18 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]
]

本题的技巧在于先将矩阵的行进行交换，底行换顶行，再交换对称位置的元素就可以得到旋转90°的矩阵

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        
        // first row -> last column
        // ith row, (n-i)th column
        
        //compute transpose matrix!!!
        int n = matrix.size();
        
        vector<int> temp;
        
        //swap the rows 
        for(int i=0;i<n/2;i++)
        {
            temp = matrix[i];
            matrix[i]   = matrix[n-i-1];
            matrix[n-i-1] = temp; 
        }
        
        //exchange positions
        int val;
        for(int i=0; i<n;i++)
        {
            for(int j=i+1;j<n;j++)
            {
                val = matrix[i][j];
                matrix[i][j] = matrix[j][i];
                matrix[j][i] = val;
            }
            
                
        }
    }
};