algorithm - Fast Fibonacci recursion

Question

I'm trying to recall an algorithm on Fibonacci recursion. The following:

public int fibonacci(int n)  {
  if(n == 0)
    return 0;
  else if(n == 1)
    return 1;
  else
    return fibonacci(n - 1) + fibonacci(n - 2);
}

is not what I'm looking for because it's greedy. This will grow exponentially (just look at Java recursive Fibonacci sequence - the bigger the initial argument the more useless calls will be made).

There is probably something like a "cyclic argument shift", where calling previous Fibonacci value will retrieve value instead of calculating it again.

Answer 1

maybe like this:

int fib(int term, int val = 1, int prev = 0)
{
 if(term == 0) return prev;
 return fib(term - 1, val+prev, val);
}

this function is tail recursive. this means it could be optimized and executed very efficiently. In fact, it gets optimized into a simple loop..