Bubble Sort - Python

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. 

• Bubble Sort algorithm, sorts an array by repeatedly comparing adjacent elements and swapping them if they are in the wrong order.
• The algorithm iterates through the array multiple times, with each pass pushing the largest unsorted element to its correct position at the end.
• Code includes an optimization: if no swaps are made during a pass, the array is already sorted, and the sorting process stops.

Below is the Python Implementation of Bubble Sort:

# Optimized Python program for implementation of Bubble Sort
def bubbleSort(arr):
    n = len(arr)
    
    # Traverse through all array elements
    for i in range(n):
        swapped = False

        # Last i elements are already in place
        for j in range(0, n-i-1):

            # Traverse the array from 0 to n-i-1
            # Swap if the element found is greater
            # than the next element
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]
                swapped = True
        if (swapped == False):
            break

# Driver code to test above
if __name__ == "__main__":
    arr = [64, 34, 25, 12, 22, 11, 90]

    bubbleSort(arr)

    print("Sorted array:")
    for i in range(len(arr)):
        print("%d" % arr[i], end=" ")

Sorted array:
11 12 22 25 34 64 90 

Time Complexity:  O(n²). However in practice, this optimized version might take less time as when array gets sorted, function would return.
Auxiliary Space: O(1).

Please refer complete article on Bubble Sort for more details!