LeetCode#48. Rotate Image

topic:

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.

Analysis of the meaning:

The title of this problem is to rotate a matrix 90 degrees clockwise. At first glance, there is no idea, but if you analyze it carefully, you can find an algorithm with a complexity of O(n^2).

1. Transpose the matrix

2. Repeatedly swap the i-th and ni-th columns from i=1 to n/2 to get the correct result

A C++ implementation method is as follows:

#include<iostream>
#include<vector>
using namespace std;

class Solution {
public:
    void rotate(vector<vector<int> >& matrix) {
        int num = matrix[0].size();
        vector<vector<int> > res;
        for(int i = 0; i < num; i++) {
        	for(int j = 0; j < num; j++) {
        		if(i == 0) {
        			vector<int> temp;
        			temp.push_back(matrix[i][j]);
        			res.push_back(temp);
				} else {
					res[j].push_back(matrix[i][j]);
				}
			}
		}
		for(int i = 0; i < num/2; i++) {
			swapcol(i,num-i-1,res);
		}
        matrix = res;
    }
    void swapcol(int n1, int n2, vector<vector<int> > &res) {
    	int num1 = res[0].size();
		for(int i = 0; i < num1; i++) {
			swap(res[i][n1],res[i][n2]);
		}
	}
	void print(vector<vector<int> > &res) {
		int num = res[0].size();
		for(int i = 0; i < num; i++) {
			for(int j = 0; j < num; j++) {
				if(j != num-1) {
					cout<<res[i][j]<<" ";
				} else {
					cout<<res[i][j]<<endl;
				}
			}
		}
	}
};