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Microsoft·Machine Learning Engineer·Technical Phone Screen·Senior

Senior
Apr 2026

Summary

Microsoft ML Engineer interview with two coding problems back to back. The k-means one was meaty and the subarray problem was more of a CS puzzle. No behavioral, just code.

Questions Asked (2)

Q1

Implement K-Means clustering from scratch given a list of points, a number of clusters k, a max iteration count, and a tolerance threshold. Use the first k points as initial centroids, handle empty clusters by keeping the centroid unchanged, and return both final centroids and cluster assignments.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

This one took most of the session.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints and edge cases, then outline the K-Means algorithm step-by-step, emphasizing the specific requirements: initial centroids from first k points, empty cluster handling, and convergence criteria. Finally, discuss implementation details, complexity, and potential improvements.

Pro tip: Mention that while the problem specifies using the first k points as initial centroids, in practice, K-Means++ initialization is preferred to avoid poor convergence; this shows awareness of real-world trade-offs.

1. Clarify requirements and edge cases

Confirm input format (list of points, k, max iterations, tolerance), output format (centroids and assignments), and how to handle edge cases like empty clusters and convergence.

2. Outline algorithm steps

Describe initialization (first k points as centroids), assignment step (assign each point to nearest centroid), update step (recompute centroids as mean of assigned points), and handle empty clusters by keeping centroid unchanged.

3. Define convergence criteria

Explain that the algorithm stops when either the maximum number of iterations is reached or the centroids shift less than the tolerance threshold (e.g., using Euclidean distance).

4. Discuss implementation details

Cover data structures (e.g., arrays for points and centroids), distance metric (Euclidean), and how to efficiently compute assignments and updates.

5. Analyze complexity and trade-offs

State time complexity O(n*k*d*iterations) and space complexity O(n*d + k*d), and mention limitations like sensitivity to initialization and empty clusters.

Key Points to Mention

  • Initialization: using first k points as centroids, but note K-Means++ as a better alternative.
  • Assignment step: compute Euclidean distance from each point to each centroid and assign to nearest.
  • Update step: recompute centroids as mean of points in each cluster; if a cluster is empty, keep its centroid unchanged.
  • Convergence: stop when max iterations reached or centroid movement is below tolerance threshold.
  • Complexity: O(n*k*d) per iteration, where n is number of points, k clusters, d dimensions.
  • Edge cases: empty clusters, duplicate points, k > n, and convergence with tolerance.

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

Q2

Given an integer array and a positive integer k, determine whether any contiguous subarray of length at least 2 has a sum divisible by k. Solve it in O(n) time.

Algorithms & Data Structures
Author's notes

Prefix sum mod k is the key insight.

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AI HintsAI Generated

Suggested Approach

Use prefix sums modulo k and a hash map to track the earliest index where each remainder occurs. If the same remainder appears at two indices with distance at least 2, then the subarray between them has sum divisible by k. This yields an O(n) solution.

Pro tip: Mention that the subarray length must be at least 2, so you need to check that the index difference is >= 2. Also, initialize the hash map with remainder 0 at index -1 to handle subarrays starting from the beginning.

1. Understand the problem

Clarify that we need to find any contiguous subarray of length >= 2 whose sum is divisible by k. The subarray can be anywhere in the array.

2. Use prefix sums modulo k

Compute prefix sums modulo k as you iterate. If two prefix sums have the same remainder, the sum of the elements between them is divisible by k.

3. Track earliest index for each remainder

Store the first index where each remainder occurs in a hash map. When you see a remainder again, check if the distance between indices is at least 2.

4. Handle edge cases

Initialize the map with remainder 0 at index -1 to account for subarrays starting at index 0. Also, consider k=1 (always true if length >=2) and negative numbers (modulo operation should yield non-negative remainders).

5. Return result

If a valid subarray is found, return true; otherwise, after the loop, return false.

Key Points to Mention

  • Prefix sum modulo k: if two prefix sums have the same remainder, the subarray sum is divisible by k.
  • Hash map to store the earliest index for each remainder to maximize the chance of length >= 2.
  • Time complexity O(n) and space complexity O(min(n, k)).
  • Handle negative numbers by using (sum % k + k) % k to get non-negative remainders.
  • Edge case: subarray length must be at least 2, so check index difference >= 2.
  • Initialization: map remainder 0 to index -1 to handle subarrays starting from the beginning.

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