This repository contains implementations of various sorting algorithms in Python. Sorting is a fundamental operation in computer science and is crucial for optimizing the performance of other algorithms that require sorted data.

- [Overview](#overview)

- [Algorithms Implemented](#algorithms-implemented)

- [Requirements](#requirements)

- [Usage](#usage)

- [Algorithm Details](#algorithm-details)

- [Bubble Sort](#bubble-sort)

- [Selection Sort](#selection-sort)

- [Insertion Sort](#insertion-sort)

- [Merge Sort](#merge-sort)

- [Quick Sort](#quick-sort)

- [Heap Sort](#heap-sort)

- [Performance Comparison](#performance-comparison)

- [Contributing](#contributing)

- [License](#license)

This repository serves as a learning tool for understanding and comparing different sorting algorithms. Each algorithm is implemented in a standalone Python file with comments explaining the key steps.

1. Bubble Sort

2. Selection Sort

3. Insertion Sort

4. Merge Sort

5. Quick Sort

6. Heap Sort

- Python 3.x

Clone the repository and navigate to the directory:

git clone https://github.com/your-username/sorting-algorithms.git

cd sorting-algorithms

You can run any of the sorting algorithms by executing the corresponding Python file. For example, to run the Bubble Sort algorithm:

python bubble_sort.py

Each script includes a sample list and outputs the sorted result.

Bubble Sort is a simple comparison-based sorting algorithm. It repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. The pass through the list is repeated until the list is sorted.

**Time Complexity**: O(n^2)

def bubble_sort(arr):

n = len(arr)

for i in range(n):

for j in range(0, n-i-1):

if arr[j] > arr[j+1]:

arr[j], arr[j+1] = arr[j+1], arr[j]

return arr

Selection Sort divides the input list into two parts: the sorted part and the unsorted part. It repeatedly selects the smallest (or largest) element from the unsorted part and moves it to the sorted part.

**Time Complexity**: O(n^2)

def selection_sort(arr):

n = len(arr)

for i in range(n):

min_idx = i

for j in range(i+1, n):

if arr[j] < arr[min_idx]:

min_idx = j

arr[i], arr[min_idx] = arr[min_idx], arr[i]

return arr

Insertion Sort builds the final sorted array one item at a time. It is much less efficient on large lists than more advanced algorithms such as quicksort, heapsort, or merge sort.

**Time Complexity**: O(n^2)

def insertion_sort(arr):

for i in range(1, len(arr)):

key = arr[i]

j = i-1

while j >= 0 and key < arr[j]:

arr[j+1] = arr[j]

j -= 1

arr[j+1] = key

return arr

Merge Sort is a divide-and-conquer algorithm. It divides the input array into two halves, calls itself for the two halves, and then merges the two sorted halves.

**Time Complexity**: O(n log n)

def merge_sort(arr):

if len(arr) > 1:

mid = len(arr) // 2

L = arr[:mid]

R = arr[mid:]

merge_sort(L)

merge_sort(R)

i = j = k = 0

while i < len(L) and j < len(R):

if L[i] < R[j]:

arr[k] = L[i]

i += 1

else:

arr[k] = R[j]

j += 1

k += 1

while i < len(L):

arr[k] = L[i]

i += 1

k += 1

while j < len(R):

arr[k] = R[j]

j += 1

k += 1

return arr

Quick Sort is another divide-and-conquer algorithm. It picks an element as a pivot and partitions the given array around the picked pivot. There are different versions of quicksort that pick pivot in different ways.

**Time Complexity**: O(n log n)

def quick_sort(arr):

if len