In a computer science class I took, algorithms were defined as a finite set of instructions which will produce an answer to a question with infinite variations.
The fact that the question must have infinite variations is only relevant because, if a question has a finite set of variations, then you could memorize all the possible answers and record them in a table somewhere and avoid using an algorithm.
In casual day-to-day usage, the word seems to refer to anything not-sentient which makes a decision.
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