Recursion question

[ho lee]

public class E09_Fibonacci {
static int fib(int n) {
if (n <= 2)
return 1;
return fib(n-1) + fib(n-2);
}
public static void main(String[] args) {
// Get the max value from the command line:
int n = Integer.parseInt(args[0]);
if(n < 0) {
System.out.println("Cannot use negative numbers");
return;
}
for(int i = 1; i <= n; i++)
System.out.print(fib(i) + ", ");
}
}

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]

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.

Now to your question……

Get a pad of paper and a pencil.

Now looking only on fib not the code in main.

Start with this….

Call Return Notes
---- -------- -----------------------
fib(1) 1 from the terminal case
fib(2) 1 from the terminal case
fib(3) fib(3-1) + fib(3-2) nominal case
which is
fib(3) fib(2) + fib(3) nominal case
which from above is
fib(3) 1 + 1 again nominal case
fib(3) 2

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]

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.