# 48. 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]
]
```

## Thought

把第i行的移到第N-i列，也就是m\[i]\[j] -> m\[j]\[N-1-i]。因此可以先转置m\[i]\[j]->m\[j]\[i]再对折m\[j]\[i]->m\[j]\[N-1-i]。

```
/*
 * @lc app=leetcode id=48 lang=cpp
 *
 * [48] Rotate Image
 */
class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        const int N = matrix.size();
        vector<int> tmp(N);
        // Transport
        for (int i = 0; i < N; ++i) {
            for (int j = 0; j < i; ++j) {
                int tmp = matrix[i][j];
                matrix[i][j] = matrix[j][i];
                matrix[j][i] = tmp;
            }
        }
        // Horizontally flip
        for (int i = 0; i < N; ++i) {
            for (int j = 0; j < N / 2; ++j) {
                int tmp = matrix[i][j];
                matrix[i][j] = matrix[i][N - 1 - j];
                matrix[i][N - 1 - j] = tmp;
            }
        } 
    }
};


```


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