Bubble Sort Algorithm

1. Compare the first two elements. If the first element is greater than the second element, swap them.

2. Move to the next pair of elements (the second and third elements), repeat the comparison and swap if necessary.

3. Continue this process, moving through the list one pair at a time, until you reach the end of the list. This completes one iteration. After each iteration, the largest unsorted element "bubbles up" to the end of the list.

4. Repeat the above steps for the number of iterations equal to the length of the list.

5. After all the iterations are completed, the list will be sorted.

Bubble Sort Demonstration

Implementation of Bubble Sort

def bubble_sort(arr, n):
    if n == 1:
        return

    for i in range(1, n):
        if arr[i - 1] > arr[i]:
            arr[i - 1], arr[i] = arr[i], arr[i - 1]

    bubble_sort(arr, n - 1)


# Example usage
arr = [7, 0, 2, 9, 6, 1, 3, 8, 5, 4]
bubble_sort(arr, len(arr))
print("Sorted array:", arr)

Complexity Analysis of Bubble Sort

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

Auxiliary Space: \(O(1)\)

Bubble Sort has a time complexity of \(O(n^2)\) in the worst and average cases, and it's not very efficient for large lists. Other sorting algorithms like QuickSort, MergeSort, and HeapSort offer better performance for larger datasets. However, Bubble Sort's simplicity makes it a good educational example for understanding the basics of sorting algorithms.