What is recursion in programming?

Recursion is a programming concept where a function calls itself in order to solve a problem. This technique is often used for problems that can be broken down into smaller, more manageable sub-problems that are similar in nature to the original problem. Each time the function calls itself, it operates on a simpler version of the problem until it reaches a base case—a condition where the recursive calls stop, and a solution can be returned.

For example, the classic case of a recursive function is calculating the factorial of a number, where the factorial of n (denoted as n!) is defined in terms of the factorial of n-1. Recursion can lead to elegant solutions for tasks such as traversing data structures like trees or performing calculations that have a natural recursive structure.

The other possibilities do not accurately capture the essence of recursion. The idea of reusing a variable does not relate to the self-referential nature of functions in recursion. Sorting data typically involves algorithms that may or may not use recursion, such as quicksort or mergesort, but those are specific applications rather than the definition of recursion itself. Similarly, iterative loops are a different programming construct that involves repeating a block of code, which contrasts with the self-calling characteristic of recursion.