Recursive Fibonacci

A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begins a new pair which from the second month on becomes productive?

Fibonacci numbers in nature

The arrangement of leaves or twigs on a stem (phyllotaxis, from the Greek word phyhllon meaning leaf and taxis meaning arrangement) correspond to Fibonacci numbers. Select one leaf as a starting point and count up the leaves on the stem until you reach a leaf directly above your starting point. The number of leaves is usually a Fibonacci number. In the above figure, starting from the bottom leaf, we count up 5 leaves to find the next one directly above the bottom leaf. Also, you can count the number of turns around the stem, as you go from a leaf to one directly above it. This too is usually a Fibonacci number. For a pussy willow, typical numbers are 13 for the number of "leaves" and 5 times around.

Recursive definition

   fib(n) = undefined for n<0
   fib(0)=fib(1)=1
   fib(n)=fib(n-1)+fib(n-2) for n>1

Recursive function

     int Fib(int n) {
       if (n < 2)
       {
           return(1);
       }
       else
       {
           return(Fib(n - 1) + Fib(n - 2));
       }
     }

Iterative function

int Fib(int n)
{
  int i, f1=1, f2=1, temp;

  if (n < 2)
  {
    return(1); 
  }
  else
  {
    for(i = 2; i < n; i++)
    {
      temp = f1;
      f1 = f2;
      f2 = temp + f2;
    }
    return (f1 + f2);
  }