## Question

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**, which means you have to modify the input 2D matrix directly. **DO NOT** allocate another 2D matrix and do the rotation.

**Example 1:**

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

## Algorithm

If you tried do it at one motion, you may not find the answer.

For matrix related questions, there are some useful movement, like image, flip(**diagonal** and **anti**-**diagonal**), __if you are solving this kind of problem, try to do such things and find a pattern.__

For this question, if you need to rotate a matrix, image first, and then flip once, then you will get the answer.

## Code

class Solution { public void rotate(int[][] matrix) { image(matrix); flip(matrix); } private void image(int[][] matrix) { int m = matrix.length; for (int i = 0; i < m; i++) { for (int j = i; j < m; j++) { if (i != j) { swap(matrix, i, j); } } } } private void flip(int[][] matrix) { int m = matrix.length - 1; for (int[] row : matrix) { int i = 0, j = m; while (i < j) { int temp = row[i]; row[i] = row[j]; row[j] = temp; i++; j--; } } } private void swap(int[][] matrix, int i, int j) { int temp = matrix[i][j]; matrix[i][j] = matrix[j][i]; matrix[j][i] = temp; } }