Rotate the image

Given an  n  ×  n  2D matrix representing an image.

Rotate the image 90 degrees clockwise. An example is as follows:

Given matrix =
[
  [ 5, 1, 9,11],
  [ 2, 4, 8,10],
  [13, 3, 6, 7],
  [15,14,12,16]
],

Rotate the input matrix in place so that it becomes:
[
  [15,13, 2, 5],
  [14, 3, 4, 1],
  [12, 6, 8, 9],
  [16, 7,10,11]
]

 

For the element matrix[i][j] in the matrix, after rotating it by 90 degrees, the corresponding position is matrix[j][Mi], and M is n-1

For example, the value of matrix[0][0] is 5, and the value of matrix[0][3-0] after rotation is 5

   The value of matrix[1][0] is 2, and the value of matrix[0][3-1] after rotation is 2

 

Implementation:

Rotate the outermost circle of the matrix first, then gradually rotate the inner circle.

as matrix

5	1	9	11
2	4	8	10
13	3	6	7
15	14	12	16

Rotate the outermost circle first, then the inner circle.

The outermost circle only needs to rotate 5, 1, and 9, and the innermost circle only needs to rotate 4.

5->11 11->16 16->15 15->5, rotate 1, 9 in the same way

 

for an nxn matrix

The first circle needs to rotate n-1 elements, matrix[0][0] - matrix[0][n-2]

The second circle needs to rotate n-3 elements, matrix[1][1] - matrix[1][n-3]

3rd lap n-5

。。。

As shown below:

 

 code show as below:

    public static void rotate(int[][] matrix) {

        int M = matrix.length - 1 ;
         // Number of elements to be rotated in each row 
        int len ​​= M;
         int temp;
         int i=0, j=0 ;
         while (len > 0 ) {

            for (j=i; j<i+len; j++ ) {
                 // rotate four elements 
                temp = matrix[j][M- i];
                matrix[j][M-i] = matrix[i][j];
                matrix[i][j] = matrix[M-j][i];
                matrix[M-j][i] = matrix[M-i][M-j];
                matrix[M-i][M-j] = temp;
            }
            i++;
            len - = 2 ;
        }
    }