这个天真的递归fibonacci实现怎么没有stackoverflow？

Question

As a joke a few months ago, a coworker of mine sought out to "speed up the heat death of the universe" by calculating fibonacci numbers using this exponential algorithm:

int Fib(int n)
{
    if (n <= 1)
        return 1;
    else
        return Fib(n - 1) + Fib(n - 2);
}

How does this not cause a stackoverflow in C#? We managed to get to Fib(52) before giving up (and Fib(51) took many hours). I would think this would hammer the stack hard enough to cause a stack overflow, since the CLR by default only allocates 1M to the stack. Also, I'm pretty sure this isn't eligible for tail recursion either.

Answer 1

The recursive calls are not computed at the same time, but sequentially, meaning that Fib(n - 2) will only compute after Fib(n - 1) (or the other way around). This means that even though you create 2^n recursive calls, only n will be active at the same time. Therefore Fib(52) will only need space for 52 stackframes of Fib , which doesn't take any noticable stack space.

Answer 2

The naive Fibonacci implementation indeed generates a large number of function calls (equal to the result, in fact), but it doesn't recurse very deeply. The maximum depth of recursion is n .