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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. [1] The algorithm produces an unbiased ...
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 ...
Caesar cipher. The action of a Caesar cipher is to replace each plaintext letter with a different one a fixed number of places down the alphabet. The cipher illustrated here uses a left shift of 3, so that (for example) each occurrence of E in the plaintext becomes B in the ciphertext. In cryptography, a Caesar cipher, also known as Caesar's ...
A small, modern tabletop shuffling machine, used on a deck of Set cards. A shuffling machine is a machine for randomly shuffling packs of playing cards.. Because standard shuffling techniques are seen as weak, and in order to avoid "inside jobs" where employees collaborate with gamblers by performing inadequate shuffles, many casinos employ automatic shuffling machines to shuffle the cards ...
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Letter frequency is the number of times letters of the alphabet appear on average in written language. Letter frequency analysis dates back to the Arab mathematician Al-Kindi ( c. 801 –873 AD), who formally developed the method to break ciphers. Letter frequency analysis gained importance in Europe with the development of movable type in 1450 ...
Random number generation is a process by which, often by means of a random number generator ( RNG ), a sequence of numbers or symbols that cannot be reasonably predicted better than by random chance is generated. This means that the particular outcome sequence will contain some patterns detectable in hindsight but impossible to foresee.
The shuffle algebra on a finite set is the graded dual of the universal enveloping algebra of the free Lie algebra on the set. Over the rational numbers, the shuffle algebra is isomorphic to the polynomial algebra in the Lyndon words . The shuffle product occurs in generic settings in non-commutative algebras; this is because it is able to ...