# Bubble Sort

- December 31, 2020
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This sorting algorithm is comparison-based algorithm in which each pair of adjacent elements is compared and the elements are swapped if they are not in order. This algorithm is not suitable for large data sets as its average and worst case complexity are of ?(n^{2}) where?**n**?is the number of items.

Although bubble sort is one of the simplest sorting algorithms to understand and implement, its?*O*(*n*^{2})?complexity means that its efficiency decreases dramatically on lists of more than a small number of elements. Even among simple?*O*(*n*^{2}) sorting algorithms, algorithms like?insertion sort?are usually considerably more efficient.

Due to its simplicity, bubble sort is often used to introduce the concept of an algorithm, or a sorting algorithm, to introductory?computer science?students. However, some researchers such as?Owen Astrachan?have gone to great lengths to disparage bubble sort and its continued popularity in computer science education, recommending that it no longer even be taught.^{}

The?Jargon File, which famously calls?bogosort?”the archetypical [sic] perversely awful algorithm”, also calls bubble sort “the generic bad algorithm”. ^{}Donald Knuth, in?*The Art of Computer Programming*, concluded that “the bubble sort seems to have nothing to recommend it, except a catchy name and the fact that it leads to some interesting theoretical problems”, some of which he then discusses.^{}

Bubble sort is?asymptotically?equivalent in running time to insertion sort in the worst case, but the two algorithms differ greatly in the number of swaps necessary. Experimental results such as those of Astrachan have also shown that insertion sort performs considerably better even on random lists. For these reasons many modern algorithm textbooks avoid using the bubble sort algorithm in favor of insertion sort.

Bubble sort also interacts poorly with modern CPU hardware. It produces at least twice as many writes as insertion sort, twice as many cache misses, and asymptotically more?branch mispredictions. Experiments by Astrachan sorting strings in?Java?show bubble sort to be roughly one-fifth as fast as an insertion sort and 70% as fast as a?selection sort.^{}

In computer graphics bubble sort is popular for its capability to detect a very small error (like swap of just two elements) in almost-sorted arrays and fix it with just linear complexity (2*n*). For example, it is used in a polygon filling algorithm, where bounding lines are sorted by their?*x*?coordinate at a specific scan line (a line parallel to the?*x*?axis) and with incrementing?*y*?their order changes (two elements are swapped) only at intersections of two lines. Bubble sort is a stable sort algorithm, like insertion sort.