Intuition

To rotate a matrix 90 degrees clockwise in-place, we can use two simple operations: transpose the matrix and then reflect each row horizontally.

Approach

• First, transpose the matrix (swap rows and columns).
• Then, reflect each row horizontally (swap elements from left to right).
• Both operations are performed in-place, so no extra space is needed.

Complexity

• Time complexity: \(O(n^2)\), where $n$ is the size of the matrix (each element is visited twice).

• Space complexity: \(O(1)\), since the rotation is done in-place.

Code

from typing import List

class Solution:
    def rotate(self, matrix: List[List[int]]) -> None:
        def transpose():
            for i in range(n):
                for j in range(i):
                    matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]

        def reflect():
            for i in range(n):
                for j in range(n // 2):
                    matrix[i][j], matrix[i][-j - 1] = matrix[i][-j - 1], matrix[i][j]

        n = len(matrix)
        transpose()
        reflect()

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