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:

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]
]

思路

1. 原数组取其转置矩阵。（转置：以对角线为轴，翻转矩阵, swap(matrix[i][j], matrix[j][i])）
2. 每行的数字翻转可得到结果

Example:

1  2  3　　　 　　 1  4  7　　　　　     7  4  1

4  5  6　　-->　　 2  5  8　　 -->  　  8  5  2　　

7  8  9 　　　 　　3  6  9　　　　       9  6  3

代码

class Solution {
    public void rotate(int[][] matrix) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
            return;
        }
        
        int row = matrix.length;
        int col = matrix[0].length;
        
        for (int i = 0; i < row; i++) {
            //1. 按对角线转置矩阵
            for (int j = i + 1; j < col; j++) {
                int temp = matrix[i][j];
                matrix[i][j] = matrix[j][i];
                matrix[j][i] = temp;
            }
            //2. 每完成一行的转置，就对该行进行翻转
            int start = 0;
            int end = col - 1;
            
            while (start < end) {
                int temp = matrix[i][start];
                matrix[i][start] = matrix[i][end];
                matrix[i][end] = temp;
                start++;
                end--;
            }
        }
    }
}