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In mathematics and computer science, an algorithm is a self-contained step-by-step set of operations to be performed. Algorithms perform calculation, data processing, and/or automated reasoning tasks. An algorithm is an effective method that can be expressed within a finite amount of space and time and in a well-defined formal language for calculating a function.Starting from an initial state and initial input (perhaps empty),the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output"and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.