# 0048. Rotate Image

<https://leetcode.com/problems/rotate-image>

## Description

You are given an `n x n` 2D `matrix` representing an image, rotate the image by **90** degrees (clockwise).

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:**

![](https://assets.leetcode.com/uploads/2020/08/28/mat1.jpg)

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

**Example 2:**

![](https://assets.leetcode.com/uploads/2020/08/28/mat2.jpg)

```
**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]]
```

**Example 3:**

```
**Input:** matrix = [[1]]
**Output:** [[1]]
```

**Example 4:**

```
**Input:** matrix = [[1,2],[3,4]]
**Output:** [[3,1],[4,2]]
```

**Constraints:**

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

## ac

it's all about imagination

```java
class Solution {
    public void rotate(int[][] matrix) {
        // layer by layer, layer = (n+1) / 2 
        // 4 edges
        int mR = matrix.length;
        int mC = matrix.length;
        for (int layer = 0; layer < (mR+1)/2; layer++) {
            int len = mR - 2*layer - 1;
            for (int diff = 0; diff < len; diff++) {
                // top -> tmp
                int tmp = matrix[layer][layer+diff];
                // left -> top
                matrix[layer][layer+diff] = matrix[mR-1-layer-diff][layer];
                // buttom -> left
                matrix[mR-1-layer-diff][layer] = matrix[mR-1-layer][mC - 1 - layer - diff];
                // right -> buttom
                matrix[mR-1-layer][mC - 1 - layer - diff] = matrix[layer + diff][mC - 1 - layer];
                // tmp -> right
                matrix[layer + diff][mC - 1 - layer] = tmp;
            }
        }

    }
}
```


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