题目描述
题目链接:48. Rotate Image
You are given an n x n 2D
matrix
representing an image, rotate the image by 90 degrees (clockwise).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.
例子
例子 1
Input:
matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output:[[7,4,1],[8,5,2],[9,6,3]]
例子 2
Input:
matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]
Output:[[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]
例子 3
Input:
matrix = [[1]]
Output:[[1]]
Follow Up
Note
Constraints
matrix.length == n
matrix[i].length == n
1 <= n <= 20
-1000 <= matrix[i][j] <= 1000
解题思路
观察一下矩阵变换的规律,可以发现顺时针旋转可以由以下两个操作完成:
- 垂直翻转
- 沿对角线翻转
代码如下:
#include <vector>
class Solution {
public:
void rotate(std::vector<std::vector<int>>& matrix) {
int n = matrix.size();
for (int i = 0; i < n / 2; ++i) {
for (int j = 0; j < n; ++j) {
std::swap(matrix[i][j], matrix[n - 1 - i][j]);
}
}
for (int i = 0; i < n; ++i) {
for (int j = i + 1; j < n; ++j) {
std::swap(matrix[i][j], matrix[j][i]);
}
}
}
};
- 时间复杂度:
O(n)
- 空间复杂度:
O(1)
GitHub 代码同步地址: 48.RotateImage.cpp
其他题目: GitHub: Leetcode-C++-Solution 博客: Leetcode-Solutions