How does a recursive function work in programming?

A recursive function in programming works by calling itself to solve smaller instances of the same problem.

In more detail, recursion is a method of solving problems that involves breaking a problem down into smaller and smaller subproblems until you get to a small enough problem that it can be solved trivially. Usually, recursion involves a function calling itself while doing so. It's a very powerful technique and is used in a wide range of applications, from sorting and searching algorithms to GUI programming and artificial intelligence.

The process of recursion in programming involves two main components: the base case and the recursive case. The base case is the simplest possible form of the problem you're trying to solve, which can be solved directly without any further recursion. The recursive case is where the function calls itself, usually with a smaller or simpler version of the original problem.

For example, consider a function that calculates the factorial of a number. The factorial of a number n (denoted as n!) is the product of all positive integers less than or equal to n. The base case here is that the factorial of 1 is 1. The recursive case is that the factorial of any other number n is n times the factorial of n-1. So, the function calls itself with the argument n-1.

One important thing to note about recursive functions is that they must always have a condition that leads to the function not making a further recursive call, i.e., reaching a base case. If this condition is not met, the function will keep calling itself indefinitely, leading to what is known as infinite recursion. This can cause the program to crash or run out of memory.

In conclusion, recursive functions are a powerful tool in programming, allowing complex problems to be broken down into simpler ones. However, they must be used with care to avoid issues such as infinite recursion.