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Given a square n x n matrix of integers matrix, rotate it by 90 degrees clockwise.

You must rotate the matrix in-place. Do not allocate another 2D matrix and do the rotation.

Approach

Rotate the matrix in-place by first transposing it, then reversing each row. Transpose swaps matrix[i][j] with matrix[j][i], and reversing rows completes the 90-degree clockwise rotation.

Why It Works

A 90-degree clockwise rotation maps (i, j) to (j, n - 1 - i). Transposing swaps indices, and reversing each row applies the column reversal, producing exactly this mapping for every cell.

Complexity

• Time: O(n^2)
• Space: O(1)

Reference Implementation (Python)

class Solution:
    def rotate(self, matrix: List[List[int]]) -> None:
        n = len(matrix)
        for i in range(n):
            for j in range(i + 1, n):
                matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]
        for row in matrix:
            row.reverse()