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An algorithm is a set of instructions for solving logical and mathematical problems, or for accomplishing some other task.
A recipe is a good example of an algorithm because it says what must be done, step by step. It takes inputs (ingredients) and produces an output (the completed dish).
The words 'algorithm' and 'algorism' come from the name of a Persian mathematician called Al-Khwārizmī (Persian: خوارزمی, c. 780–850).