Medium — Array | Matrix | Math | Simulation

The Problem

Given an n x n 2D matrix representing an image, rotate the image by 90 degrees clockwise in-place without using extra space.

Approach

The solution uses a two-step mathematical approach: first transpose the matrix by swapping elements across the main diagonal, then reverse each row to achieve the 90-degree clockwise rotation.

Time: O(n²) · Space: O(1)

Code

class Solution:
    def rotate(self, matrix: List[List[int]]) -> None:
        

        n = len(matrix)

        # Transpose the matrix
        for i in range(n):
            for j in range(i, n):
                matrix[i][j], matrix[j][i] = matrix[j][i], matrix[i][j]

        # Reverse each row
        for i in range(n):
            matrix[i].reverse()

Watch It Run

Try it yourself: Open TraceLit and step through every line.

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