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This question is commonly asked for Machine Learning Engineer candidates at Apple during technical interviews.

Rotate a Matrix In Place | Apple Coding Question

Quick Overview

This question evaluates proficiency in in-place matrix and array manipulation, spatial data transformation, and reasoning about time and space complexity.

Rotate a Matrix In Place

Company: Apple

Role: Machine Learning Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Technical Screen

Given an `n x n` matrix of integers, rotate the matrix 90 degrees clockwise. Implement the function in Python. You may use a straightforward approach with loops, but the preferred solution should rotate the matrix in place without allocating another `n x n` matrix. Example: ```python Input: [ [1, 2, 3], [4, 5, 6], [7, 8, 9] ] Output: [ [7, 4, 1], [8, 5, 2], [9, 6, 3] ] ``` Discuss the time and space complexity of your approach.

Quick Answer: This question evaluates proficiency in in-place matrix and array manipulation, spatial data transformation, and reasoning about time and space complexity.

Given an n x n matrix of integers, rotate the matrix 90 degrees clockwise. Return the rotated matrix. The preferred solution modifies the matrix in place without allocating another n x n matrix, although straightforward loop-based reasoning is acceptable. For example, rotating [[1, 2, 3], [4, 5, 6], [7, 8, 9]] produces [[7, 4, 1], [8, 5, 2], [9, 6, 3]].

Constraints

0 <= n <= 200
-10^9 <= matrix[i][j] <= 10^9
The input matrix is square (has exactly n rows and n columns)

Examples

Input: ([[1, 2, 3], [4, 5, 6], [7, 8, 9]],)

Expected Output: [[7, 4, 1], [8, 5, 2], [9, 6, 3]]

Explanation: The first column becomes the first row in reverse order, producing the 90-degree clockwise rotation.

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

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

Explanation: Each layer of the 4x4 matrix shifts clockwise, yielding the rotated matrix.

Input: ([[42]],)

Expected Output: [[42]]

Explanation: A 1x1 matrix is unchanged after rotation.

Input: ([],)

Expected Output: []

Explanation: An empty matrix remains empty after rotation.

Input: ([[-1, 0], [2, 3]],)

Expected Output: [[2, -1], [3, 0]]

Explanation: After a clockwise rotation, the left column becomes the top row in reverse order.

Hints

Track where each value moves: an element at row r, column c ends up at row c, column n - 1 - r after a clockwise rotation.
Try decomposing the rotation into two simpler in-place operations instead of moving every value directly to its final position.

Last updated: May 23, 2026

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