Question

Write a method which finds the maximum of two numbers. You should not use if-else or any other comparison operator.

EXAMPLE

Input: 5, 10

Output: 10

This is also on CC150v5 Q17.4.

Solution

We can’t use >, < or if-else statement, but we can use mathematical operator like subtract and bit operators.

Calculate (a-b) and do (a + K(a-b)) can help us (where K is either 0 or -1).

Updated on Sep 29th: according to CC150v5 Q17.4, there can be errros when (a-b) is overflows. So this is the modified version of solution:

  1. do a sign check of a and b
  2. if a and b are same sign, do it just like before
  3. if a and b are different sign, the ‘K’ value only depends on a.

I posted the modified solution below as well.

Code

first solution from v4, written by me:

public static int getMax(int a, int b) {
	int c = a - b;
	int signBit = c >> 31 & 1;
	// if (a-b) is negative, sign = 1
	// otherwise, sign = 0
	return a - signBit * c;
}

modified solution, no overflow issues. 

public static int getMax(int a, int b) {
	int sign;
	// if a,b have different sign, then go with first number
	if (sign(a) == sign(b)) {
		sign = sign(a - b);
	} else {
		sign = sign(a);
	}
	// sign is 0 if a >= b
	// sign is -1 is a < b
	return a + (a - b) * sign;
}

private static int sign(int c) {
	return c >> 31;
}