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| Gareth is awesome | |||
| '''Bubble sort''', sometimes shortened to '''bubblesort''', also known as '''exchange sort''', is a simple ]. It works by repeatedly stepping through the list to be sorted, comparing two items at a time and ]ping them if they are in the wrong order. The pass through the list is repeated until no swaps are needed, which means the list is sorted. The algorithm gets its name from the way smaller elements "bubble" to the top (i.e. the beginning) of the list via the swaps. Because it only uses comparisons to operate on elements, it is a ]. | |||
| Bubbles are awesome | |||
| ⚫ | Bubble sort isn't. | ||
| A simple way to express bubble sort in ] is as follows: | |||
| '''function''' bubble_sort(''list'' L, ''number'' listsize) | |||
| '''loop''' | |||
| has_swapped := 0 <span style="color:green">//reset flag</span> | |||
| '''for''' ''number'' i '''from''' 1 '''to''' listsize | |||
| '''if''' L > L <span style="color:green">//if they are in the wrong order</span> | |||
| swap(L, L) <span style="color:green">//exchange them</span> | |||
| has_swapped := 1 <span style="color:green">//we have swapped at least once, list may not be sorted yet</span> | |||
| '''endif''' | |||
| '''endfor''' | |||
| <span style="color:green">//if no swaps were made during this pass, the list has been sorted</span> | |||
| '''if''' has_swapped = 0 | |||
| '''exit''' | |||
| '''endif''' | |||
| '''endloop''' | |||
| '''endfunction''' | |||
| ==Analysis== | |||
| ===Worst-case performance=== | |||
| Bubble sort has worst-case complexity ''](n<sup>2</sup>)'' on lists of size ''n''. To see why, note that each element is moved no more than one step each time. No element can be more than a distance of ''n'' away from its final sorted position, so we use at most ''O(n)'' operations to move an element to its final sorted position, and use no more than ''O(n<sup>2</sup>)'' operations in the worst case. | |||
| However, on a list where the smallest element is at the bottom, each pass through the list will only move it up by one step, so we will take ''n'' passes to move it to its final sorted position. As each pass traverses the whole list a pass will take ''O(n)'' time. Thus the least number of operations in the worst case is also ''O(n<sup>2</sup>)''. | |||
| ===Best-case performance=== | |||
| When a list is already sorted, bubblesort will pass through the list once, and find that it does not need to swap any elements. This means the list is already sorted. Thus bubblesort will take ''O(n)'' time when the list is completely sorted. It will also use considerably less time if the elements in the list are not too far from their sorted places. | |||
| ===Rabbits and turtles=== | |||
| The positions of the elements in bubble sort will play a large part in determining its performance. Large elements at the top of the list do not pose a problem, as they are quickly swapped downwards. Small elements at the bottom, however, as mentioned earlier, move to the top extremely slowly. This has led to these types of elements being named ], respectively. | |||
| Various efforts have been made to eliminate turtles to inprove upon the speed of bubble sort. ] does pretty well, but it still retains ''O(n<sup>2</sup>)'' worst-case complexity. ] compares elements large gaps apart and can move turtles extremely quickly, before proceeding to smaller and smaller gaps to smoothen out the list. It clocks in at a respectable ''O(n log n)'' time, rivaling in speed and simplicity more complex competitors like ] and ]. | |||
| ===Alternative implementations=== | |||
| One way to optimize bubblesort is to note that, after each pass, the largest element will always move down to the bottom. During each comparison, it is clear that the largest element will move downwards. Given a list of size ''n'', the ''n<sup>th</sup>'' element will be guaranteed to be in its proper place. Thus it suffices to sort the remaining ''n - 1'' elements. Again, after this pass, the ''n - 1<sup>th</sup>'' element will be in its final place. | |||
| We can then do bubbling passes over increasingly smaller parts of the list. More precisely, instead of doing ''n<sup>2</sup>'' comparisons (and swaps), we can use only ''n + (n-1) + (n-2) + ... + 2 + 1'' comparisons. This ] up to ''n(n + 1) / 2'', which is still ''O(n<sup>2</sup>)'', but which can be considerably faster in practice. | |||
| ==In practice== | |||
| Although bubble sort is one of the simplest sorting algorithms to understand and implement, its ''O(n<sup>2</sup>)'' complexity means it is far too inefficient for use on lists having more than a few elements. Even among simple ''O(n<sup>2</sup>)'' sorting algorithms, algorithms like ] are 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 ] 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 ], which famously calls ] "the archetypical perversely awful algorithm", also calls bubble sort "the generic '''bad''' algorithm". ], in his famous '']'', 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 discusses therein. | |||
| Bubble sort is ] equivalent in running time to ] 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 requires at least twice as many writes as insertion sort, twice as many cache misses, and asymptotically more ]. Experiments by Astrachan sorting strings in Java show bubble sort to be roughly 5 times slower than insertion sort and 40% slower than ]. | |||
| == Variations == | |||
| *'''Odd-even sort''' is a parallel version of bubble sort, for message passing systems. | |||
| == References == | |||
| * ]. ''The Art of Computer Programming'', Volume 3: ''Sorting and Searching'', Third Edition. Addison-Wesley, 1997. ISBN 0-201-89685-0. Pages 106–110 of section 5.2.2: Sorting by Exchanging. | |||
| * ], ], ], and ]. '']'', Second Edition. MIT Press and McGraw-Hill, 2001. ISBN 0262032937. Problem 2-2, pg.38. | |||
| * | |||
| == External links== | |||
| {{wikibookschapter | |||
| | book = Algorithm implementation | |||
| | chapter = Sorting/Bubble_sort | |||
| | name = Bubble sort | |||
| }} | |||
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Revision as of 04:35, 18 August 2006
Gareth is awesome Bubbles are awesome Bubble sort isn't.