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 list until no elements remain. 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, and is also known as the Knuth shuffle after Donald Knuth. A variant of the Fisher–Yates shuffle, known as Sattolo's algorithm, may be used to generate random cyclic permutations of length n instead of random permutations.