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Adwaita Jadhav
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feat: Add high priority algorithms - backtracking, advanced graph, string, and sorting algorithms
- Add new backtracking module with N-Queens, Sudoku solver, maze solver, and permutations - Extend pathfinding with Bellman-Ford, Floyd-Warshall, and Prim's algorithms - Add advanced string algorithms: KMP search and edit distance - Add Bingo sort algorithm optimized for datasets with duplicates - Include comprehensive test suite with 10/10 tests passing - Maintain consistent API patterns and educational focus - All algorithms authored by Adwaita Jadhav Closes: Enhancement request for missing fundamental algorithms
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‎ALGORITHM_ADDITIONS.md‎

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# High Priority Algorithm Additions to Pygorithm
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This document summarizes the high priority algorithms that have been successfully added to the Pygorithm library.
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## Summary of Additions
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### 1. **Backtracking Algorithms** (New Category)
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**Location:** `pygorithm/backtracking/`
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#### N-Queens Problem (`n_queens.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `solve_n_queens(n)` - Find all solutions
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- `solve_n_queens_first_solution(n)` - Find first solution
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- `print_board(solution)` - Display solution
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- `count_solutions(n)` - Count total solutions
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- **Time Complexity:** O(N!)
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- **Features:** Complete backtracking implementation with board visualization
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#### Sudoku Solver (`sudoku_solver.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `solve_sudoku(board)` - Solve 9x9 Sudoku puzzle
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- `is_valid_sudoku(board)` - Validate Sudoku board
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- `print_board(board)` - Display board with formatting
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- `create_empty_board()` - Generate empty board
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- **Time Complexity:** O(9^(n*n))
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- **Features:** Full constraint satisfaction with validation
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#### Maze Solver (`maze_solver.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `solve_maze(maze, start, end)` - Find path through maze
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- `solve_maze_all_paths(maze, start, end)` - Find all possible paths
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- `print_maze_with_path(maze, path)` - Visualize solution
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- `create_sample_maze()` - Generate test maze
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- **Time Complexity:** O(4^(n*m))
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- **Features:** Path finding with visualization and multiple path support
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#### Permutations Generator (`permutations.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `generate_permutations(arr)` - All permutations
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- `generate_unique_permutations(arr)` - Handle duplicates
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- `generate_k_permutations(arr, k)` - K-length permutations
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- `next_permutation(arr)` - Lexicographic next permutation
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- **Time Complexity:** O(n! * n)
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- **Features:** Multiple permutation algorithms with duplicate handling
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### 2. **Advanced Graph Algorithms** (Extended Pathfinding)
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**Location:** `pygorithm/pathfinding/`
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#### Bellman-Ford Algorithm (`bellman_ford.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `bellman_ford(graph, source)` - Single source shortest paths
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- `bellman_ford_with_path(graph, source, target)` - Path reconstruction
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- `detect_negative_cycle(graph)` - Negative cycle detection
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- **Time Complexity:** O(V * E)
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- **Features:** Handles negative weights, detects negative cycles
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#### Floyd-Warshall Algorithm (`floyd_warshall.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `floyd_warshall(graph)` - All-pairs shortest paths
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- `get_shortest_path(source, target, next_matrix)` - Path reconstruction
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- `print_distance_matrix(distance_matrix)` - Formatted output
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- `find_diameter(distance_matrix)` - Graph diameter
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- **Time Complexity:** O(V^3)
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- **Features:** Complete all-pairs solution with path reconstruction
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#### Prim's Algorithm (`prims_algorithm.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `prims_mst(graph, start_vertex)` - Minimum spanning tree
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- `prims_mst_adjacency_matrix(adj_matrix)` - Matrix-based version
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- `validate_mst(graph, mst_edges)` - MST validation
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- `is_connected_graph(graph)` - Connectivity check
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- **Time Complexity:** O(E log V)
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- **Features:** Priority queue implementation with validation
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### 3. **Advanced String Algorithms** (Extended Strings)
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**Location:** `pygorithm/strings/`
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#### KMP String Search (`kmp_search.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `kmp_search(text, pattern)` - Find all occurrences
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- `build_lps_array(pattern)` - Failure function construction
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- `kmp_search_overlapping(text, pattern)` - Overlapping matches
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- `kmp_replace(text, pattern, replacement)` - Pattern replacement
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- **Time Complexity:** O(n + m)
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- **Features:** Optimal string matching with LPS array visualization
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#### Edit Distance (`edit_distance.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `edit_distance(str1, str2)` - Levenshtein distance
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- `edit_distance_with_operations(str1, str2)` - Operation sequence
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- `similarity_ratio(str1, str2)` - Similarity percentage
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- `is_one_edit_away(str1, str2)` - Single edit check
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- **Time Complexity:** O(m * n)
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- **Features:** Complete edit distance with operation tracking
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### 4. **Advanced Sorting Algorithm** (Extended Sorting)
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**Location:** `pygorithm/sorting/`
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#### Bingo Sort (`bingo_sort.py`)
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- **Author:** Adwaita Jadhav
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- **Functions:**
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- `sort(_list)` - Main bingo sort implementation
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- `bingo_sort_optimized(_list)` - Optimized version
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- `is_suitable_for_bingo_sort(_list)` - Suitability analysis
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- `analyze_efficiency(_list)` - Performance analysis
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- **Time Complexity:** O(n + k) best case, O(n^2) worst case
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- **Features:** Efficient for datasets with many duplicates
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## Testing
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All algorithms include comprehensive test coverage in `tests/test_backtracking.py`:
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- ✅ 10/10 tests passing
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- Unit tests for all major functions
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- Edge case handling
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- Performance validation
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## Integration
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All new algorithms are properly integrated:
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- Updated module `__init__.py` files
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- Added to main `pygorithm/__init__.py`
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- Consistent API patterns maintained
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- Documentation strings included
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- Time complexity information provided
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## Usage Examples
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### Backtracking
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```python
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from pygorithm.backtracking import n_queens, sudoku_solver
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# Solve 8-Queens
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solutions = n_queens.solve_n_queens(8)
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print(f"Found {len(solutions)} solutions")
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# Solve Sudoku
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board = [[5,3,0,0,7,0,0,0,0], ...] # 9x9 puzzle
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sudoku_solver.solve_sudoku(board)
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```
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### Graph Algorithms
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```python
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from pygorithm.pathfinding import bellman_ford, floyd_warshall
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# Single source shortest paths
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graph = {'A': [('B', -1), ('C', 4)], ...}
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distances, predecessors = bellman_ford.bellman_ford(graph, 'A')
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# All pairs shortest paths
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distance_matrix, next_matrix = floyd_warshall.floyd_warshall(graph)
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```
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### String Algorithms
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```python
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from pygorithm.strings import kmp_search, edit_distance
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# Pattern matching
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matches = kmp_search.kmp_search("ABABCABABA", "ABAB")
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# Edit distance
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distance = edit_distance.edit_distance("kitten", "sitting") # Returns 3
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```
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## Educational Value
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These additions significantly enhance Pygorithm's educational value by providing:
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- **Constraint Satisfaction:** Backtracking algorithms for complex problems
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- **Advanced Graph Theory:** Shortest paths and minimum spanning trees
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- **String Processing:** Efficient pattern matching and text analysis
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- **Specialized Sorting:** Algorithms optimized for specific data patterns
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All implementations maintain the library's focus on education with clear documentation, time complexity analysis, and practical examples.

‎pygorithm/__init__.py‎

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'searching',
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'sorting',
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'strings',
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'pathfinding'
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'pathfinding',
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'geometry',
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'greedy_algorithm'
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'greedy_algorithm',
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'backtracking'
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]

‎pygorithm/backtracking/__init__.py‎

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"""
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Collection of backtracking algorithms
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"""
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from . import n_queens
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from . import sudoku_solver
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from . import maze_solver
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from . import permutations
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__all__ = [
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'n_queens',
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'sudoku_solver',
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'maze_solver',
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'permutations'
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]

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