leetcode 48. Rotate Image

Discription

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]
]

思路

模拟题，找规律即可。要注意循环边界，避免重复。

时间复杂度：$?$
空间复杂度：$?$

代码

class Solution {
public:
    // matrix[i][j]                             -> matrix[j][n - 1 - i]
    // matrix[j][n - 1 - i]                     -> matrix[n - 1 - i][n - 1 - j]
    // matrix[n - 1 - i][n - 1 - j]             -> matrix[n - 1 - j][n - 1 - (n - 1 - i)]
    // matrix[n - 1 - j][n - 1 - (n - 1 - i))]  -> matrix[i][j]
    void rotate(vector<vector<int>>& matrix) {
        int n = matrix.size();
        for (int i = 0; i < (n + 1) / 2; i++)
        {
            for (int j = 0; j < n / 2; j++)
            {
                int temp4 = matrix[j][n - 1 - i];
                matrix[j][n - 1 - i] = matrix[i][j];

                int temp16 = matrix[n - 1 - i][n - 1 - j];
                matrix[n - 1 - i][n - 1 - j] = temp4;

                int temp13 = matrix[n - 1 - j][n - 1 - (n - 1 - i)];
                matrix[n - 1 - j][n - 1 - (n - 1 - i)] = temp16;

                matrix[i][j] = temp13;
            }
        }
    }
};