Question

I am reading an analysis of a fibanocci number program, shown below. It is mentioned that this implementation is inefficient. Indeed, the number of recursive calls to compute Fn is F(n+1).

My question is: what does “the number of recursive calls to compute Fn is F(n+1)” mean?

int F(int i)
{ 
  if (i < 1) return 0;
  if (i == 1) return 1;
  return F(i-1) + F(i-2);
}

Answer 1

The naive implementation to compute fibonacci numbers takes F(n+1) recursive calls to compute the number F(n); i.e. to compute f(10)=55 you need 89 recursive calls, and 89 is F(11).