Recursion

Recursion is a powerful programming technique where a function solves a problem by calling itself. It provides an elegant and often intuitive way to solve problems that can be broken down into smaller, self-similar instances of the same problem. Many complex algorithms, particularly in data structures like trees and graphs, are most easily expressed recursively. A recursive function must have two essential components to work correctly. First, it needs a **base case**: a condition under which the function stops calling itself and returns a value directly. The base case is crucial for preventing infinite recursion, which would lead to a stack overflow error as the program runs out of memory. Second, it needs a **recursive step**: a part of the function where it calls itself, but with a modified argument that moves it closer to the base case. The classic example of recursion is calculating the factorial of a number. The factorial of a non-negative integer `n`, denoted as `n!`, is the product of all positive integers up to `n`. This can be defined recursively: `factorial(n)` is `n * factorial(n-1)`. The base case is `factorial(0)`, which is 1. When a recursive function is called, each new call is placed on the call stack. The function unwinds, returning values back up the stack, only after it hits the base case. While recursion can lead to very clean and readable code, it's not always the most efficient solution. Each function call adds overhead, and for some problems, an iterative solution using loops might be faster and use less memory.