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.

 

Example 1:

Input: matrix = [[1,2,3],[4,5,6],[7,8,9]]
Output: [[7,4,1],[8,5,2],[9,6,3]]

Example 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]]

Example 3:

Input: matrix = [[1]]
Output: [[1]]

Example 4:

Input: matrix = [[1,2],[3,4]]
Output: [[3,1],[4,2]]

 

Constraints:

• matrix.length == n
• matrix[i].length == n
• 1 <= n <= 20
• -1000 <= matrix[i][j] <= 1000

Ideas:

1. notice that (i, j) need to go to (j, n - i - 1)

2. use a visited as a hash to store whether it has been swapped before.   # if ask for O(1) Space, then we could add 3000 for example to each num to mark it has been visited. 

3. mark bother (i, j) and (j, n - i - 1)

4. two for loop to go through the image.

 

Code:

class Solution:
    def rotate(self, matrix: List[List[int]]) -> None:
        """
        Do not return anything, modify matrix in-place instead.
        """
        visited, n = set(), len(matrix)
        for i in range(n):
            for j in range(n):
                if (i, j) not in visited:
                    visited.add((i, j))
                    visited.add((j, n - i - 1))
                    self.swap(matrix, i, j, j, n - i - 1)
                    
    
    
    def swap(self, matrix, sr, sc, er, ec):
        matrix[sr][sc], matrix[er][ec] = matrix[er][ec], matrix[sr][sc]