") + } + child.Delete(tree, key) +} + +func (tree *BTree[T]) Delete(key T) { + if tree.root == nil { + return + } + tree.root.Delete(tree, key) + if tree.root.numKeys == 0 { + tree.root = tree.root.children[0] + } +} diff --git a/structure/tree/btree_test.go b/structure/tree/btree_test.go new file mode 100644 index 000000000..056461b1c --- /dev/null +++ b/structure/tree/btree_test.go @@ -0,0 +1,133 @@ +package tree_test + +import ( + bt "github.com/TheAlgorithms/Go/structure/tree" + "math/rand" + "testing" +) + +func TestBTreeIncreasing(t *testing.T) { + maxKeysCases := []int{4, 16} + sizes := []int{100, 0xBA5, 0xF00} + for _, maxKeys := range maxKeysCases { + for _, size := range sizes { + tree := bt.NewBTree[int](maxKeys) + if tree.Search(0) { + t.Errorf("Tree expected to contain 0") + } + for i := 0; i < size; i++ { + tree.Insert(i) + } + for i := 0; i < size; i++ { + if !tree.Search(i) { + t.Errorf("Tree expected to contain %d", i) + } + } + if tree.Search(size + 1) { + t.Errorf("Tree not expected to contain %d", size+1) + } + + for i := 0; i < size; i += 5 { + tree.Delete(i) + } + for i := 0; i < size; i++ { + hasKey := tree.Search(i) + if i%5 == 0 && hasKey { + t.Errorf("Tree not expected to contain %d", i) + } else if i%5 != 0 && !hasKey { + t.Errorf("Tree expected to contain %d", i) + } + } + } + } +} + +func TestBTreeDecreasing(t *testing.T) { + maxKeysCases := []int{4, 16} + sizes := []int{100, 1000} + for _, maxKeys := range maxKeysCases { + for _, size := range sizes { + tree := bt.NewBTree[int](maxKeys) + if tree.Search(0) { + t.Errorf("Tree expected to contain 0") + } + for i := size - 1; i >= 0; i-- { + tree.Insert(i) + } + for i := 0; i < size; i++ { + if !tree.Search(i) { + t.Errorf("Tree expected to contain %d", i) + } + } + if tree.Search(size + 1) { + t.Errorf("Tree not expected to contain %d", size+1) + } + + for i := 0; i < size; i += 5 { + tree.Delete(i) + } + for i := 0; i < size; i++ { + hasKey := tree.Search(i) + if i%5 == 0 && hasKey { + t.Errorf("Tree not expected to contain %d", i) + } else if i%5 != 0 && !hasKey { + t.Errorf("Tree expected to contain %d", i) + } + } + } + } +} + +func TestBTreeRandom(t *testing.T) { + maxKeysCases := []int{4, 16} + sizes := []int{100, 0xBA5, 0xF00} + for _, maxKeys := range maxKeysCases { + for _, size := range sizes { + rnd := rand.New(rand.NewSource(0)) + tree := bt.NewBTree[int](maxKeys) + nums := rnd.Perm(size) + if tree.Search(0) { + t.Errorf("Tree expected to contain 0") + } + for i := 0; i < size; i++ { + tree.Insert(nums[i]) + } + for i := 0; i < size; i++ { + if !tree.Search(nums[i]) { + t.Errorf("Tree expected to contain %d", nums[i]) + } + } + + for i := 0; i < size; i += 5 { + tree.Delete(nums[i]) + } + for i := 0; i < size; i++ { + hasKey := tree.Search(nums[i]) + if i%5 == 0 && hasKey { + t.Errorf("Tree not expected to contain %d", i) + } else if i%5 != 0 && !hasKey { + t.Errorf("Tree expected to contain %d", i) + } + } + } + } +} + +func TestBTreeDeleteEverything(t *testing.T) { + tree := bt.NewBTree[int](4) + size := 128 + for i := 0; i < size; i++ { + tree.Insert(i) + } + for i := 0; i < size; i++ { + tree.Delete(i) + } + tree.Delete(-1) + tree.Delete(1000) + + for i := 0; i < size; i++ { + if tree.Search(i) { + t.Errorf("Tree not expected to contain %d", i) + } + } +} diff --git a/structure/tree/example_test.go b/structure/tree/example_test.go new file mode 100644 index 000000000..2d3c384c8 --- /dev/null +++ b/structure/tree/example_test.go @@ -0,0 +1,167 @@ +package tree_test + +import ( + "fmt" + "github.com/TheAlgorithms/Go/constraints" + "testing" + + bt "github.com/TheAlgorithms/Go/structure/tree" +) + +type TestTree[T constraints.Ordered] interface { + Push(...T) + Delete(T) bool + Get(T) (bt.Node[T], bool) + Empty() bool + Has(T) bool + Depth() int + Max() (T, bool) + Min() (T, bool) + Predecessor(T) (T, bool) + Successor(T) (T, bool) + PreOrder() []T + InOrder() []T + PostOrder() []T + LevelOrder() []T + AccessNodesByLayer() [][]T +} + +// BinarySearch, AVL and RB have completed the `TestTree` interface. +var ( + _ TestTree[int] = (*bt.BinarySearch[int])(nil) + _ TestTree[int] = (*bt.AVL[int])(nil) + _ TestTree[int] = (*bt.RB[int])(nil) +) + +var tree TestTree[int] + +func TestBinarySearch(t *testing.T) { + tree = bt.NewBinarySearch[int]() + + if tree.Empty() { + t.Log("Binary Search Tree is empty now.") + } + + tree.Push(1, 4, 10) + tree.Push(-8) + nums := []int{87, 18, 10, -34} + tree.Push(nums...) + tree.Push(4) // duplicate key, dismiss it + + if tree.Has(4) { + t.Logf("There is a node of 4") + } + + if n, ok := tree.Get(10); ok { + t.Logf("node of 10: %T", n) + } + + if ret, ok := tree.Min(); ok { + t.Logf("tree.Min() = %v", ret) + } + + if ret, ok := tree.Max(); ok { + t.Logf("tree.Max() = %v", ret) + } + + if ret, ok := tree.Predecessor(1); ok { + t.Logf("tree.Preducessor(1) = %v", ret) + } + + if ret, ok := tree.Successor(18); ok { + t.Logf("tree.Successor(18) = %v", ret) + } + + fmt.Println(tree.InOrder()) + fmt.Println(tree.AccessNodesByLayer()) + + tree.Delete(18) + fmt.Println("Delete 18") + fmt.Println(tree.InOrder()) +} + +func TestAVL(t *testing.T) { + tree = bt.NewAVL[int]() + + if tree.Empty() { + t.Log("AVL Tree is empty now.") + } + + tree.Push(1, 4, 10) + tree.Push(-8) + nums := []int{87, 18, 10, -34} + tree.Push(nums...) + tree.Push(4) // duplicate key, dismiss it + + if tree.Has(4) { + t.Logf("There is a node of 4") + } + + if n, ok := tree.Get(10); ok { + t.Logf("node of 10: %T", n) + } + + if ret, ok := tree.Min(); ok { + t.Logf("tree.Min() = %v", ret) + } + + if ret, ok := tree.Max(); ok { + t.Logf("tree.Max() = %v", ret) + } + + if ret, ok := tree.Predecessor(1); ok { + t.Logf("tree.Preducessor(1) = %v", ret) + } + + if ret, ok := tree.Successor(18); ok { + t.Logf("tree.Successor(18) = %v", ret) + } + + fmt.Println(tree.InOrder()) + fmt.Println(tree.AccessNodesByLayer()) + + tree.Delete(18) + fmt.Println("Delete 18") + fmt.Println(tree.InOrder()) +} + +func TestRB(t *testing.T) { + tree = bt.NewRB[int]() + + if tree.Empty() { + t.Log("RB Tree is empty now.") + } + + tree.Push(1, 4, 10) + tree.Push(-8) + nums := []int{87, 18, 10, -34} + tree.Push(nums...) + tree.Push(4) // duplicate key, dismiss it + + if tree.Has(4) { + t.Logf("There is a node of 4") + } + + if n, ok := tree.Get(10); ok { + t.Logf("node of 10: %T", n) + } + + if ret, ok := tree.Min(); ok { + t.Logf("tree.Min() = %v", ret) + } + + if ret, ok := tree.Max(); ok { + t.Logf("tree.Max() = %v", ret) + } + + if ret, ok := tree.Predecessor(1); ok { + t.Logf("tree.Preducessor(1) = %v", ret) + } + + if ret, ok := tree.Successor(18); ok { + t.Logf("tree.Successor(18) = %v", ret) + } + + fmt.Println(tree.InOrder()) + fmt.Println(tree.AccessNodesByLayer()) +} diff --git a/structure/tree/rbtree.go b/structure/tree/rbtree.go new file mode 100644 index 000000000..de6f2ed6d --- /dev/null +++ b/structure/tree/rbtree.go @@ -0,0 +1,424 @@ +// Red-Black Tree is a kind of self-balancing binary search tree. +// Each node stores "color" ("red" or "black"), used to ensure that the tree remains balanced during insertions and deletions. +// +// For more details check out those links below here: +// Programiz article : https://www.programiz.com/dsa/red-black-tree +// Wikipedia article: https://en.wikipedia.org/wiki/Red_black_tree +// authors [guuzaa](https://github.com/guuzaa) +// see rbtree.go + +package tree + +import "github.com/TheAlgorithms/Go/constraints" + +type Color byte + +const ( + Red Color = iota + Black +) + +// Verify Interface Compliance +var _ Node[int] = &RBNode[int]{} + +// RBNode represents a single node in the RB. +type RBNode[T constraints.Ordered] struct { + key T + parent *RBNode[T] + left *RBNode[T] + right *RBNode[T] + color Color +} + +func (n *RBNode[T]) Key() T { + return n.key +} + +func (n *RBNode[T]) Parent() Node[T] { + return n.parent +} + +func (n *RBNode[T]) Left() Node[T] { + return n.left +} + +func (n *RBNode[T]) Right() Node[T] { + return n.right +} + +// RB represents a Red-Black tree. +// By default, _NIL = leaf, a dummy variable. +type RB[T constraints.Ordered] struct { + Root *RBNode[T] + _NIL *RBNode[T] // a sentinel value for nil +} + +// NewRB creates a new Red-Black Tree +func NewRB[T constraints.Ordered]() *RB[T] { + leaf := &RBNode[T]{color: Black, left: nil, right: nil} + leaf.parent = leaf + return &RB[T]{ + Root: leaf, + _NIL: leaf, + } +} + +// Empty determines the Red-Black tree is empty +func (t *RB[T]) Empty() bool { + return t.Root == t._NIL +} + +// Push a chain of Node's into the Red-Black Tree +func (t *RB[T]) Push(keys ...T) { + for _, key := range keys { + t.pushHelper(t.Root, key) + } +} + +// Delete a node of Red-Black Tree +// Returns false if the node does not exist, otherwise returns true. +func (t *RB[T]) Delete(data T) bool { + return t.deleteHelper(t.Root, data) +} + +// Get a Node from the Red-Black Tree +func (t *RB[T]) Get(key T) (Node[T], bool) { + return searchTreeHelper[T](t.Root, t._NIL, key) +} + +// Has Determines the tree has the node of Key +func (t *RB[T]) Has(key T) bool { + _, ok := searchTreeHelper[T](t.Root, t._NIL, key) + return ok +} + +// PreOrder Traverses the tree in the following order Root --> Left --> Right +func (t *RB[T]) PreOrder() []T { + traversal := make([]T, 0) + preOrderRecursive[T](t.Root, t._NIL, &traversal) + return traversal +} + +// InOrder Traverses the tree in the following order Left --> Root --> Right +func (t *RB[T]) InOrder() []T { + return inOrderHelper[T](t.Root, t._NIL) +} + +// PostOrder traverses the tree in the following order Left --> Right --> Root +func (t *RB[T]) PostOrder() []T { + traversal := make([]T, 0) + postOrderRecursive[T](t.Root, t._NIL, &traversal) + return traversal +} + +// LevelOrder returns the level order traversal of the tree +func (t *RB[T]) LevelOrder() []T { + traversal := make([]T, 0) + levelOrderHelper[T](t.Root, t._NIL, &traversal) + return traversal +} + +// AccessNodesByLayer accesses nodes layer by layer (2-D array), instead of printing the results as 1-D array. +func (t *RB[T]) AccessNodesByLayer() [][]T { + return accessNodeByLayerHelper[T](t.Root, t._NIL) +} + +// Depth returns the calculated depth of a Red-Black tree +func (t *RB[T]) Depth() int { + return calculateDepth[T](t.Root, t._NIL, 0) +} + +// Max returns the Max value of the tree +func (t *RB[T]) Max() (T, bool) { + ret := maximum[T](t.Root, t._NIL) + if ret == t._NIL { + var dft T + return dft, false + } + return ret.Key(), true +} + +// Min returns the Min value of the tree +func (t *RB[T]) Min() (T, bool) { + ret := minimum[T](t.Root, t._NIL) + if ret == t._NIL { + var dft T + return dft, false + } + return ret.Key(), true +} + +// Predecessor returns the Predecessor of the node of Key +// if there is no predecessor, return default value of type T and false +// otherwise return the Key of predecessor and true +func (t *RB[T]) Predecessor(key T) (T, bool) { + node, ok := searchTreeHelper[T](t.Root, t._NIL, key) + if !ok { + var dft T + return dft, ok + } + return predecessorHelper[T](node, t._NIL) +} + +// Successor returns the Successor of the node of Key +// if there is no successor, return default value of type T and false +// otherwise return the Key of successor and true +func (t *RB[T]) Successor(key T) (T, bool) { + node, ok := searchTreeHelper[T](t.Root, t._NIL, key) + if !ok { + var dft T + return dft, ok + } + return successorHelper[T](node, t._NIL) +} + +func (t *RB[T]) pushHelper(x *RBNode[T], key T) { + y := t._NIL + for x != t._NIL { + y = x + switch { + case key < x.Key(): + x = x.left + case key > x.Key(): + x = x.right + default: + return + } + } + + node := &RBNode[T]{ + key: key, + left: t._NIL, + right: t._NIL, + parent: y, + color: Red, + } + if y == t._NIL { + t.Root = node + } else if node.key < y.key { + y.left = node + } else { + y.right = node + } + + if node.parent == t._NIL { + node.color = Black + return + } + + if node.parent.parent == t._NIL { + return + } + + t.pushFix(node) +} + +func (t *RB[T]) leftRotate(x *RBNode[T]) { + y := x.right + x.right = y.left + + if y.left != t._NIL { + y.left.parent = x + } + + y.parent = x.parent + if x.parent == t._NIL { + t.Root = y + } else if x == x.parent.left { + x.parent.left = y + } else { + x.parent.right = y + } + + y.left = x + x.parent = y +} + +func (t *RB[T]) rightRotate(x *RBNode[T]) { + y := x.left + x.left = y.right + if y.right != t._NIL { + y.right.parent = x + } + + y.parent = x.parent + if x.parent == t._NIL { + t.Root = y + } else if x == y.parent.right { + y.parent.right = y + } else { + y.parent.left = y + } + + y.right = x + x.parent = y +} + +func (t *RB[T]) pushFix(k *RBNode[T]) { + for k.parent.color == Red { + if k.parent == k.parent.parent.right { + u := k.parent.parent.left + if u.color == Red { + u.color = Black + k.parent.color = Black + k.parent.parent.color = Red + k = k.parent.parent + } else { + if k == k.parent.left { + k = k.parent + t.rightRotate(k) + } + k.parent.color = Black + k.parent.parent.color = Red + t.leftRotate(k.parent.parent) + } + } else { + u := k.parent.parent.right + if u.color == Red { + u.color = Black + k.parent.color = Black + k.parent.parent.color = Red + k = k.parent.parent + } else { + if k == k.parent.right { + k = k.parent + t.leftRotate(k) + } + k.parent.color = Black + k.parent.parent.color = Red + t.rightRotate(k.parent.parent) + } + } + if k == t.Root { + break + } + } + + t.Root.color = Black +} + +func (t *RB[T]) deleteHelper(node *RBNode[T], key T) bool { + z := t._NIL + for node != t._NIL { + switch { + case node.key == key: + z = node + fallthrough + case node.key <= key: + node = node.right + case node.key > key: + node = node.left + } + } + + if z == t._NIL { + return false + } + + var x *RBNode[T] + y := z + yOriginColor := y.color + if z.left == t._NIL { + x = z.right + t.transplant(z, z.right) + } else if z.right == t._NIL { + x = z.left + t.transplant(z, z.left) + } else { + y = minimum[T](z.right, t._NIL).(*RBNode[T]) + yOriginColor = y.color + x = y.right + if y.parent == z { + x.parent = y + } else { + t.transplant(y, y.right) + y.right = z.right + y.right.parent = y + } + + t.transplant(z, y) + y.left = z.left + y.left.parent = y + y.color = z.color + } + + if yOriginColor == Black { + t.deleteFix(x) + } + + return true +} + +func (t *RB[T]) deleteFix(x *RBNode[T]) { + var s *RBNode[T] + for x != t.Root && x.color == Black { + if x == x.parent.left { + s = x.parent.right + if s.color == Red { + s.color = Black + x.parent.color = Red + t.leftRotate(x.parent) + s = x.parent.right + } + + if s.left.color == Black && s.right.color == Black { + s.color = Red + x = x.parent + } else { + if s.right.color == Black { + s.left.color = Black + s.color = Red + t.rightRotate(s) + s = x.parent.right + } + + s.color = x.parent.color + x.parent.color = Black + s.right.color = Black + t.leftRotate(x.parent) + x = t.Root + } + } else { + s = x.parent.left + if s.color == Red { + s.color = Black + x.parent.color = Red + t.rightRotate(x.parent) + s = x.parent.left + } + + if s.right.color == Black && s.left.color == Black { + s.color = Red + x = x.parent + } else { + if s.left.color == Black { + s.right.color = Black + s.color = Red + t.leftRotate(s) + s = x.parent.left + } + + s.color = x.parent.color + x.parent.color = Black + s.left.color = Black + t.rightRotate(x.parent) + x = t.Root + } + } + } + + x.color = Black +} + +func (t *RB[T]) transplant(u, v *RBNode[T]) { + switch { + case u.parent == t._NIL: + t.Root = v + case u == u.parent.left: + u.parent.left = v + default: + u.parent.right = v + } + + v.parent = u.parent +} diff --git a/structure/tree/rbtree_test.go b/structure/tree/rbtree_test.go new file mode 100644 index 000000000..1b6b38265 --- /dev/null +++ b/structure/tree/rbtree_test.go @@ -0,0 +1,167 @@ +package tree_test + +import ( + "math/rand" + "sort" + "testing" + "time" + + bt "github.com/TheAlgorithms/Go/structure/tree" +) + +func TestRBTreePush(t *testing.T) { + tree := bt.NewRB[int]() + + ret := tree.InOrder() + + if !sort.IntsAreSorted(ret) || len(ret) != 0 { + t.Errorf("Error with Push: %v", ret) + } + + if r, ok := tree.Min(); ok { + t.Errorf("Error with Min: %v", r) + } + + if r, ok := tree.Max(); ok { + t.Errorf("Error with Max: %v", r) + } + + nums := []int{10, 8, 88, 888, 4, 1<<63 - 1, -(1 << 62), 188, -188, 4, 1 << 32} + + tree.Push(nums...) + + ret = tree.InOrder() + + if !sort.IntsAreSorted(ret) { + t.Errorf("Error with Push: %v", ret) + } + + if r, ok := tree.Min(); !ok || ret[0] != r { + t.Errorf("Error with Min: %v", r) + } + + if r, ok := tree.Max(); !ok || ret[len(ret)-1] != r { + t.Errorf("Error with Max: %v", r) + } +} + +func TestRBTreeDelete(t *testing.T) { + tree := bt.NewRB[int]() + var ok bool + + nums := []int{10, 8, 88, 888, 4, 1<<63 - 1, -(1 << 62), 188, -188, 4, 88, 1 << 32} + tree.Push(nums...) + + ok = tree.Delete(188) + + if ret := tree.InOrder(); !ok || !sort.IntsAreSorted(ret) { + t.Errorf("Error with Delete: %v", ret) + } + + ok = tree.Delete(188) + if ret := tree.InOrder(); ok || !sort.IntsAreSorted(ret) { + t.Errorf("Error with Delete: %v", ret) + } + + ok = tree.Delete(1<<63 - 1) + if ret := tree.InOrder(); !ok || !sort.IntsAreSorted(ret) { + t.Errorf("Error with Delete: %v", ret) + } + + ok = tree.Delete(4) + if ret := tree.InOrder(); !ok || !sort.IntsAreSorted(ret) { + t.Errorf("Error with Delete: %v", ret) + } + + if ret, ok := tree.Max(); !ok || ret != (1<<32) { + t.Errorf("Error with Delete, max: %v, want: %v", ret, (1 << 32)) + } + + if ret, ok := tree.Min(); !ok || ret != -(1<<62) { + t.Errorf("Error with Delete, min: %v, want: %v", ret, (1 << 32)) + } +} + +func TestRBTree(t *testing.T) { + testcases := []int{100, 200, 1000, 10000} + for _, n := range testcases { + rnd := rand.New(rand.NewSource(time.Now().UnixNano())) + tree := bt.NewRB[int]() + nums := rnd.Perm(n) + tree.Push(nums...) + + rets := tree.InOrder() + if !sort.IntsAreSorted(rets) { + t.Error("Error with Push") + } + + if res, ok := tree.Min(); !ok || res != rets[0] { + t.Errorf("Error with Min, get %d, want: %d", res, rets[0]) + } + + if res, ok := tree.Max(); !ok || res != rets[n-1] { + t.Errorf("Error with Max, get %d, want: %d", res, rets[n-1]) + } + + for i := 0; i < n-1; i++ { + if ret, ok := tree.Successor(rets[0]); ret != rets[1] || !ok { + t.Error("Error with Successor") + } + if ret, ok := tree.Predecessor(rets[1]); ret != rets[0] || !ok { + t.Error("Error with Predecessor") + } + + ok := tree.Delete(nums[i]) + rets = tree.InOrder() + if !ok || !sort.IntsAreSorted(rets) { + t.Errorf("Error With Delete") + } + } + } +} + +func TestRBTreeString(t *testing.T) { + tree := bt.NewRB[string]() + + if tree.Has("Golang") { + t.Errorf("Error with Has when T is string.") + } + + strs := []string{"Hello", "World", "Golang", "Python", "Rust", "C", "JavaScript", "Haskell", "Pascal", "ZZ"} + for _, str := range strs { + tree.Push(str) + } + + if !tree.Has("Golang") { + t.Errorf("Error with Has when T is string.") + } + + if tree.Has("Pasc") { + t.Errorf("Error with Has when T is string.") + } + + if ok := tree.Delete("Hello"); !ok { + t.Errorf("Error with Delete when T is string.") + } + + if ok := tree.Delete("Pasc"); ok { + t.Errorf("Error with Delete when T is string.") + } + + if tree.Has("Hello") { + t.Errorf("Error with Has when T is string.") + } + + ret := tree.InOrder() + if !sort.StringsAreSorted(ret) { + t.Errorf("Error with Push when T is string") + } + + if ret, ok := tree.Min(); !ok || ret != "C" { + t.Errorf("Error with Min when T is string") + } + + if ret, ok := tree.Max(); !ok || ret != "ZZ" { + t.Errorf("Error with Max when T is string") + } +} diff --git a/structure/tree/tree.go b/structure/tree/tree.go new file mode 100644 index 000000000..53f89ec74 --- /dev/null +++ b/structure/tree/tree.go @@ -0,0 +1,189 @@ +// Binary-Search tree is the tree, with the key of each internal node +// being greater than keys in the respective node's left subtree +// and less than the ones in its right subtree. + +// For more details check out those links below here: +// Wikipedia article: https://en.wikipedia.org/wiki/Binary_search_tree +// authors [guuzaa](https://github.com/guuzaa) +package tree + +import ( + "github.com/TheAlgorithms/Go/constraints" + "github.com/TheAlgorithms/Go/math/max" +) + +type Node[T constraints.Ordered] interface { + Key() T + Parent() Node[T] + Left() Node[T] + Right() Node[T] +} + +// The following is a collection of helper functions for BinarySearch, AVL and RB. + +func accessNodeByLayerHelper[T constraints.Ordered](root, nilNode Node[T]) [][]T { + if root == nilNode { + return [][]T{} + } + var q []Node[T] + var n Node[T] + var idx = 0 + q = append(q, root) + var res [][]T + + for len(q) != 0 { + res = append(res, []T{}) + qLen := len(q) + for i := 0; i < qLen; i++ { + n, q = q[0], q[1:] + res[idx] = append(res[idx], n.Key()) + if n.Left() != nilNode { + q = append(q, n.Left()) + } + if n.Right() != nilNode { + q = append(q, n.Right()) + } + } + idx++ + } + return res +} + +func searchTreeHelper[T constraints.Ordered](node, nilNode Node[T], key T) (Node[T], bool) { + if node == nilNode { + return node, false + } + + if key == node.Key() { + return node, true + } + if key < node.Key() { + return searchTreeHelper(node.Left(), nilNode, key) + } + return searchTreeHelper(node.Right(), nilNode, key) +} + +func inOrderHelper[T constraints.Ordered](node, nilNode Node[T]) []T { + var stack []Node[T] + var ret []T + + for node != nilNode || len(stack) > 0 { + for node != nilNode { + stack = append(stack, node) + node = node.Left() + } + + node = stack[len(stack)-1] + stack = stack[:len(stack)-1] + ret = append(ret, node.Key()) + node = node.Right() + } + + return ret +} + +func preOrderRecursive[T constraints.Ordered](n, nilNode Node[T], traversal *[]T) { + if n == nilNode { + return + } + + *traversal = append(*traversal, n.Key()) + preOrderRecursive(n.Left(), nilNode, traversal) + preOrderRecursive(n.Right(), nilNode, traversal) + +} + +func postOrderRecursive[T constraints.Ordered](n, nilNode Node[T], traversal *[]T) { + if n == nilNode { + return + } + + postOrderRecursive(n.Left(), nilNode, traversal) + postOrderRecursive(n.Right(), nilNode, traversal) + *traversal = append(*traversal, n.Key()) +} + +func calculateDepth[T constraints.Ordered](n, nilNode Node[T], depth int) int { + if n == nilNode { + return depth + } + + return max.Int(calculateDepth(n.Left(), nilNode, depth+1), calculateDepth(n.Right(), nilNode, depth+1)) +} + +func minimum[T constraints.Ordered](node, nilNode Node[T]) Node[T] { + if node == nilNode { + return node + } + + for node.Left() != nilNode { + node = node.Left() + } + return node +} + +func maximum[T constraints.Ordered](node, nilNode Node[T]) Node[T] { + if node == nilNode { + return node + } + + for node.Right() != nilNode { + node = node.Right() + } + return node +} + +func levelOrderHelper[T constraints.Ordered](root, nilNode Node[T], traversal *[]T) { + var q []Node[T] // queue + var tmp Node[T] + + q = append(q, root) + + for len(q) != 0 { + tmp, q = q[0], q[1:] + *traversal = append(*traversal, tmp.Key()) + if tmp.Left() != nilNode { + q = append(q, tmp.Left()) + } + + if tmp.Right() != nilNode { + q = append(q, tmp.Right()) + } + } +} + +func predecessorHelper[T constraints.Ordered](node, nilNode Node[T]) (T, bool) { + if node.Left() != nilNode { + return maximum(node.Left(), nilNode).Key(), true + } + + p := node.Parent() + for p != nilNode && node == p.Left() { + node = p + p = p.Parent() + } + + if p == nilNode { + var dft T + return dft, false + } + return p.Key(), true +} + +func successorHelper[T constraints.Ordered](node, nilNode Node[T]) (T, bool) { + if node.Right() != nilNode { + return minimum(node.Right(), nilNode).Key(), true + } + + p := node.Parent() + for p != nilNode && node == p.Right() { + node = p + p = p.Parent() + } + + if p == nilNode { + var dft T + return dft, false + } + return p.Key(), true +} diff --git a/structure/tree/tree_test.go b/structure/tree/tree_test.go new file mode 100644 index 000000000..3653f7355 --- /dev/null +++ b/structure/tree/tree_test.go @@ -0,0 +1,635 @@ +package tree_test + +import ( + "math/rand" + "reflect" + "sort" + "testing" + + bt "github.com/TheAlgorithms/Go/structure/tree" +) + +func TestTreeGetOrHas(t *testing.T) { + helper := func(tree TestTree[int], nums []int) { + tree.Push(nums...) + for _, num := range nums { + if !tree.Has(num) { + t.Errorf("Error with Has or Push method") + } + } + + min, _ := tree.Min() + max, _ := tree.Max() + + if _, ok := tree.Get(min - 1); ok { + t.Errorf("Error with Get method") + } + + if _, ok := tree.Get(max + 1); ok { + t.Errorf("Error with Get method") + } + } + + lens := []int{100, 1_000, 10_000, 100_000} + for _, ll := range lens { + nums := rand.Perm(ll) + t.Run("Test Binary Search Tree", func(t *testing.T) { + bsTree := bt.NewBinarySearch[int]() + helper(bsTree, nums) + }) + + t.Run("Test Red-Black Tree", func(t *testing.T) { + rbTree := bt.NewRB[int]() + helper(rbTree, nums) + }) + + t.Run("Test AVL Tree", func(t *testing.T) { + avlTree := bt.NewAVL[int]() + helper(avlTree, nums) + }) + } +} + +func TestTreePreOrder(t *testing.T) { + t.Run("Test for Binary-Search Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{90, 80, 70, 85, 100, 95, 105}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, []int{90, 80, 70, 1, 21, 31, 41, 51, 61, 71, 85, 100, 95, 105}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}}, + } + for _, tt := range tests { + tree := bt.NewBinarySearch[int]() + tree.Push(tt.input...) + if ret := tree.PreOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("Error with PreOrder") + } + } + }) + + t.Run("Test for AVL Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{90, 80, 70, 85, 100, 95, 105}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, []int{70, 41, 21, 1, 31, 51, 61, 90, 80, 71, 85, 100, 95, 105}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{7, 3, 2, 1, 5, 4, 6, 9, 8, 10}}, + } + for _, tt := range tests { + tree := bt.NewAVL[int]() + tree.Push(tt.input...) + if ret := tree.PreOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("Error with PreOrder") + } + } + }) + + t.Run("Test for Red-Black Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{90, 80, 70, 85, 100, 95, 105}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, []int{80, 41, 21, 1, 31, 61, 51, 70, 71, 90, 85, 100, 95, 105}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{7, 5, 3, 2, 1, 4, 6, 9, 8, 10}}, + } + for _, tt := range tests { + tree := bt.NewRB[int]() + tree.Push(tt.input...) + if ret := tree.PreOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("Error with PreOrder") + } + } + }) +} + +func TestTreeInOrder(t *testing.T) { + lens := []int{100, 1_000, 10_000, 100_000} + for _, ll := range lens { + nums := rand.Perm(ll) + + t.Run("Test Binary Search Tree", func(t *testing.T) { + bsTree := bt.NewBinarySearch[int]() + bsTree.Push(nums...) + if ret := bsTree.InOrder(); !sort.IntsAreSorted(ret) { + t.Errorf("Error with InOrder") + } + }) + + t.Run("Test Red-Black Tree", func(t *testing.T) { + rbTree := bt.NewRB[int]() + rbTree.Push(nums...) + if ret := rbTree.InOrder(); !sort.IntsAreSorted(ret) { + t.Errorf("Error with InOrder") + } + }) + + t.Run("Test AVL Tree", func(t *testing.T) { + avlTree := bt.NewAVL[int]() + avlTree.Push(nums...) + if ret := avlTree.InOrder(); !sort.IntsAreSorted(ret) { + t.Errorf("Error with InOrder") + } + }) + } +} + +func TestTreePostOrder(t *testing.T) { + t.Run("Test for Binary-Search Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{70, 85, 80, 95, 105, 100, 90}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + []int{61, 51, 41, 31, 21, 1, 71, 70, 85, 80, 95, 105, 100, 90}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}}, + } + for i, tt := range tests { + tree := bt.NewBinarySearch[int]() + tree.Push(tt.input...) + if ret := tree.PostOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with Post", i) + } + } + }) + + t.Run("Test for AVL Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{70, 85, 80, 95, 105, 100, 90}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + []int{1, 31, 21, 61, 51, 41, 71, 85, 80, 95, 105, 100, 90, 70}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{1, 2, 4, 6, 5, 3, 8, 10, 9, 7}}, + } + for i, tt := range tests { + tree := bt.NewAVL[int]() + tree.Push(tt.input...) + if ret := tree.PostOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with PostOrder", i) + } + } + }) + + t.Run("Test for Red-Black Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{70, 85, 80, 95, 105, 100, 90}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + []int{1, 31, 21, 51, 71, 70, 61, 41, 85, 95, 105, 100, 90, 80}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{1, 2, 4, 3, 6, 5, 8, 10, 9, 7}}, + } + for i, tt := range tests { + tree := bt.NewRB[int]() + tree.Push(tt.input...) + if ret := tree.PostOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with PostOrder", i) + } + } + }) +} + +func TestTreeLevelOrder(t *testing.T) { + t.Run("Test for Binary-Search Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{90, 80, 100, 70, 85, 95, 105}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + []int{90, 80, 100, 70, 85, 95, 105, 1, 71, 21, 31, 41, 51, 61}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}}, + } + for i, tt := range tests { + tree := bt.NewBinarySearch[int]() + tree.Push(tt.input...) + if ret := tree.LevelOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with LevelOrder", i) + } + } + }) + + t.Run("Test for AVL Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{90, 80, 100, 70, 85, 95, 105}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + []int{70, 41, 90, 21, 51, 80, 100, 1, 31, 61, 71, 85, 95, 105}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{7, 3, 9, 2, 5, 8, 10, 1, 4, 6}}, + } + for i, tt := range tests { + tree := bt.NewAVL[int]() + tree.Push(tt.input...) + if ret := tree.LevelOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with LevelOrder", i) + } + } + }) + + t.Run("Test for Red-Black Tree", func(t *testing.T) { + tests := []struct { + input []int + want []int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, []int{90, 80, 100, 70, 85, 95, 105}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + []int{80, 41, 90, 21, 61, 85, 100, 1, 31, 51, 70, 95, 105, 71}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, []int{7, 5, 9, 3, 6, 8, 10, 2, 4, 1}}, + } + for i, tt := range tests { + tree := bt.NewRB[int]() + tree.Push(tt.input...) + if ret := tree.LevelOrder(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with LevelOrder %v", i, ret) + } + } + }) +} + +func TestTreeMinAndMax(t *testing.T) { + helper := func(tree TestTree[int], nums []int) { + ll := len(nums) + if _, ok := tree.Min(); ok { + t.Errorf("Error with Min method.") + } + if _, ok := tree.Max(); ok { + t.Errorf("Error with Max method.") + } + tree.Push(nums...) + if min, ok := tree.Min(); !ok || min != nums[0] { + t.Errorf("Error with Min method.") + } + if max, ok := tree.Max(); !ok || max != nums[ll-1] { + t.Errorf("Error with Max method.") + } + } + + lens := []int{500, 1_000, 10_000} + for _, ll := range lens { + nums := rand.Perm(ll) + sort.Ints(nums) + + t.Run("Test Binary Search Tree", func(t *testing.T) { + helper(bt.NewBinarySearch[int](), nums) + }) + + t.Run("Test Red-Black Tree", func(t *testing.T) { + helper(bt.NewRB[int](), nums) + }) + + t.Run("Test AVL Tree", func(t *testing.T) { + helper(bt.NewAVL[int](), nums) + }) + } +} + +func TestTreeDepth(t *testing.T) { + t.Run("Test for Binary-Search Tree", func(t *testing.T) { + tests := []struct { + input []int + want int + }{ + {[]int{}, 0}, + {[]int{90, 80, 100, 70, 85, 95, 105}, 3}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, 9}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, 10}, + } + for _, tt := range tests { + tree := bt.NewBinarySearch[int]() + tree.Push(tt.input...) + if ret := tree.Depth(); ret != tt.want { + t.Errorf("Error with Depth") + } + } + }) + + t.Run("Test for AVL Tree", func(t *testing.T) { + tests := []struct { + input []int + want int + }{ + {[]int{}, 0}, + {[]int{90, 80, 100, 70, 85, 95, 105}, 3}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, 4}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, 4}, + } + for i, tt := range tests { + tree := bt.NewAVL[int]() + tree.Push(tt.input...) + if ret := tree.Depth(); ret != tt.want { + t.Errorf("#%d Error with Depth", i) + } + } + }) + + t.Run("Test for Red-Black Tree", func(t *testing.T) { + tests := []struct { + input []int + want int + }{ + {[]int{}, 0}, + {[]int{90, 80, 100, 70, 85, 95, 105}, 3}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, 5}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, 5}, + } + for i, tt := range tests { + tree := bt.NewRB[int]() + tree.Push(tt.input...) + if ret := tree.Depth(); ret != tt.want { + t.Errorf("#%d Error with Depth", i) + } + } + }) +} + +func TestTreeAccessNodesByLayer(t *testing.T) { + t.Run("Test for Binary-Search Tree", func(t *testing.T) { + tests := []struct { + input []int + want [][]int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, [][]int{{90}, {80, 100}, {70, 85, 95, 105}}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + [][]int{{90}, {80, 100}, {70, 85, 95, 105}, {1, 71}, {21}, {31}, {41}, {51}, {61}}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, [][]int{{10}, {9}, {8}, {7}, {6}, {5}, {4}, {3}, {2}, {1}}}, + {[]int{}, [][]int{}}, + } + for i, tt := range tests { + tree := bt.NewBinarySearch[int]() + tree.Push(tt.input...) + if ret := tree.AccessNodesByLayer(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with AccessNoedsByLayer", i) + } + } + }) + + t.Run("Test for AVL Tree", func(t *testing.T) { + tests := []struct { + input []int + want [][]int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, [][]int{{90}, {80, 100}, {70, 85, 95, 105}}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + [][]int{{70}, {41, 90}, {21, 51, 80, 100}, {1, 31, 61, 71, 85, 95, 105}}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, [][]int{{7}, {3, 9}, {2, 5, 8, 10}, {1, 4, 6}}}, + {[]int{}, [][]int{}}, + } + for i, tt := range tests { + tree := bt.NewAVL[int]() + tree.Push(tt.input...) + if ret := tree.AccessNodesByLayer(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with AccessNoedsByLayer", i) + } + } + }) + + t.Run("Test for Red-Black Tree", func(t *testing.T) { + tests := []struct { + input []int + want [][]int + }{ + {[]int{90, 80, 100, 70, 85, 95, 105}, [][]int{{90}, {80, 100}, {70, 85, 95, 105}}}, + {[]int{90, 80, 100, 70, 85, 95, 105, 1, 21, 31, 41, 51, 61, 71}, + [][]int{{80}, {41, 90}, {21, 61, 85, 100}, {1, 31, 51, 70, 95, 105}, {71}}}, + {[]int{10, 9, 8, 7, 6, 5, 4, 3, 2, 1}, [][]int{{7}, {5, 9}, {3, 6, 8, 10}, {2, 4}, {1}}}, + {[]int{}, [][]int{}}, + } + for i, tt := range tests { + tree := bt.NewRB[int]() + t.Log(reflect.TypeOf(tree).String() == "*tree.RB[int]") + tree.Push(tt.input...) + if ret := tree.AccessNodesByLayer(); !reflect.DeepEqual(ret, tt.want) { + t.Errorf("#%d Error with AccessNoedsByLayer, %v", i, ret) + } + } + }) +} + +func TestTreePredecessorAndSuccessor(t *testing.T) { + helper := func(tree TestTree[int]) { + nums := []int{10, 8, 88, 888, 4, -1, 100} + tree.Push(nums...) + if ret, ok := tree.Predecessor(100); !ok || ret != 88 { + t.Error("Error with Predecessor") + } + + if _, ok := tree.Predecessor(-1); ok { + t.Error("Error with Predecessor") + } + + tree.Push(-100) + if ret, ok := tree.Predecessor(-1); !ok || ret != -100 { + t.Error("Error with Predecessor") + } + + if _, ok := tree.Predecessor(-12); ok { + t.Error("Error with Predecessor") + } + + if ret, ok := tree.Predecessor(4); !ok || ret != -1 { + t.Error("Error with Predecessor") + } + + if ret, ok := tree.Successor(4); !ok || ret != 8 { + t.Error("Error with Successor") + } + + if ret, ok := tree.Successor(8); !ok || ret != 10 { + t.Error("Error with Successor") + } + + if ret, ok := tree.Successor(88); !ok || ret != 100 { + t.Error("Error with Successor") + } + + if ret, ok := tree.Successor(100); !ok || ret != 888 { + t.Error("Error with Successor") + } + + tree.Delete(888) + if _, ok := tree.Successor(100); ok { + t.Error("Error with Successor") + } + + if ret, ok := tree.Successor(-1); !ok || ret != 4 { + t.Error("Error with Successor") + } + + if _, ok := tree.Successor(888); ok { + t.Error("Error with Successor") + } + + if _, ok := tree.Successor(188); ok { + t.Error("Error with Successor") + } + } + + t.Run("Test for Binary Search Tree", func(t *testing.T) { + tree := bt.NewBinarySearch[int]() + helper(tree) + }) + + t.Run("Test for Red-Black Tree", func(t *testing.T) { + tree := bt.NewRB[int]() + helper(tree) + }) + + t.Run("Test for AVL Tree", func(t *testing.T) { + tree := bt.NewAVL[int]() + helper(tree) + }) +} + +// Benchmark the comparisons between BST, AVL and RB Tree +const testNum = 10_000 + +func BenchmarkBSTree_Insert(b *testing.B) { + helper := func() { + tree := bt.NewBinarySearch[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} + +func BenchmarkBSTree_Has(b *testing.B) { + helper := func() { + tree := bt.NewBinarySearch[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + + for i := 1; i <= testNum; i++ { + tree.Has(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} + +func BenchmarkBSTree_Delete(b *testing.B) { + helper := func() { + tree := bt.NewBinarySearch[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + + for i := 1; i <= testNum; i++ { + tree.Delete(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} + +func BenchmarkRBTree_Insert(b *testing.B) { + helper := func() { + tree := bt.NewRB[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} + +func BenchmarkRBTree_Has(b *testing.B) { + helper := func() { + tree := bt.NewRB[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + + for i := 1; i <= testNum; i++ { + tree.Has(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} + +func BenchmarkRBTree_Delete(b *testing.B) { + helper := func() { + tree := bt.NewRB[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + + for i := 1; i <= testNum; i++ { + tree.Delete(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} + +func BenchmarkAVLTree_Insert(b *testing.B) { + helper := func() { + tree := bt.NewAVL[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } + +} + +func BenchmarkAVLTree_Has(b *testing.B) { + helper := func() { + tree := bt.NewAVL[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + + for i := 1; i <= testNum; i++ { + tree.Has(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} + +func BenchmarkAVLTree_Delete(b *testing.B) { + helper := func() { + tree := bt.NewAVL[int]() + for i := 1; i <= testNum; i++ { + tree.Push(i) + } + + for i := 1; i <= testNum; i++ { + tree.Delete(i) + } + } + + for i := 0; i < b.N; i++ { + helper() + } +} diff --git a/structure/trie/trie.go b/structure/trie/trie.go new file mode 100644 index 000000000..3665e2c3c --- /dev/null +++ b/structure/trie/trie.go @@ -0,0 +1,107 @@ +// Package trie provides Trie data structures in golang. +// +// Wikipedia: https://en.wikipedia.org/wiki/Trie +package trie + +// Node represents each node in Trie. +type Node struct { + children map[rune]*Node // map children nodes + isLeaf bool // current node value +} + +// NewNode creates a new Trie node with initialized +// children map. +func NewNode() *Node { + n := &Node{} + n.children = make(map[rune]*Node) + n.isLeaf = false + return n +} + +// insert a single word at a Trie node. +func (n *Node) insert(s string) { + curr := n + for _, c := range s { + next, ok := curr.children[c] + if !ok { + next = NewNode() + curr.children[c] = next + } + curr = next + } + curr.isLeaf = true +} + +// Insert zero, one or more words at a Trie node. +func (n *Node) Insert(s ...string) { + for _, ss := range s { + n.insert(ss) + } +} + +// Find words at a Trie node. +func (n *Node) Find(s string) bool { + next, ok := n, false + for _, c := range s { + next, ok = next.children[c] + if !ok { + return false + } + } + return next.isLeaf +} + +// Capacity returns the number of nodes in the Trie +func (n *Node) Capacity() int { + r := 0 + for _, c := range n.children { + r += c.Capacity() + } + return 1 + r +} + +// Size returns the number of words in the Trie +func (n *Node) Size() int { + r := 0 + for _, c := range n.children { + r += c.Size() + } + if n.isLeaf { + r++ + } + return r +} + +// remove lazily a word from the Trie node, no node is actually removed. +func (n *Node) remove(s string) { + if len(s) == 0 { + return + } + next, ok := n, false + for _, c := range s { + next, ok = next.children[c] + if !ok { + // word cannot be found - we're done ! + return + } + } + next.isLeaf = false +} + +// Remove zero, one or more words lazily from the Trie, no node is actually removed. +func (n *Node) Remove(s ...string) { + for _, ss := range s { + n.remove(ss) + } +} + +// Compact will remove unecessay nodes, reducing the capacity, returning true if node n itself should be removed. +func (n *Node) Compact() (remove bool) { + + for r, c := range n.children { + if c.Compact() { + delete(n.children, r) + } + } + return !n.isLeaf && len(n.children) == 0 +} diff --git a/structure/trie/trie_bench_test.go b/structure/trie/trie_bench_test.go new file mode 100644 index 000000000..7243a1bd9 --- /dev/null +++ b/structure/trie/trie_bench_test.go @@ -0,0 +1,81 @@ +package trie + +import ( + "fmt" + "math/rand" + "testing" +) + +// CAUTION : make sure to limit the benchmarks to 3000 iterations, +// or removal will mostly process an empty Trie, giving absurd results. + +func BenchmarkTrie_Insert(b *testing.B) { + insert := make([]string, 3000) + for i := 0; i < len(insert); i++ { + insert[i] = fmt.Sprintf("%f", rand.Float64()) + } + + b.ResetTimer() + for i := 0; i < b.N; i++ { + n := NewNode() + n.Insert(insert...) + } +} + +func BenchmarkTrie_Find_non_existent(b *testing.B) { + + insert := make([]string, 3000) + for i := 0; i < len(insert); i++ { + insert[i] = fmt.Sprintf("%f", rand.Float64()) + } + n := NewNode() + n.Insert(insert...) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + n.Find("0.3213213244346546546546565465465") // does not exists + } +} + +func BenchmarkTrie_Find_existent(b *testing.B) { + insert := make([]string, 3000) + for i := 0; i < len(insert); i++ { + insert[i] = fmt.Sprintf("%f", rand.Float64()) + } + n := NewNode() + n.Insert(insert...) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + n.Find(insert[i%3000]) // always exists ! + } +} + +func BenchmarkTrie_Remove_lazy(b *testing.B) { + insert := make([]string, 3000) + for i := 0; i < len(insert); i++ { + insert[i] = fmt.Sprintf("%f", rand.Float64()) + } + n := NewNode() + n.Insert(insert...) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + n.Remove(insert[i%3000]) // exists, at least until removed ... + } +} + +func BenchmarkTrie_Remove_and_Compact(b *testing.B) { + insert := make([]string, 3000) + for i := 0; i < len(insert); i++ { + insert[i] = fmt.Sprintf("%f", rand.Float64()) + } + n := NewNode() + n.Insert(insert...) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + n.Remove(insert[i%3000]) + n.Compact() + } +} diff --git a/structure/trie/trie_test.go b/structure/trie/trie_test.go new file mode 100644 index 000000000..7080b5898 --- /dev/null +++ b/structure/trie/trie_test.go @@ -0,0 +1,157 @@ +package trie + +import ( + "testing" +) + +func TestTrieInsert(t *testing.T) { + n := NewNode() + + insertWords := []string{ + "nikola", + "tesla", + } + + checkWords := map[string]bool{ + "thomas": false, + "edison": false, + "nikola": true, + } + + n.Insert(insertWords...) + n.verify(t, checkWords) + n.verifySizeCapa(t, 2, 12) + +} + +func TestTrieInsert_substrings(t *testing.T) { + n := NewNode() + + insertWords := []string{ + "aa", + "aaaa", + "aaaaa", + } + + checkWords := map[string]bool{ + "a": false, + "aa": true, + "aaa": false, + "aaaa": true, + "aaaaa": true, + "aaaaaa": false, + "aaaaaaa": false, + } + + n.Insert(insertWords...) + n.verify(t, checkWords) + n.verifySizeCapa(t, 3, 5+1) + + n.Remove("aaaa") + checkWords["aaaa"] = false + n.verify(t, checkWords) + n.verifySizeCapa(t, 2, 5+1) + + if n.Compact() { + t.Fatalf("it should not be possible to remove the node") + } + n.verify(t, checkWords) + n.verifySizeCapa(t, 2, 5+1) +} + +func TestTrieRemove(t *testing.T) { + n := NewNode() + + insertWords := []string{ + "nikola", + "tesla", + "albert", + "einstein", + } + + checkWords := map[string]bool{ + "thomas": false, + "edison": false, + "nikola": true, + "albert": true, + "einstein": true, + } + + n.Insert(insertWords...) + n.verify(t, checkWords) + size, capa := n.Size(), n.Capacity() // 4 words ... + + n.Remove("albert") + checkWords["albert"] = false + size-- // 3 words in size, but no change in capacity + n.verify(t, checkWords) + n.verifySizeCapa(t, size, capa) + + n.Remove("albert") // no effect since already removed + n.verify(t, checkWords) + n.verifySizeCapa(t, size, capa) + + n.Remove("marcel") // no effect since ,o, existent + n.verify(t, checkWords) + n.verifySizeCapa(t, size, capa) + + n.Remove("nikola", "tesla") // 1 word + checkWords["nikola"] = false + checkWords["tesla"] = false + size -= 2 // t1 word left, but still no change in capacity + n.verify(t, checkWords) + n.verifySizeCapa(t, size, capa) + + // compact the Tree + if n.Compact() { + t.Fatal("the Trie should not be completely removable after compaction") + } + if capa <= n.Capacity() { + t.Fatal("capacity should have reduced following compaction") + } + capa = n.Capacity() + n.verify(t, checkWords) + n.verifySizeCapa(t, size, capa) // still 1 word, reduced capacity + + n.Remove("einstein") + checkWords["einstein"] = false + size-- // No more words + n.verify(t, checkWords) + n.verifySizeCapa(t, size, capa) // no words, but still have some nodes left capacity + + if !n.Compact() { + t.Fatal("the root node of an empty Trie should be marked as removable after compaction") + } + n.verifySizeCapa(t, 0, 1) // no words, only the root node left +} + +// --------------- helper functions --------------------------- + +// verify if provided words are present +func (n *Node) verify(t *testing.T, checkWords map[string]bool) { + for k, v := range checkWords { + ok := n.Find(k) + if ok != v { + t.Fatalf( + "%q is %s supposed to be in the Trie.", + k, + map[bool]string{true: "", false: "NOT "}[v], + ) + } + // t.Logf( + // "\"%s\" is %sin the Trie.", + // k, + // map[bool]string{true: "", false: "NOT "}[ok], + // ) + } +} + +// verify expected size and capacity +func (n *Node) verifySizeCapa(t *testing.T, expectedSize, expectedCapacity int) { + if got := n.Size(); got != expectedSize { + t.Fatalf("Expected Size was %d but got %d", expectedSize, got) + } + if got := n.Capacity(); got != expectedCapacity { + t.Fatalf("Expected Capacity was %d but got %d", expectedCapacity, got) + } +} diff --git a/structure/trie/trieexample_test.go b/structure/trie/trieexample_test.go new file mode 100644 index 000000000..fb3f9bc0f --- /dev/null +++ b/structure/trie/trieexample_test.go @@ -0,0 +1,39 @@ +package trie + +import "fmt" + +func ExampleNode() { + // creates a new node + node := NewNode() + + // adds words + node.Insert("nikola") + node.Insert("tesla") + + // check size and capacity + fmt.Println(node.Size()) // 2 words + fmt.Println(node.Capacity()) // 12 nodes + + // finds words + fmt.Println(node.Find("thomas")) // false + fmt.Println(node.Find("edison")) // false + fmt.Println(node.Find("nikola")) // true + + // remove a word, and check it is gone + node.Remove("tesla") + fmt.Println(node.Find("tesla")) // false + + // size and capacity have changed + fmt.Println(node.Size()) // 1 word left + fmt.Println(node.Capacity()) // 12 nodes remaining + + // output: + // 2 + // 12 + // false + // false + // true + // false + // 1 + // 12 +}