leetcode Rotate Image

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本文介绍了一种高效的算法，用于将一个 n x n 的二维矩阵顺时针旋转90度，并且要求直接修改输入矩阵而非使用额外的空间。通过详细的示例展示了如何实现这一操作，适用于图像处理等领域。

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]
]

When you can't distinguish the indexes, draw a figure like that:

So the code is lkie:

class Solution {
 public:
  void rotate(vector<vector<int> > &matrix) {
    // IMPORTANT: Please reset any member data you declared, as
    // the same Solution instance will be reused for each test case.
    int i, j, n = matrix.size();
    for (i = 0; i < n; ++i) {
      for (j = i; j < n - i -1; ++j) {
        int t = matrix[i][j];
        matrix[i][j] = matrix[n - 1 - j][i];
        matrix[n - 1 - j][i] = matrix[n - 1 - i][n - 1 - j];
        matrix[n - 1 - i][n - 1 - j] = matrix[j][n - 1 - i];
        matrix[j][n - 1 - i] = t;
      }
    }
  }
};