# Rotate Image

`Array`

**Medium**

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]
]
```

## Analysis & Solution

### Approach 1

* Reverse Each Row
* Flip Diagonally

```java
class Solution {
    public void rotate(int[][] matrix) {
        // reverse
        reverse(matrix);

        // flip
        flip(matrix);
    }
    public void swap(int[] num, int i, int j) {
        int tmp = num[i];
        num[i] = num[j];
        num[j] = tmp;
    }

    public void reverse(int[][] matrix) {
        int n = matrix.length;
        // reverse each row
        for (int[] row: matrix) {
            int i = 0, j = n - 1;
            while (i < j) {
                swap(row, i, j);
                i++;
                j--;
            }
        }
    }

    // flip by diagonal
    public void flip(int[][] matrix) {
        int n = matrix.length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n - 1 - i; j++) {
                int tmp = matrix[i][j];
                matrix[i][j] = matrix[n - 1 - j][n - 1 - i];
                matrix[n - 1 - j][n - 1 - i] = tmp;
            }
        }
    }
}
```

## Reference

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