Bubble sort

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Bubble sort

Static visualization of bubble sort[1]
Class	Sorting algorithm
Data structure	Array
Worst-case performance	${\displaystyle O(n^{2})}$ comparisons, ${\displaystyle O(n^{2})}$ swaps
Best-case performance	${\displaystyle O(n)}$ comparisons, ${\displaystyle O(1)}$ swaps
Average performance	${\displaystyle O(n^{2})}$ comparisons, ${\displaystyle O(n^{2})}$ swaps
Worst-case space complexity	${\displaystyle O(n)}$ total, ${\displaystyle O(1)}$ auxiliary
Optimal	No

Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list.

This simple algorithm performs poorly in real-world use and is used primarily as an educational tool. More efficient algorithms such as quicksort, timsort, or merge sort are used by the sorting libraries built into popular programming languages such as Python and Java. However, if parallel processing is allowed, bubble sort sorts in O(n) time, making it considerably faster than parallel implementations of insertion sort or selection sort which do not parallelize as effectively.^[2][3]