Caching Fixes Recursion

Solution: Caching

        @fib = (0, 1);
        sub fib {
          my ($n) = @_; 
          return $fib[$n] if defined $fib[$n];
          return $fib[$n] = fib($n-1) + fib($n-2);
        }

fib(20) computes fib(18) and fib(19)
fib(19) goes to compute fib(18)
But it is already in $fib[18]
Function is now very fast
- Almost as fast as a pure iterative version
- Unlike the iterative version, this version required no ingenuity