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# Recursion question

ho lee
Greenhorn
Posts: 1

Hello Folks!
Can someone please break down fib method shown above. I can't understand how the magic is happening inside that recursion.

Steve Fahlbusch
Bartender
Posts: 612
7
Greetings,

Well first to help yourself out, you should really indent your code so that a) you can better understand it, and 2) to make it easier for other to help.

Get a pad of paper and a pencil.

Now looking only on fib not the code in main.

So there you go, the magic of the recursive call, i.e.: the nominal cases.

fib(4) and above are for you.

-steve

Campbell Ritchie
Marshal
Posts: 56529
172
Welcome to the Ranch
What have they told you about that recursive Fibonacci program? You realise that to work out fib(4) you call fib(2) and fib(3) and fib(3) calls fib(2), so you end up calling fib(2) twice. If you try fib(5), you call fib(3) twice and fib(2) thrice. It is a classic example of what can go wrong with recursion if you design it badly.
You can design Fibonacci programs where the number of recursive calls is proportional to the argument (so fib(12) would need 2 more calls than fib(10), but they are slightly more complicated. That is linear complexity O(n).
Kaldewaij shows a version of Fibonacci numbers where the number of calls is approximately proportional to the logarithm of n: O(logn).
What you have there runs in exponential complexity, which you can verify by adding a counter to your fib method: O(1.618ⁿ) approximately. 1.618 is the golden ratio.