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1690s, from French algorithme, refashioned (under mistaken connection with Greek arithmos "number") from Old French algorisme "the Arabic numeral system" (13c.), from Medieval Latin algorismus, a mangled transliteration of Arabic al-Khwarizmi "native of Khwarazm," surname of the mathematician whose works introduced sophisticated mathematics to the West (see algebra). The earlier form in Middle English was algorism (early 13c.), from Old French.
algorithm al·go·rithm (āl'gə-rĭð'əm)
A step-by-step protocol, as for management of health care problems.
A set of instructions for solving a problem, especially on a computer. An algorithm for finding your total grocery bill, for example, would direct you to add up the costs of individual items to find the total.