Problem Narrative

You’re on an AR (augmented reality) team at a large e-commerce marketplace with 20M+ daily active users. Product pages render interactive 3D previews, and a performance regression has been traced to a hot path that rotates square “texture tiles” represented as integer matrices. Allocating a second matrix for every rotation spikes memory and causes frame drops on mid-range devices.

Your task is to rotate these tiles in-place.

Formal Problem Statement

Given an n × n matrix matrix of integers, rotate it 90 degrees clockwise in-place.

• Input: matrix: list[list[int]] where matrix[i][j] is the value at row i, column j.
• Output: Do not return anything. Modify matrix directly.

A 90° clockwise rotation means the element at position (r, c) moves to (c, n - 1 - r).

Examples

Example 1

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

After rotation (in-place): [[7,4,1],[8,5,2],[9,6,3]]

Explanation (key moves):

• 1 at (0,0) moves to (0,2)
• 7 at (2,0) moves to (0,0)
• The outer ring rotates as a cycle.

Example 2

Input: matrix = [[5,1,9,11],[2,4,8,10],[13,3,6,7],[15,14,12,16]]

After rotation (in-place): [[15,13,2,5],[14,3,4,1],[12,6,8,9],[16,7,10,11]]

Requirements

1. Must run in O(n²) time.
2. Must use O(1) extra space (in-place).
3. Assume the matrix is always square (n × n).

Notes / Clarifications

• n = 1 should leave the matrix unchanged.
• Negative values and duplicates are allowed.
• “In-place” means you may use a few temporary variables, but not allocate another n × n matrix.