How do you add one to a number represented as a digit array?

Q: How do you add one to a number represented as a digit array?

**Target Audience:** Beginners preparing for coding interviews — you only need Python lists and loops. **Difficulty:** Easy **Language:** Python 3 > **How to read this doc:** Each idea is explained in plain language first, then tagged with `📌 Interview term:` so you also learn the word an interviewer expects. Every program here was run with `python3`, and the output shown in the **Verified** section is copied from that run. ## 1. Why This Even Matters — A Story First Picture an old car odometer with rolling number wheels: `0 1 2 9`. You drive one more kilometre. The rightmost wheel rolls from 9 to 0, and as it passes 9 it nudges the wheel to its left one step, from 2 to 3. That wheel was not at 9, so nothing further happens: the odometer now reads `0 1 3 0`. Only when every wheel shows 9 does the nudge travel all the way to the left end, and a real odometer would need one more wheel. That is the whole problem. The number is stored as an array of digits, most significant first (`[1

The problem

Question presented to candidate: "A non-negative integer is stored as a Python list of its digits, most significant digit first, so [1, 2, 9] means 129. Write a function that returns the digits of the number plus one."

What a strong answer should cover:

Walk from the last digit: a digit below 9 is incremented and the function returns; a 9 becomes 0 and the carry moves left.
If every digit was 9, return [1] followed by the zeros (one digit longer).
O(n) worst case, and only one digit touched for most inputs (early exit); O(1) extra space except the all-9s case.
Python specifics: int("".join(map(str, digits))) + 1 works because Python integers have no fixed size, but it is O(n) both ways and Python 3 refuses to convert strings of more than 4300 digits by default; range(len(digits) - 1, -1, -1) walks backwards; [1] + digits builds a new list.

Clarifying questions expected:

"Most significant digit first, and no leading zeros?"
"May I modify the input list?"

Code / implementation expected: Yes — a Python plus_one(digits) with a backwards loop and the all-9s case.

arrays
math

Try it yourself

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

Stuck? Get a hint.

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

Solution

Target Audience: Beginners preparing for coding interviews — you only need Python lists and loops. Difficulty: Easy Language: Python 3

How to read this doc: Each idea is explained in plain language first, then tagged with 📌 Interview term: so you also learn the word an interviewer expects. Every program here was run with python3, and the output shown in the Verified section is copied from that run.

1. Why This Even Matters — A Story First

Picture an old car odometer with rolling number wheels: 0 1 2 9. You drive one more kilometre. The rightmost wheel rolls from 9 to 0, and as it passes 9 it nudges the wheel to its left one step, from 2 to 3. That wheel was not at 9, so nothing further happens: the odometer now reads 0 1 3 0. Only when every wheel shows 9 does the nudge travel all the way to the left end, and a real odometer would need one more wheel.

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10 min read · 11 sections

Python code

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

PythonPlus one on ordinary inputs, trailing 9s and all 9s

Practice

PythonHow many digits are touched, and numbers too big for 64-bit integers

Practice

PythonGeneralisation: add any integer k to a digit array

Practice

Discussion

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