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# 48. 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.

### Constraints

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

### Approach

### Links

* GeeksforGeeks
* [Leetcode](https://leetcode.com/problems/rotate-image/)
* [ProgramCreek](https://www.programcreek.com/2013/01/leetcode-rotate-image-java/)
* YouTube

### **Examples**

{% tabs %}
{% tab title="Example 1" %}
**Input:** matrix = \[\[1, 2, 3], \[4, 5, 6], \[7, 8, 9]]

**Output:** \[\[7, 4, 1], \[8, 5, 2], \[9, 6, 3]]

<div align="left"><img src="/files/-MKEaDkZNzkVWdWM99f3" alt=""></div>
{% endtab %}

{% tab title="Example 2" %}
**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]]

<div align="left"><img src="/files/-MKEbCLovGqMudSyc6R5" alt=""></div>
{% endtab %}

{% tab title="Example 3" %}
**Input:** matrix = \[\[1]]

**Output:** \[\[1]]
{% endtab %}

{% tab title="Example 4" %}
**Input:** matrix = \[\[1, 2], \[3, 4]]

**Output:** \[\[3, 1], \[4, 2]]
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : O(N*N)
 * Space complexity : O(1)
 */

class Solution {
    public void rotate(int[][] matrix) {
        if(matrix == null || matrix.length == 0) return;
        
        int row = matrix.length,
            col = matrix.length;
        
        // trnspose of a matrix
        for(int r = 0; r < row; r++) {
            for(int c = r+1; c < col; c++) {
                int tmp = matrix[r][c];
                matrix[r][c] = matrix[c][r];
                matrix[c][r] = tmp;
            }
        }
        
        // swap columns
        for(int c = 0; c < col/2; c++) {
            for(int r = 0; r < row; r++) {
                int tmp = matrix[r][c];
                matrix[r][c] = matrix[r][col-c-1];
                matrix[r][col-c-1] = tmp;
            }
        }
                
    }
}
```

{% endtab %}

{% tab title="Solution 2" %}

```java
/**
 * Time complexity : O(N*N)
 * Space complexity : O(1)
 */
 
class Solution {
    public void rotate(int[][] matrix) {
        if(matrix == null || matrix.length <= 1) return;
        
        int n = matrix.length;

        for(int layer = 0; layer < n/2; layer++) {
            for(int i = layer; i < n-layer-1; i++) {
                int tmp = matrix[layer][i];
                matrix[layer][i] = matrix[n-i-1][layer];
                matrix[n-i-1][layer] = matrix[n-layer-1][n-i-1];
                matrix[n-layer-1][n-i-1] = matrix[i][n-layer-1];
                matrix[i][n-layer-1] = tmp;
            }
        }     
    }
}
```

{% endtab %}
{% endtabs %}

### **Follow up**

*