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Google·Machine Learning Engineer·Technical Phone Screen·Senior

Senior
Apr 2026

Summary

Google ML Engineer interview with a graph traversal problem that had a decent follow-up about scaling. The core question was straightforward if you've done BFS/DFS before, but the optimization discussion is where it got interesting.

Questions Asked (2)

Q1

You have a set of unordered coordinate points, a start point, an end point, and a function getDistance(x, y). Two points are directly connected if their distance is less than r. Can the start point reach the end point through a chain of such hops?

Algorithms & Data Structures
Author's notes

Pretty much a connectivity problem once you see it.

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AI HintsAI Generated

Suggested Approach

Model the points as nodes in a graph where edges exist between points within distance r, then use BFS or DFS to check connectivity from start to end. Alternatively, use Union-Find to dynamically connect points and check if start and end are in the same component. Discuss time and space complexity, and consider optimizations like spatial indexing for large datasets.

Pro tip: Mention that while BFS/DFS is straightforward, Union-Find can be more efficient if connectivity queries are repeated or if points are added incrementally. Also, highlight the importance of early termination when the end point is reached.

1. Clarify the problem

Confirm assumptions: points are in a 2D plane, distance is Euclidean, r is a given threshold, and connectivity is transitive. Ask if the graph is static or dynamic, and if multiple queries are expected.

2. Choose the right algorithm

For a single query, BFS/DFS from start is simple and efficient. For multiple queries or incremental additions, Union-Find is preferable. Consider the trade-offs.

3. Optimize edge construction

Naively checking all pairs is O(n^2). For large n, use spatial indexing (e.g., k-d tree, grid) to find neighbors within distance r efficiently, reducing time complexity.

4. Analyze complexity and edge cases

Discuss time and space complexity of your approach. Handle edge cases: start equals end, no points, r <= 0, disconnected components, and floating-point precision issues.

5. Test and validate

Walk through a small example to verify logic. Consider writing pseudocode and testing with edge cases. Mention potential pitfalls like integer overflow in distance calculations.

Key Points to Mention

  • Graph modeling: points as nodes, edges if distance < r
  • BFS/DFS for single query, Union-Find for multiple queries
  • Time complexity: O(n^2) for naive edge construction, can be improved with spatial indexing
  • Space complexity: O(n + E) for adjacency list, O(n) for Union-Find
  • Edge cases: start == end, no points, r <= 0, disconnected components
  • Floating-point precision: use squared distances to avoid sqrt

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

Q2

Follow-up: the point set is now huge and computing all pairwise distances is too expensive. How do you handle this?

Algorithms & Data StructuresTechnical Trade-offsSystem Design
Author's notes

This is where the interview actually got interesting.

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AI HintsAI Generated

Suggested Approach

Acknowledge that exact all-pairs distances are infeasible for huge point sets, then pivot to approximate or exact methods that avoid O(n²) computation. Discuss algorithmic choices like spatial partitioning, approximate nearest neighbor (ANN) libraries, and distributed computing, while emphasizing trade-offs between accuracy, speed, and memory.

Pro tip: Mention that for many ML tasks (e.g., clustering, k-NN), you don't need all pairwise distances—only nearest neighbors or a sampled subset—so clarify the downstream use case before choosing a method.

1. Clarify the goal and constraints

Ask whether exact distances are required or if approximate results suffice, and understand the scale (n, dimensionality) and latency/memory budget.

2. Choose an algorithmic strategy

Select from spatial indexing (KD-trees, ball trees), locality-sensitive hashing (LSH), or approximate nearest neighbor (ANN) libraries like FAISS, Annoy, or ScaNN.

3. Leverage distributed or out-of-core computation

If exact distances are needed, use distributed frameworks (Spark, Dask) or block-wise computation with GPUs to handle memory limits.

4. Consider dimensionality reduction

Apply PCA, random projections, or UMAP to reduce feature space before distance computation, mitigating the curse of dimensionality.

5. Evaluate trade-offs and validate

Benchmark accuracy vs. speed, and validate that the chosen method preserves the quality of downstream ML tasks (e.g., recall of nearest neighbors).

Key Points to Mention

  • Approximate nearest neighbor (ANN) algorithms and libraries (FAISS, Annoy, ScaNN)
  • Locality-sensitive hashing (LSH) for sublinear time
  • Spatial data structures (KD-trees, ball trees) and their limitations in high dimensions
  • Distributed computing (Spark, Dask) and GPU acceleration for exact distances
  • Dimensionality reduction (PCA, random projections) to mitigate curse of dimensionality
  • Trade-offs between exact vs. approximate results and their impact on ML pipeline

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