Understanding Java behaviour in recursive factorial

Question

I created two recursive methods to calculate factorial as follows:

private int fact1(int n) {
    if (n == 0 || n == 1)
        return 1;
    return n * fact1(--n);

}

private int fact2(int n) {
    if (n == 0 || n == 1)
        return 1;
    return fact2(--n) * n;
}

When I call fact1(4) it returns 24. When I call fact2(4) it returns 6 (EDIT: is not returning 18 but 6). I know the second method is making 3 * 2 * 1, but I don't understand why not 4 * 3 * 2 * 1.

The same happens if I change the return to

//fact3(4) returns 60.
return (n + 1) * fact3(--n); // wrong
//fact4(4) returns 24
return fact4(--n) * (n + 1); // works

Why is the method exhibiting this behavior??

The question is about the different behaviour. I know n * fact(n-1) is the better way to solve it.

Can someone help me to understand the evaluation of this expression? Thanks!

Answer 1

It all comes down to the difference between these expressions:

return n * f(--n);

return f(--n) * n;

When n = 4, these expressions are evaluated like this:

return 4 * f(3);

return f(3) * 3;

Because the moment --n is evaluated, the value of n is decreased by 1. This is how the prefix -- operator works.

It might help to recursively evaluate the entire expressions by hand. The first one:

// first
return 4 * f(3);
return 4 * 3 * f(2);
return 4 * 3 * 2 * f(1);
return 4 * 3 * 2 * 1;

// second
return f(3) * 3;
return f(2) * 2 * 3;
return f(1) * 1 * 2 * 3;
return 1 * 1 * 2 * 3;

On a related note, guess how this will be evaluated:

return f(n--) * n;

It will be:

return f(4) * 3;

Because here the postfix -- operator is used: the -1 decrement will be applied after the evaluation of n in f(...).