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Randomizing functions are used to turn algorithms that have good [[expected value|expected]] performance for ''random'' inputs, into algorithms that have the same performance for ''any'' input. For example, consider a [[sorting algorithm]] like [[quicksort]], which has small expected running time when the input items are presented in random order, but is very slow when they are presented in certain unfavorable orders. A randomizing function from the integers 1 to ''n'' to the integers 1 to ''n'' can be used used to rerrange the ''n'' input items in "random" order, before calling that algorithm. This modified (randomized) algorithm will have small expected running time, whatever the input order.
==Requirements==
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