it is possible to determine the maximum of two integers without using if-else or any other comparison operator. This can be done using bitwise operators and principles of arithmetic in the world of computer science.
Let’s denote the two numbers as ‘a‘ and ‘b‘.
The key idea is to get the difference between ‘b‘ and ‘a‘, and then extract the sign of this difference, which can either be 0 when ‘b >= a‘ or 1 when ‘b < a‘.
Firstly, notice that we can obtain the sign of any number ‘x‘ by performing the bitwise AND operation on ‘x‘ and the most significant bit mask, and then shifting right by 31 bits (on a 32-bit system). This gives us 1 if ‘x‘ is negative and 0 if ‘x‘ is non-negative.
Therefore, the expression for the sign of the difference ‘b - a‘ is:
diff = b - a
sign = (diff & (1 << 31)) >> 31So, now we have the sign of the difference, we can use it to return either ‘a‘ or ‘b‘ as the maximum.
We can create an expression that equals ‘a‘ when ‘sign = 0‘ and ‘b‘ when ‘sign = 1‘, which is equivalent to:
maximum = a * (sign ^ 1) + b * signHere is a python code snippet which demonstrates this:
def maxOfTwo(a, b):
diff = b - a
sign = (diff & (1 << 31)) >> 31 # get the sign of diff
maximum = a * (sign ^ 1) + b * sign
return maximumThis solution works because the bitwise XOR of any bit with 1 flips the bit, whereas XOR with 0 leaves it unchanged.
Keep in mind that this solution may not work as expected with overflow integers and corner cases should be handled properly in a production-level code.
Moreover, it’s worth noting that this solution assumes the numbers are 32 bits wide, but it can be easily generalized to work for numbers of any bit width.