题目描述

You are given an n x n 2D matrix representing an image.

Rotate the image by 90 degrees (clockwise).

样例

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]
]

算法1

$O(n^2)$

外圈旋转n/2次，内圈旋转i->n-i-1次

时间复杂度分析：

C++ 代码

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        int n=matrix.size();
        for(int i=0;i<n/2;i++)//好好理解，四个数旋转，最终旋转回来，但是
            //要注意旋转次数判定以及位置选取（重点）
            for(int j=i;j<n-1-i;j++){
                int tmp=matrix[i][j];
                matrix[i][j]=matrix[n-1-j][i];//四次循环，每次行列交换，行变为n-1-j
                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]=tmp;
            }
    }
};