> For the complete documentation index, see [llms.txt](https://liuxue2010.gitbook.io/data-structure-and-algorithms/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://liuxue2010.gitbook.io/data-structure-and-algorithms/array-and-numbers/rotate-image.md).

# Rotate Image

You are given an\_n\_x\_n\_2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

**Note:**

You have to rotate the image[**in-place**](https://en.wikipedia.org/wiki/In-place_algorithm), which means you have to modify the input 2D matrix directly.**DO NOT**allocate another 2D matrix and do the rotation.

**Example 1:**

```
Given 
input matrix
 = 
[
  [1,2,3],
  [4,5,6],
  [7,8,9]
],

rotate the input matrix 
in-place
 such that it becomes:
[
  [7,4,1],
  [8,5,2],
  [9,6,3]
]
```

**Example 2:**

```
Given 
input matrix
 =
[
  [ 5, 1, 9,11],
  [ 2, 4, 8,10],
  [13, 3, 6, 7],
  [15,14,12,16]
], 

rotate the input matrix 
in-place
 such that it becomes:
[
  [15,13, 2, 5],
  [14, 3, 4, 1],
  [12, 6, 8, 9],
  [16, 7,10,11]
]
```

Solution1:

## 方法一

* 将原始矩阵中的元素复制到新矩阵中
* 矩阵中元素位置计算：横纵坐标分别计算
  * 原始矩阵中横坐标为新矩阵中纵坐标
  * 原始矩阵中纵坐标j为新矩阵中height-j-1坐标

## 方法二

原地坐标转换。如图所示：

![](https://upload-images.jianshu.io/upload_images/1322408-7de1f9a8a2df5797.png?imageMogr2/auto-orient/strip%7CimageView2/2/w/389/format/webp)