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The algorithm produces an unbiased permutation: every permutation is equally likely. The modern version of the algorithm takes time proportional to the number of items being shuffled and shuffles them in place. The Fisher–Yates shuffle is named after Ronald Fisher and Frank Yates, who first described it.
In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer. [2] The sequence of permutations of n objects generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects.
In sequences of permutations with this recursive structure, each permutation differs from the previous one either by the single-position-at-a-time motion of , or by a change of two smaller numbers inherited from the previous sequence of shorter permutations. In either case this difference is just the transposition of two adjacent elements.
In computer science, bogosort [1] [2] (also known as permutation sort and stupid sort [3]) is a sorting algorithm based on the generate and test paradigm. The function successively generates permutations of its input until it finds one that is sorted. It is not considered useful for sorting, but may be used for educational purposes, to contrast ...
A simple algorithm to generate a permutation of n items uniformly at random without retries, known as the Fisher–Yates shuffle, is to start with any permutation (for example, the identity permutation), and then go through the positions 0 through n − 2 (we use a convention where the first element has index 0, and the last element has index n − 1), and for each position i swap the element ...
In the reverse direction, a stack-sortable permutation may be decoded into a tree in which the first value x of the permutation corresponds to the root of the tree, the next x − 1 values are decoded recursively to give the left child of the root, and the remaining values are again decoded recursively to give the right child. [1]
Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, M ( n ) {\displaystyle M(n)} below stands in for the complexity of the chosen multiplication algorithm.
In combinatorial mathematics and theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation.Any permutation may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the sequence 123...; for instance the sequence 213 represents the permutation on three elements that swaps elements 1 and 2.