Bubble sort is a simple sorting algorithm. The algorithm starts at the beginning of the data set. It compares the first two elements, and if the first is greater than the second, it swaps them. It continues doing this for each pair of adjacent elements to the end of the data set. It then starts again with the first two elements, repeating until no swaps have occurred on the last pass. This algorithm's average and worst case performance is O(n2), so it is rarely used to sort large, unordered, data sets. Bubble sort can be used to sort a small number of items (where its inefficiency is not a high penalty). Bubble sort may also be efficiently used on a list that is already sorted except for a very small number of elements. For example, if only one element is not in order, bubble sort will take only 2n time. If two elements are not in order, bubble sort will take only at most 3n time.
Each of these algorithms requires n-1 passes: each pass places one item in its correct place. (The nth is then in the correct place also.) The ith pass makes either ior n - i comparisons and moves. So:
or O(n2) - but we already know we can use heaps to get an O(n logn) algorithm. Thus these algorithms are only suitable for small problems where their simple code makes them faster than the more complex code of the O(n logn) algorithm. As a rule of thumb, expect to find an O(n logn) algorithm faster for n>10 - but the exact value depends very much on individual machines!.
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