Sum of Two Integers

Given two integers a and b, return the sum of the two integers without using the + and - operators.

Approach

Use bitwise operations to simulate addition. a ^ b computes sum without carry, and (a & b) << 1 computes carry. Repeat until there is no carry. Use a 32-bit mask to handle negatives.

Why It Works

Binary addition is equivalent to repeated computation of partial sums and carries. Iterating until carry is zero yields the exact sum. The mask keeps results within 32-bit two's complement, matching typical integer behavior.

Complexity

• Time: O(1) (bounded by word size)
• Space: O(1)

Reference Implementation (Python)

class Solution:
    def getSum(self, a: int, b: int) -> int:
        MASK = 0xFFFFFFFF
        MAX_INT = 0x7FFFFFFF
        while b != 0:
            a, b = (a ^ b) & MASK, ((a & b) << 1) & MASK
        return a if a <= MAX_INT else ~(a ^ MASK)