How do you add two numbers stored as linked lists?

Q: How do you add two numbers stored as linked lists?

**Target Audience:** Beginners preparing for coding interviews — you should know what a linked list node is; everything else is explained **Difficulty:** Medium **Language:** Python 3 > **How to read this doc:** Every idea is explained in plain language first, then tagged with `📌 Interview term:` so you also learn the exact word an interviewer expects. All code is Python, and every output block in the **Verified** section was copied from a real run of the examples on this page. ## 1. Why This Even Matters — A Story First Remember adding numbers on paper in primary school? You line the numbers up on the right, add the ones column, write down the last digit and **carry** the 1 into the next column, then move left. You never needed to know how big the numbers were; you just worked column by column until both numbers and the carry ran out. Now imagine the digits come to you on a conveyor belt, one at a time, **ones digit first**. 342 arrives as 2, then 4, then 3. Another belt brings 4

The problem

Question presented to candidate: "Two non-negative integers are stored as linked lists, one digit per node, ones digit first: 342 is 2 → 4 → 3. Return their sum as a linked list in the same format. Please write it in Python."

What a strong answer should cover:

Column addition: walk both lists together, total = carry + x + y, append total % 10, carry total // 10.
Loop while either list or the carry remains, treating a missing digit as 0; a dummy head avoids a special case for the first node.
O(max(m, n)) time, output of at most max(m, n) + 1 nodes.
The forward-order follow-up: stacks (or reversing) plus prepending.
Python specifics: divmod(total, 10); Python ints never overflow, so "convert, add, convert back" does work for moderate sizes, but int(str) refuses inputs over 4300 digits by default and the interviewer is testing list handling anyway.

Clarifying questions expected:

"Ones digit first? Can the lists have different lengths?"
"May I modify the inputs, and how long can the numbers be?"

Code / implementation expected: Yes — add_two_numbers(l1, l2) in Python, building a new list.

linked-list
math

Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

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A short nudge toward the approach. It will not give the answer away.

Solution

Target Audience: Beginners preparing for coding interviews — you should know what a linked list node is; everything else is explained Difficulty: Medium Language: Python 3

How to read this doc: Every idea is explained in plain language first, then tagged with 📌 Interview term: so you also learn the exact word an interviewer expects. All code is Python, and every output block in the Verified section was copied from a real run of the examples on this page.

1. Why This Even Matters — A Story First

Remember adding numbers on paper in primary school? You line the numbers up on the right, add the ones column, write down the last digit and carry the 1 into the next column, then move left. You never needed to know how big the numbers were; you just worked column by column until both numbers and the carry ran out.

Now imagine the digits come to you on a conveyo

The solution is hidden so you can try first

11 min read · 10 sections

Python code

Edit the code and run it here. Each printed line with an expected value becomes a test.

PythonDigit-by-digit addition with a carry (ones digit first)

Practice

PythonForward-order digits with stacks, including 30-digit numbers

Practice

Discussion

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