Sum of Two Integers

You should aim for a solution with O(1) time and O(1) space.

A brute force approach would use the addition operator. Can you think of a way to perform addition without using it? Maybe you should consider solving this using bit manipulation.

We can use the bitwise XOR operator to perform addition. If both a and b have 1 at the same bit position, the sum at that position is 0, and a carry of 1 is generated. If the bits are different, the sum at that position is 1. Additionally, we account for the carry from the previous step in the next iteration.

We iterate bit by bit from 0 to 31 since the given integers are 32-bit. We track the carry, initially set to 0, and initialize the result as res. During iteration, the XOR of the bits at the i-th position of both integers and the carry determines the current bit of res. How can you handle negative numbers?

To handle negative numbers, if the final result exceeds the maximum positive 32-bit integer, it means the number should be negative. We adjust it using bitwise operations: flipping the bits with res ^ ((2 ^ 32) - 1) and applying ~ to restore the correct two’s complement representation. This ensures the result correctly represents signed 32-bit integers.