How can recursion lead to stack overflow errors?

Recursion can lead to stack overflow errors when the recursive calls are too deep, exceeding the stack size limit.

Recursion is a powerful programming concept where a function calls itself to solve a smaller instance of the same problem. However, each recursive call creates a new stack frame in the call stack, which is a limited resource. The call stack is a data structure that stores information about the active subroutines or functions in a program. Each time a function is called, a new frame is pushed onto the stack. This frame contains the function's local variables, return address, and other information necessary for the function's execution.

When a recursive function is called, it continues to push new frames onto the stack until it reaches a base case, at which point it begins to pop frames off the stack. If the recursion is too deep, meaning there are too many recursive calls before reaching the base case, the stack can become full. This is known as a stack overflow. When a stack overflow occurs, the program will typically crash or throw a stack overflow error.

The depth of recursion that leads to a stack overflow can vary depending on several factors, including the size of the stack, the amount of memory each stack frame requires, and the specific programming language or environment being used. In some cases, a recursion depth of just a few thousand calls can lead to a stack overflow.

To avoid stack overflow errors, it's important to ensure that recursive functions have a base case that can be reached within a reasonable number of recursive calls. In some cases, it may also be possible to optimise the recursion using techniques such as tail recursion or memoisation, which can reduce the amount of memory required for each recursive call. Alternatively, an iterative solution could be used instead of a recursive one, as iteration does not use the call stack and therefore does not risk causing a stack overflow.