Web Reference: Dec 8, 2025 · Below is the implementation of the bubble sort. It can be optimized by stopping the algorithm if the inner loop didn't cause any swap. Although bubble sort is one of the simplest sorting algorithms to understand and implement, its O (n2) complexity means that its efficiency decreases dramatically on lists of more than a small number of elements. Let's say we are going to sort a sequence of length in non-decreasing order. Bubble sort swaps two adjacent numbers when they are not in the correct order. Swaps are done by repeatedly passing through the sequence. Precisely speaking, in a pass, we swap and if , for in this order.
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