LeetCode 48. Rotate Image

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 NOT allocate another 2D matrix and do the rotation.

Example 1:

Giveninput matrix =

[

[1,2,3],

[4,5,6],

[7,8,9]

],

rotate the input matrixin-place such that it becomes:

[

[7,4,1],

[8,5,2],

[9,6,3]

]

Example 2:

Giveninput matrix =

[

[ 5, 1, 9,11],

[ 2, 4, 8,10],

[13, 3, 6, 7],

[15,14,12,16]

],

rotate the input matrixin-place such that it becomes:

[

[15,13, 2, 5],

[14, 3, 4, 1],

[12, 6, 8, 9],

[16, 7,10,11]

]

思路分析：

顺时针旋转：

1.以矩阵对角线为轴，交换matrix[i][j] = matrix[j][i];

2.Then flip the matrix horizontally. (swap(matrix[i][j], matrix[i][matrix.length-1-j])

[ 5,   1,   9,  11],                 【5   2   13   15】                    【15   13   2   5】

[ 2,   4,   8,  10],                 【1   4    3    14】                    【14    3    4   1】

[13,  3,   6,    7],                 【9   8    6    12】                    【12    6    8   9】

[15, 14, 12, 16]                 【11 10  7    16】                    【16    7  10  11】

逆时针旋转：

1.flip the matrix horizontally. (swap(matrix[i][j], matrix[i][matrix.length-1-j])

2.以矩阵对角线为轴，交换matrix[i][j] = matrix[j][i];

[ 5,   1,   9,  11],                   11   9    1   5                             11   10   7   16

[ 2,   4,   8,  10],                   10   8    4   2                             9      8    6    12

[13,  3,   6,    7],                    7    6    3   13                           1      4    3    14

[15, 14,  12,16]                    16  12  14  15                          5      2   13   15

代码实现如下;

class Solution {

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

        

/* clockwise rotate

* first reverse symmetry

* 1 2 3   1 4 7

* 4 5 6   2 5 8

* 7 8 9   3 6 9

*/

        for(int i = 0; i < matrix.length; i++){

            for(int j = i + 1; j < matrix[0].length; j++){

                int temp = matrix[i][j];

                matrix[i][j] = matrix[j][i];

                matrix[j][i] = temp;

            }

        }

        

/* then reverse every row

* 1 4 7   7 4 1

* 2 5 8   8 5 2

* 3 6 9   9 6 3

*/

        for(int i = 0; i < matrix.length; i++){

            for(int j = 0; j < matrix[i].length / 2; j++){

                int temp = matrix[i][j];

                matrix[i][j] = matrix[i][matrix[i].length - 1 - j];

                matrix[i][matrix[i].length - 1 - j] = temp;

            }

        }

    }

}