LeetCode 48. Rotate Image（矩阵旋转相关）

LeetCode 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:

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]
]

---

矩阵旋转问题，再浏览题目时发现了这个题，觉得一直很困扰我，因为没有解决这种问题的思路，再思考了一会后，还是按照原来的硬解思路来，就是没有一个算法思路，这样是不行的，所以就干脆直接再discuss里面进行学习。

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顺时针旋转90

思路是先将矩阵的行逆转，然后以左上角为中心点，不断交换中心点所在行列的坐标。
比如，流程如下：

[               [              [              [           [
  [1,2,3],        [7,8,9],      [7,4,1],       [7,4,1],     [7,4,1],
  [4,5,6],        [4,5,6],      [8,            [8,5,2],     [8,5,2],
  [7,8,9]         [1,2,3]       [9,            [9,6,        [9,6,3],
]               ]              ]              ]           ]

代码：

void rotate(vector<vector<int>>& matrix) {
        reverse(matrix.begin(),matrix.end());
        for(int i=0;ifor(int j=i+1;j0].size();j++){
                swap(matrix[i][j],matrix[j][i]);
            }
        }
    }

---

逆时针旋转90

这次行逆转变成了列逆转，在将矩阵的列逆转了以后，继续以左上角为中心进行调换。

[               [              [              [           [
  [1,2,3],        [3,2,1],      [3,6,9],       [3,6,9],     [3,6,9],
  [4,5,6],        [6,5,4],      [2,            [2,5,8],     [2,5,8],
  [7,8,9]         [9,8,7]       [1,            [1,4,        [1,4,7],
]               ]              ]              ]           ]

代码：

void rotate(vector<vector<int>>& matrix) {
        for(int i=0;ifor(int j=0;j<(int)matrix.size()/2;j++){
            swap(matrix[i][j],matrix[i][matrix.size()-j-1]);
        }
        }
        for(int i=0;ifor(int j=i+1;j0].size();j++){
                swap(matrix[i][j],matrix[j][i]);
            }
        }
    }

---

旋转180

上下逆转，左右逆转，顺序无所谓，比如下面就是先列后行。

[               [              [            
  [1,2,3],        [3,2,1],      [9,8,7],    
  [4,5,6],        [6,5,4],      [6,5,4],            
  [7,8,9]         [9,8,7]       [3,2,1]            
]               ]              ]             

代码：

void rotate(vector<vector<int>>& matrix) {
        for(int i=0;ifor(int j=0;j<(int)matrix.size()/2;j++){
            swap(matrix[i][j],matrix[i][matrix.size()-j-1]);
        }
        }
        reverse(matrix.begin(),matrix.end());
    }