Question

Please explain this simple code:

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

I’m confused with the last line especially because if n = 5 for example, then fibonacci(4) + fibonacci(3) would be called and so on but I don’t understand how this algorithm calculates the value at index 5 by this method. Please explain with a lot of detail!

Answer 1

In fibonacci sequence each item is the sum of the previous two. So, you wrote a recursive algorithm.

So,

fibonacci(5) = fibonacci(4) + fibonacci(3)

fibonacci(3) = fibonacci(2) + fibonacci(1)

fibonacci(4) = fibonacci(3) + fibonacci(2)

fibonacci(2) = fibonacci(1) + fibonacci(0)

Now you already know fibonacci(1)==1 and fibonacci(0) == 0. So, you can subsequently calculate the other values.

Now,

fibonacci(2) = 1+0 = 1
fibonacci(3) = 1+1 = 2
fibonacci(4) = 2+1 = 3
fibonacci(5) = 3+2 = 5

And from fibonacci sequence 0,1,1,2,3,5,8,13,21.... we can see that for 5th element the fibonacci sequence returns 5.

See here for Recursion Tutorial.