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From French algorithme; from the Old French algorisme, from Medieval Latin algorismus, a transliteration of the Arabic form of the name of the Persian mathematician al-Khwārizmī (الخَوَارِزْمِيّ(al-ḵawārizmiyy, native of Khwarezm), from Persian خوارزم(xvârezm)). The spelling change (-s- > -th-) was influenced by unrelated Ancient Greek ἀριθμός (arithmós) (whence English arithmo-).


  • (Received Pronunciation) enPR: ălʹgə-rĭ-thəm, ălʹgə-rĭth-m, IPA(key): /ˈælɡəɹɪðəm/, /ˈælɡəɹɪðm̩/
  • (General American) enPR: ălʹgə-rĭ'thəm, ălʹgə-rĭth'm, IPA(key): /ˈælɡəˌɹɪðəm/, /ˈælɡəˌɹɪðm̩/
  • (file)
  • Hyphenation UK: al‧gorithm, US: al‧go‧rithm


algorithm (plural algorithms)

  1. Ordered steps that solve a mathematical problem. A precise step-by-step plan for a computational procedure that possibly begins with an input value and yields an output value in a finite number of steps.
    • 1990, Cormen, Leiserson, and Rivest, Introduction to Algorithms: page 1. Cambridge, MA, The MIT Press, 1999 (23rd printing)
      Informally, an algorithm is any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values, as output. An algorithm is thus a sequence of computational steps that transform the input into the output.
    • 2013 July 26, Leo Hickman, “How algorithms rule the world”, in The Guardian Weekly, volume 189, number 7, page 26:
      The use of algorithms in policing is one example of their increasing influence on our lives. And, as their ubiquity spreads, so too does the debate around whether we should allow ourselves to become so reliant on them – and who, if anyone, is policing their use.
    • 2018 June 25, Sam Jones, “Ex-Nato chief refused visa waiver to US because of Iran trips”, in The Guardian:
      It’s a computer – an algorithm – and if you’ve been in Iran lately, they take you out of the system.
  2. (archaic) Calculation with Arabic numerals; algorism.

Usage notesEdit

  • Though some technical definitions require that an algorithm always terminate in a finite number of steps, this distinction is not generally observed in practice.


Related termsEdit


See alsoEdit