Fibonacci Function Question

Question

I was calculating the Fibonacci sequence, and stumbled across this code, which I saw a lot:

    int Fibonacci (int x)
{
    if (x<=1) {
        return 1;
         


        

Answer 1

return Fibonacci (x-1)+Fibonacci (x-2);

This is terribly inefficient. I suggest the following linear alternative:

unsigned fibonacci(unsigned n, unsigned a, unsigned b, unsigned c)
{
    return (n == 2) ? c : fibonacci(n - 1, b, c, b + c);
}

unsigned fibonacci(unsigned n)
{
    return (n < 2) ? n : fibonacci(n, 0, 1, 1);
}

The fibonacci sequence can be expressed more succinctly in functional languages.

fibonacci = 0 : 1 : zipWith (+) fibonacci (tail fibonacci)

> take 12 fibonacci
[0,1,1,2,3,5,8,13,21,34,55,89]