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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 ...
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 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
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).
In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of items that can be obtained by a single riffle shuffle, in which a sorted deck of cards is cut into two packets and then the two packets are interleaved (e.g. by moving cards one at a time from the bottom of one or the other of the packets to the top ...
Perfect shuffle may refer to: Faro shuffle , in particular the interpretation whereby cards (or more generally, entities in sequence) are divided into two equal piles and interleaved. Any shuffling algorithm that guarantees perfect randomness (all possible orders with equal probability), such as the Fisher–Yates shuffle .
A Gilbreath shuffle is a way to shuffle a deck of cards, named after mathematician Norman Gilbreath (also known for Gilbreath's conjecture). Gilbreath's principle describes the properties of a deck that are preserved by this type of shuffle, and a Gilbreath permutation is a permutation that can be formed by a Gilbreath shuffle.
Cards lifted after a riffle shuffle, forming what is called a bridge which puts the cards back into place After a riffle shuffle, the cards cascade. A common shuffling technique is called the riffle, or dovetail shuffle or leafing the cards, in which half of the deck is held in each hand with the thumbs inward, then cards are released by the thumbs so that they fall to the table interleaved.