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.
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..