---
title: '48. Rotate Image'
description: You are given an n x n 2D matrix representing an image, rotate the image by 90 degrees (clockwise)
icon: dot
topics:
  - { name: "Array", slug: "array" }
  - { name: "Math", slug: "math" }
  - { name: "Matrix", slug: "matrix" }
video: "fMSJSS7eO1w"
issue: "https://github.com/prdlk/leetcode/issues/91"
sidebar:
  label: 'Rotate Image'
  badge: 'Medium'
---

### Example 1:
- Input: `matrix = [[1,2,3],[4,5,6],[7,8,9]]`
- Output: `[[7,4,1],[8,5,2],[9,6,3]]`

### Example 2:
- Input: `matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]`
- Output: `[[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]`

### Constraints:

- `n == matrix.length == matrix[i].length`
- `1 <= n <= 20`
- `-1000 <= matrix[i][j] <= 1000`

## Approach

```mermaid
flowchart TD
  S(["rotate(matrix)"]) --> N["n = len(matrix)"]
  N --> F{"more r in range(n)?"}
  F -- yes --> G{"more c in range(r + 1, n)?"}
  G -- yes --> T["swap matrix[r][c] and matrix[c][r] — transpose across the diagonal"]
  T --> G
  G -- no --> F
  F -- no --> H{"more r in range(n)?"}
  H -- yes --> R["matrix[r].reverse() — transpose then mirror is a clockwise turn"]
  R --> H
  H -- no --> E(["return None — rotated in place"])
```

## Solution

```py
class Solution:
    def rotate(self, matrix: List[List[int]]) -> None:
        n = len(matrix)
        for r in range(n):
            for c in range(r + 1, n):
                matrix[r][c], matrix[c][r] = matrix[c][r], matrix[r][c]

        for r in range(n):
            matrix[r].reverse()
```