as its optimized version achieves O(n) performance in the best case. Time Space Complexity Metric / OperationComplexityDescription Best Case O(n) When the array is already sorted and the optimized version detects no swaps in the first pass. Average Case O(n²) On average， Bubble Sort Visualization Bubble Sort is a simple sorting algorithm that works by repeatedly swapping adjacent elements if they are in the wrong order. This process continues until the list is fully sorted. While its easy to understand。
they are swapped. The algorithm then moves to the next pair and repeats the comparison. After one complete pass through the array，。
every possible swap must be performed. Space Complexity O(1) Bubble Sort is an in-place algorithm that only requires a constant amount of additional memory for the swap variable. ， the largest element will have bubbled up to the last position. The algorithm then repeats the process for the remaining unsorted portion， more efficient divide-and-conquer algorithms are preferred for large datasets. However， ignoring the already-sorted elements at the end. This continues until no swaps are needed in a full pass， Bubble Sort can be useful for very small arrays or when the data is nearly sorted， indicating the array is sorted. When To Use Bubble Sort is primarily used as a teaching tool to introduce sorting concepts because of its simplicity. In practice， each element must be compared with every other element. Worst Case O(n²) When the array is sorted in reverse order， Bubble Sort is not very efficient for large datasets due to its quadratic time complexity. It’s often used for educational purposes or as a baseline for comparison with other sorting algorithms. Pseudocode for i = 1 to (n - 1): swapped = false for j = 1 to (n - i):if arr[j] arr[j - 1]:swap(j。
j - 1)swapped = true if not swapped: break Visualizer Select number of elements: How It Works Bubble Sort begins at the start of the array and compares the first two elements. If the first element is greater than the second。