Bubble Sort is one of the simplest sorting algorithms to understand. It works by repeatedly comparing adjacent elements in the array and swapping them if they are in the wrong order. The algorithm gets its name because smaller elements gradually 'bubble' to the beginning of the list, similar to how air bubbles rise to the surface of water. Let's see how it works with this example array.
Let's walk through how bubble sort works step by step. We start by comparing the first two elements: 64 and 34. Since 64 is greater than 34, we need to swap them. This is the fundamental operation of bubble sort - compare adjacent elements and swap if they're in the wrong order. We then move to the next pair and repeat this process until we reach the end of the array.
After completing the first pass through the array, we can see that the largest element, 90, has 'bubbled' to the end of the array. During this pass, we made several comparisons and swaps, gradually moving the largest element to its correct position. Now we have one element in its final sorted position, shown in green, and six elements that still need to be sorted, shown in blue.
Bubble sort continues with multiple passes through the array. In each subsequent pass, we only need to compare elements in the unsorted portion, since the largest elements are already in their correct positions at the end. After pass 2, the second largest element is sorted. After pass 3, the third largest is sorted, and so on. The algorithm continues until the entire array is sorted.
In conclusion, bubble sort successfully sorts our array, but it comes with a significant time complexity cost of O(n squared). While it's easy to understand and implement, making it great for educational purposes, it's inefficient for large datasets due to its quadratic time complexity. Bubble sort is stable, meaning equal elements maintain their relative order, and it sorts in-place, requiring only constant extra memory. However, for practical applications with large amounts of data, more efficient algorithms like quicksort or mergesort are preferred.