Apple·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

May 2026

Summary

Apple ML Engineer interview with a classic matrix problem. Nothing flashy, but the in-place constraint is where they actually want to see if you know what you're doing.

Questions Asked (1)

Given an n x n integer matrix, rotate it 90 degrees clockwise in place without allocating a second matrix. Walk through your approach and discuss time and space complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I started with the naive transpose-into-a-new-matrix approach just to get something on the board, and they let me finish before asking about the space.

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AI HintsAI Generated

Suggested Approach

Explain the two-step in-place rotation: first transpose the matrix by swapping elements across the main diagonal, then reverse each row to achieve a 90-degree clockwise rotation. Emphasize that this uses O(1) extra space and O(n^2) time, which is optimal since every element must be moved.

Pro tip: Mention that the same technique can be adapted for counter-clockwise rotation (transpose then reverse columns) and that in-place operations are crucial for memory-constrained ML deployments on edge devices.

1. Clarify the problem and constraints

Restate the problem to ensure understanding: rotate an n x n matrix 90 degrees clockwise in place, without allocating a second matrix. Confirm that the matrix is square and that in-place means O(1) extra space.

2. Describe the two-step approach

Explain that the rotation can be decomposed into two operations: (1) transpose the matrix (swap matrix[i][j] with matrix[j][i] for i < j), and (2) reverse each row. This yields the 90-degree clockwise rotation.

3. Walk through the algorithm with an example

Use a small matrix (e.g., 3x3) to illustrate the steps. Show the matrix before and after transpose, and then after row reversal, to demonstrate the transformation.

4. Analyze time and space complexity

State that the algorithm performs O(n^2) operations (each element is visited a constant number of times) and uses O(1) extra space, which is optimal for this problem.

5. Discuss edge cases and potential pitfalls

Mention handling of 1x1 matrices, empty matrices (if allowed), and ensure that the in-place swaps are done correctly without overwriting values. Also note that the order of operations (transpose then reverse rows) is crucial for clockwise rotation.

Key Points to Mention

In-place rotation avoids extra memory, which is important for large matrices in memory-constrained environments.
The transpose step swaps elements across the main diagonal, and the row reversal step flips the matrix horizontally.
Time complexity is O(n^2) because each element is accessed a constant number of times.
Space complexity is O(1) as only a temporary variable is used for swapping.
The approach can be easily adapted for counter-clockwise rotation by transposing and then reversing columns instead of rows.
Ensure that the matrix is square; for non-square matrices, in-place rotation is not possible without additional space.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.