48. Rotate image

Subject description:

　　Given an n × n represents a two-dimensional matrix image.

　　The image is rotated 90 degrees clockwise.

　　Description:

　　You have to rotate the image in place, which means you need to directly modify the two-dimensional matrix input. Do not use another matrix to rotate an image.

　　Example 1:

　　Given = Matrix
　　　　[
　　　　　　[l, 2,3],
　　　　　　[4,5,6],
　　　　　　[7,8,9]
　　　　],

　　In situ rotation of the input matrix, so that it becomes:
　　　　[
　　　　　　[7,4,1],
　　　　　　[8,5,2],
　　　　　　[9,6,3]
　　　　]
　　Example 2:

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

　　In situ rotation of the input matrix, so that it becomes:
　　　　[
　　　　　　[15, 13, 2, 5],
　　　　　　[14, 3, 4, 1],
　　　　　　[12, 6, 8, 9],
　　　　　　[16, 7, 10 ]
　　　　]

answer:

   由于：matrix[x][y] = matrix[length-1-y][x];

             matrix[length-1-y][x] = matrix[length-1-x][length-1-y];

             matrix[length-1-x][length-1-y] = matrix[y][length-1-x];

             matrix[y][length-1-x] = matrix[x][y];

  According to the principle of space-saving, using a four rotation region, as shown:

                          

package array;
public class L48 {
    public static void rotate(int[][] matrix) {
        for(int index_x = 0;index_x <=(matrix.length-1)/2;index_x++){
            for(int index_y = index_x;index_y < matrix.length -1 - index_x;index_y++){
                int temp = matrix[index_x][index_y];
                matrix[index_x][index_y] = matrix[matrix.length-1-index_y][index_x];
                matrix[matrix.length-1-index_y][index_x] = matrix[matrix.length-1-index_x][matrix.length-1-index_y];
                matrix[matrix.length-1-index_x][matrix.length-1-index_y] = matrix[index_y][matrix.length-1-index_x];
                matrix[index_y][matrix.length-1-index_x] = temp;
            }
        }
    }
    public static void main(String[] args) {
        int[][] matrix = {{1,2,3},{4,5,6},{7,8,9}};
        rotate(matrix);
        for(int index = 0;index<matrix.length;index++){
            for(int de = 0;de <matrix.length;de++){
                System.out.println(matrix[index][de]);
            }
        }
    }
}