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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 ...
The order-4 shuffle-exchange network, with its vertices arranged in numerical order. In graph theory, the shuffle-exchange network is an undirected cubic multigraph, whose vertices represent binary sequences of a given length and whose edges represent two operations on these sequence, circular shifts and flipping the lowest-order bit.
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Example of shuffling five letters using Durstenfeld's in-place version of the Fisher–Yates shuffle The Fisher–Yates shuffle is an algorithm for shuffling a finite sequence . The algorithm takes a list of all the elements of the sequence, and continually determines the next element in the shuffled sequence by randomly drawing an element from ...
The shuffle product of words of lengths m and n is a sum over the (m+n)! / m!n! ways of interleaving the two words, as shown in the following examples: ab ⧢ xy = abxy + axby + xaby + axyb + xayb + xyab
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The Knuth shuffle example was intended to show the "inside-out" variant where initialization of the array is combined with the shuffle, rather than a pure shuffle of an existing array (which got broken by the 2014/11/30 edit).
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