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Bubble sort is a sorting algorithm that compares 2 adjacent items at a time, starting from the beginning of a list, and swapping them if they are out of sequence. Each comparison gradually moves the largest item to the end of the list (likened to a bubble making its way to the surface of water). After n*n passes, all the items will be sorted. The big O for a standard bubble sort is therefore O(n*n).

The algorithm can be improved somewhat. Since it is clear that the last item is sorted on each pass, the unsorted set can be reduced by 1 element on each pass. Moreover, since the final swap on each pass indicates that everything from that point on is already sorted, the unsorted set can often be reduced by more than 1 element on each pass. For an already sorted list, the worst case is reduced to O(n), constant time.

For small sets of data, perhaps 10 to 20 items, the bubble sort is reasonably efficient, especially on partially sorted lists. However the insert sort algorithm offers similar or better performance on average. With larger sets, the quick sort algorithm is hard to beat, but is let down by inefficiencies when dealing with partially sorted lists. Hybrid sorts can improve things a little, however, there is no efficient way to check the state of a list to determine the most efficient algorithm to use at any given point.

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What is the running time of the bubble sort algorithm?

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What are the advantages for bubble sort?

Bubble sort has no practical applications other than that it is often cited as an example of how not to write an algorithm. Insert sort is the best algorithm for sorting small lists of items and is often used in conjunction with quick sort to sort larger lists. Like insert sort, bubble sort is simple to implement and is a stable sort (equal items remain in the same order they were input). However, insert sort uses copy or move operations rather than swaps (which is actually three operations per swap) and is therefore quicker. The only time a bubble sort will work quicker than insert sort is when the array is already sorted, which renders the entire algorithm redundant. A modified algorithm that specifically tests if an array is sorted or not would be more efficient than a single-pass bubble sort.