48. Rotate Image

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每日一题 2019 - 03 - 30

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 NOTallocate another 2D matrix and do the rotation.

Example 1:

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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:

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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]
]

解答：

这道题让我们实现矩阵的顺时针旋转90°，可以根据矩阵的性质来进行题解，也即先对矩阵进行转置，随后对转置后的矩阵进行关于垂直对称轴的交换，即可求得相应的结果。

代码：

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