Recursion

Recursion is a problem-solving technique in which a function calls itself multiple times until the full solution is computed. Every recursive function must contain a base case that halts further recursion and a recursive case that reduces the input size or complexity, ensuring eventual termination.

In both mathematics and computer science, recursive definitions allow us to express infinite (or finite) computations using a finite set of rules, which makes them powerful tools for formalizing and solving problems.

Using recursion can result in simpler and cleaner code, especially when solving problems like tree (graph) traversal, factorial computation, or sequence generation, where the recursive structure is natural and intuitive.

Unlike loops, recursion provides a direct reflection of mathematical definitions, which makes recursions easier to code. However, recursion often consumes more memory than iteration due to repeated function calls and stack usage, unless the language or compiler performs tail-call optimization. As such, programmers must be careful to ensure that the number of function calls to itself is finite to prevent infinite recursion and stack overflows.