Which recursive functions cannot be rewritten using loops? [duplicate]

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When you use a function recursively, the compiler takes care of stack management for you, which is what makes recursion possible. Anything you can do recursively, you can do by managing a stack yourself (for indirect recursion, you just have to make sure your different functions share that stack).

So, no, there is nothing that can be done with recursion and that cannot be done with a loop and a stack.

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