Bubble Sort

Bubble Sort is a simple sorting algorithm that works by repeatedly swapping adjacent elements if they are in the wrong order. It is named so because smaller elements “bubble” to the top of the list like bubbles rising in a liquid.

The algorithm starts by comparing the first two elements of the array, swapping them if they are not in the correct order, and then moving to the next pair of elements. It continues this process until it reaches the end of the array. At this point, the largest element will have “bubbled” to the end of the array. The algorithm then starts again, but this time it only needs to compare and swap the elements up to the second-to-last element, since the last element is already in its correct position. This process repeats until the entire array is sorted.

Bubble Sort has a worst-case and average time complexity of O(n^2), making it inefficient for large data sets. However, it is simple to understand and implement, making it a good choice for small data sets or educational purposes.

Here’s an example of Bubble Sort code in Python:

def bubble_sort(arr):
    n = len(arr)
    
    # Traverse through all array elements
    for i in range(n):
        
        # Last i elements are already sorted
        for j in range(0, 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]
    
    return arr

In this code, the outer loop iterates through the array n times, where n is the length of the array. The inner loop iterates through the array up to the n-i-1th element, since the last i elements are already sorted. The conditional statement checks if the current element is greater than the next element and swaps them if necessary.

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