What is the time and space complexity of Add Two Numbers?

Time complexity: O(max(n, m)). Space complexity: O(max(n, m)).

Add Two Numbers

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Concept

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Solution Guide: Add Two Numbers

Approach

Use a dummy node to build the result list. Traverse both input lists simultaneously, summing corresponding digits plus any carry from the previous column. Create a new node for each digit and propagate the carry until both lists and the carry are exhausted.

Complexity Analysis

Time: O(max(n, m))
Space: O(max(n, m))

Pattern

Linked List (Dummy Node + Carry)

Why It Works

Since digits are stored in reverse order, the head of each list is the ones place, which is exactly where addition starts. Processing left to right mirrors grade-school addition from least significant to most significant digit.

Updated Feb 2026