How do you traverse a matrix in spiral order?

Q: How do you traverse a matrix in spiral order?

**Target Audience:** Beginners preparing for coding interviews — you only need Python lists of lists, `range` and `while` loops. **Difficulty:** Medium **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 Think of mowing a rectangular lawn the way many people do: start at one corner, drive along the edge, turn right at each corner, and keep going round and round, each lap a little further inside, until you reach the middle. You never cross a strip you have already cut, and you never miss one. Reading a matrix in spiral order is that lawn mower. Start at the top-left, go right along the top row, down the right column, left along the bottom row, up the left column, and then repeat one ring fur

The problem

Question presented to candidate: "Given an m by n matrix as a Python list of lists, return all of its elements in spiral order: start at the top-left, go right along the top, down the right side, left along the bottom, up the left side, and keep going inward."

What a strong answer should cover:

Four boundaries (top, bottom, left, right) that shrink after each side is walked; loop while top <= bottom and left <= right.
The two guards before the bottom row and the left column, which stop a single remaining row or column from being read twice.
O(m·n) time, O(1) extra space besides the output list.
The direction-vector alternative (turn right when blocked) and its O(m·n) visited grid.
Python specifics: check not matrix or not matrix[0] before reading matrix[0], range(right, left - 1, -1) for walking backwards, negative indices silently read from the end instead of raising, and the matrix.pop(0) + zip one-liner destroys the input.

Clarifying questions expected:

"Can the matrix be non-square or empty?"
"May I modify the input?"

Code / implementation expected: Yes — a Python spiral_order(matrix) using four boundaries.

matrix
simulation

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 of lists, range and while loops. Difficulty: Medium 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

Think of mowing a rectangular lawn the way many people do: start at one corner, drive along the edge, turn right at each corner, and keep going round and round, each lap a little further inside, until you reach the middle. You never cross a strip you have already cut, and you never miss one.

Reading a matrix in spiral order is that lawn mower. Start at the top-left, go right along the top row

The solution is hidden so you can try first

6 min read · 10 sections

Python code

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

PythonBoundary method on square, wide, tall, single-row, single-column and empty matrices

Practice

PythonDirection-vector simulation checked on all 36 shapes, plus generating a spiral matrix