What is the time and space complexity of Sum of Two Integers?

Time complexity: O(1). Space complexity: O(1).

Sum of Two Integers

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Concept

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Solution Guide: Sum of Two Integers

Approach

Simulate binary addition without arithmetic operators. XOR gives the sum bits without carry, and AND shifted left gives the carry bits. Repeat until there is no carry left.

Complexity Analysis

Time: O(1)
Space: O(1)

Pattern

Bit Arithmetic

Why It Works

XOR performs addition ignoring carries, while AND identifies positions where both bits are 1 (carry). Shifting the carry left and repeating propagates all carries to completion.

Updated Feb 2026