how does this (max) function work using while loop?

Question

I had a homework to use functions in java to get the maximum number in a set of 3 numbers and this is what I came up with:

public static int max(int b, int a ,int d) {
    int o =0;
    while (b!=0 && a!=0 && d!=0)
    {
        b++;
        a++;
        d++;
        o--;
    }
    return o;
}

The thing is if it is given 3 numbers it will work but I do not understand how it works.

Answer 1

Ok, so what it's doing is increasing all three variables b, a, and d, until any of them equals zero. It keeps a count o of the number of times it's looped (i.e. the number of iterations necessary for any variable to hit zero), except negative.

If b, a, and d are negative, then they would approach 0 relatively quickly, and o would come out negative - but that's not what's happening is it? You're putting in positive numbers, and getting out a positive result.

That's because this solution relies on integer overflow. When b, a, or d reaches the integer max value of 2147483647, it wraps back around to -2147483648, and keeps counting back up towards zero. Meanwhile, o does the same thing in the opposite direction, wrapping the other direction. The math works out such that, when b, a, or d reaches zero, then o reaches the exact value that b, a, or d started at.

(for negative numbers, the convergence happens much more quickly - but you might be in for a shock if you put both a negative and a positive number into this function. It'll tell you that the negative number is larger than the positive number!)

---

Now that you understand how it works, you also understand why this is a terrible solution to this problem. It will run for much, much longer than necessary in order to get a result (unless the input is negative, in which case it will only run for a little longer than necessary).

The more reasonable common-sense implementation would look like this:

public static int max(int b, int a ,int d) {
    if (a >= b && a >= d) {
        return a;
    } else if (b >= a && b >= d) {
        return b;
    } else {
        return d;
    }
}

which incorpoates at most four operations, no matter how large a, b, or d is.