LEETCODE算法:48.Rotate Image

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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 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]]

题解

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//先水平翻转，在主对角线翻转
class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        int n=matrix.size();
        for(int i=0;i<matrix.size()/2;i++)
        {
            for(int j=0;j<matrix.size();j++)
            {
                swap(matrix[i][j],matrix[matrix.size()-i-1][j]);
            }
        }
        for(int i=0;i<n;i++)
        {
            for(int j=0;j<i;j++)
            {
                swap(matrix[i][j],matrix[j][i]);
            }
        }
    }
};

说明

水平轴翻转

\(matrix[row][col]\longrightarrow matrix[n-row-1][col]\)

主对角线翻转

\(matrix[n-row-1][col]\longrightarrow matrix[col][n-row-1]\)

本题不管何种方式，要找到规律，即matrix[row][col]经过旋转后的位置为matrix[col][n-row-1].

无视题目原地旋转的要求的话，可以新建矩阵，完整遍历。

或者以四分之一元素为起点旋转遍历全部元素。