?? Understanding Bubble Sort: A Simple Sorting Algorithm

Bubble Sort , a fundamental sorting algorithm, operates by stepping through a list, comparing adjacent elements, and swapping them if they're in the incorrect order. This uncomplicated process continues until the entire list is correctly arranged.

How Bubble Sort Works:

Algorithm Overview:

1. Comparing Adjacent Elements:

- Bubble sort examines each pair of neighboring items in the list.

2. Swapping Elements:

- If elements are out of order, they get swapped (e.g., if a smaller element appears after a larger one in ascending order).

3. Repeating Until Sorted:

- The algorithm repeats these steps for multiple passes until no more swaps are necessary.

4. Optimization:

- After each pass, the largest (or smallest) element reaches its correct position at the end of the array.

Bubble Sort in Action:

Initial Array: [5, 4, 3, 2, 1]

Step-by-Step Progress:

• Pass 1: [4, 3, 2, 1, 5]
• Pass 2: [3, 2, 1, 4, 5]
• Pass 3: [2, 1, 3, 4, 5]
• Pass 4: [1, 2, 3, 4, 5]

Through iterative comparisons and swaps, Bubble Sort arranges the array in ascending order.

A simple implementation of the Bubble Sort algorithm in C++ :

#include <iostream>
using namespace std;
int main(){
    int n;
    cout << "Enter the size of array : ";
    cin >> n;
    int* arr = new int[n];
    cout << "Enter "<<n<< " elements for the array : ";
    for(int i = 0; i < n; i++){
        cin >> arr[i];
    }
 
    for(int i = n-2; i >= 0; i--){
        bool swapped = 0;
        for(int j = 0; j <= i; j++){
            if(arr[j] > arr[j+1]){
                swap(arr[j], arr[j+1]);
                swapped = 1;
            }
            if(swapped == 0)
            break;
        }
    }
    cout << "Sorted array by Bubble Sort : ";
    for(int i = 0; i < n; i++){
        cout << arr[i]<<" ";
    }
    delete[] arr;
    return 0;
}        

Complexity Analysis:

- Time Complexity: O(n^2) - Involves nested loops for comparison and swapping.

- Space Complexity: O(1) - Sorts the array in-place without additional space.

Bubble sort's simplicity makes it ideal for educational purposes or small datasets. However, its quadratic time complexity makes it less efficient for larger datasets.