Question

I was making my way through project Euler, and I came across a combination problem. Combination logic means working out factorials. So, I decided to create a factorial method. And then I hit upon a problem – since I could quite easily use both iteration and recursion to do this, which one should I go for? I quickly wrote 2 methods – iterative:

public static long factorial(int num) {
        long result = 1;
        if(num == 0) {
            return 1;
        }
        else {
            for(int i = 2; i <= num; i++) {
                result *= i;
            }
            return result;
        }

and recursive:

public static long factorial(int num) {
        if(num == 0) {
            return 1;
        }
        else {
            return num * factorial(num - 1);
        }
    }

If I am (obviously) talking about speed and functionality here, which one should I use? And, in general, is one of the techniques generally better than the other (so if I come across this choice later, what should I go for)?

Answer 1

Both are hopelessly naive. No serious application of factorial would use either one. I think both are inefficient for large n, and neither int nor long will suffice when the argument is large.

A better way would be to use a good gamma function implementation and memoization.

Here’s an implementation from Robert Sedgewick.

Large values will require logarithms.