Algorithm function
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This topic is essentially a furphy. A function and an algorithm are two different descriptions of the same kind of thing. It is a little like saying a spherical box.
An algorithm is roughly synonymous with a method. An algorithm / method may return some kind of value to the calling code, but is essentially a block of code used to perform a series of actions or modifications.
To contrast, a function is something which is required to return a value. It is probably true that there are some programming languages for which this is not a syntactic requirement, but that's the philosophical distinction.
This may be a disambiguation page.