Sum of Two Integers

The problem

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

Function: def getSum(a,b):

Example input (a JSON list of arguments): [1, 2]
Expected output: 3

Operands and their mathematical sum fit signed 32-bit integers.

Hints

1. XOR adds bits without carries and AND followed by a shift computes carries.
2. Check the supplied examples, empty/boundary cases and the stated answer policy before optimizing.

Worked answer

Try it yourself first. When you are ready, open the answer below.

def getSum(a,b):
    mask=0xffffffff
    while b:a,b=(a^b)&mask,((a&b)<<1)&mask
    return a if a<2**31 else ~(a^mask)

Why it works

XOR adds bits without carries and AND followed by a shift computes carries. Use a 32-bit mask because Python negative integers have unbounded sign extension; decode the final signed result.

Complexity: O(32) iterations / O(1) fixed-width state.

Time: O(32) iterations · Space: O(1) fixed-width state