How do you rotate an N×N matrix by 90 degrees in place?

Q: How do you rotate an N×N matrix by 90 degrees in place?

**Target Audience:** Beginners preparing for coding interviews — you only need Python lists of lists and nested 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 You are holding a printed photo and you turn it a quarter turn to the right. The top edge of the picture is now on the right side, the left edge is now the top, and the person who was standing upright is now lying on their side. Every point of the photo moved, but nothing was added or lost. A digital image is a grid of pixels, and turning it is exactly this question: rotate an N×N matrix by 90 degrees. The interview twist is **in place**: you may not make a second grid. Picture rearranging tiles on a

The problem

Question presented to candidate: "You are given an n by n matrix as a Python list of lists, for example an image. Rotate it 90 degrees clockwise, in place: modify the given lists rather than returning a new matrix."

What a strong answer should cover:

The mapping: cell (r, c) goes to (c, n - 1 - r); a copy-based version is easy but O(n²) extra space.
Transpose (swap m[i][j] with m[j][i] for j > i only), then reverse each row; O(n²) time, O(1) extra space.
The alternative four-way swap per layer, and the counter-clockwise variant (transpose, then reverse the row order).
Only square matrices can be rotated in place; R×C becomes C×R.
Python specifics: list(zip(*m[::-1])) is a neat one-liner but builds new tuples, row.reverse() is in place while row = row[::-1] only rebinds a name, and [[0] * n] * n creates n references to the same row.

Clarifying questions expected:

"Clockwise or counter-clockwise, and is it always square?"
"Is a new matrix acceptable, or must it be in place?"

Code / implementation expected: Yes — a Python rotate(matrix) that transposes and reverses rows in place.

matrix
in-place

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 and nested 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

You are holding a printed photo and you turn it a quarter turn to the right. The top edge of the picture is now on the right side, the left edge is now the top, and the person who was standing upright is now lying on their side. Every point of the photo moved, but nothing was added or lost.

A digital image is a grid of pixels, and turning it is exactly this question: rotate an N×N matrix by 90 degrees.

The solution is hidden so you can try first

14 min read · 11 sections

Python code

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

PythonTranspose, then reverse each row (1x1 to 4x4)

Practice

PythonFour-way layer swap vs transpose + reverse vs copying, counting writes

Practice

PythonCounter-clockwise, 180 degrees, four turns, and a non-square matrix

Practice

Discussion

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