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, which means you have to modify the input 2D matrix directly. DO NOTallocate 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]
]

here give a common method to solve the image rotation problems.

/*
 * clockwise rotate
 * first reverse up to down, then swap the symmetry 
 * 1 2 3     7 8 9     7 4 1
 * 4 5 6  => 4 5 6  => 8 5 2
 * 7 8 9     1 2 3     9 6 3
*/

　　

public void rotate(int[][] image) {
        transposeImage(image);

        // reverse each row of the image
        for(int row = 0; row < image.length; row++) {
            int i = 0;
            int j = image[row].length - 1;
            while(i < j) {
                int tmp = image[row][i];
                image[row][i++] = image[row][j];
                image[row][j--] = tmp;
            }
        }
    }

    // Turns rows into cols and vice versa
    private void transposeImage(int[][] image) {
        for(int i = 0; i < image.length; i++) {
            for(int j = i + 1; j < image[i].length; j++) {
                int tmp = image[i][j];
                image[i][j] = image[j][i];
                image[j][i] = tmp;
            }
        }
    }