Leetcode算法學習日誌-48 Rotate Image

Leetcode 48 Rotate Image

題目原文

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]
]

題意分析

將一個方陣表示的圖像向順時針旋轉90度，方法中不能使用額外的方陣空間，也就是旋轉需要在原址操作。

解法分析

本題解法比較巧妙，對一個方陣，如果需要順時針旋轉90度，只需要先將所有的行反向排列，再對新的方陣做一次轉置。如果是逆時針旋轉，則是將所有行反向排列。C++代碼如下：

class Solution {
public:
    void rotate(vector<vector<int>>& matrix) {
        reverse(matrix.begin(),matrix.end());
        for(int i=0;i<matrix.size();i++){
            for(int j=i+1;j<matrix[i].size();j++)
                swap(matrix[i][j],matrix[j][i]);
        }  
    }
};

轉置操作用swap進行，注意對角線上的元素不用操作。