48. Rotate Image

题目

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

第一种方法是直接根据题意，做翻转，又外到内，示意图如下：

代码如下：

class Solution {public:    void rotate(vector<vector<int>>& matrix) {        int layer = matrix.size()/2;        for(int i=0;i<layer;i++)        {            for(int j=i;j<matrix.size()-i-1;j++)            {                int temp = matrix[i][j];                matrix[i][j] = matrix[matrix.size()-j-1][i];                matrix[matrix.size()-j-1][i] = matrix[matrix.size()-i-1][matrix.size()-j-1];                matrix[matrix.size()-i-1][matrix.size()-j-1] = matrix[j][matrix.size()-i-1];                matrix[j][matrix.size()-i-1] = temp;            }        }        return ;    }};

虽然由外到内逐步翻转，思路简单，但是写起来还是很容易写错，而且时间效率比较低，所以，用另外一种方法，对矩阵做两次变换，一次是沿对角线翻转，一次是沿水平线反转，示意图如下：

代码如下：

class Solution {  public:      void rotate(vector<vector<int> > &matrix) {          int i,j,temp;          int n=matrix.size();          // 沿着副对角线反转          for (int i = 0; i < n; ++i) {              for (int j = 0; j < n - i; ++j) {                  temp = matrix[i][j];                  matrix[i][j] = matrix[n - 1 - j][n - 1 - i];                  matrix[n - 1 - j][n - 1 - i] = temp;              }          }          // 沿着水平中线反转          for (int i = 0; i < n / 2; ++i){              for (int j = 0; j < n; ++j) {                  temp = matrix[i][j];                  matrix[i][j] = matrix[n - 1 - i][j];                  matrix[n - 1 - i][j] = temp;              }          }      }  };