Google·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Google ML Engineer interview with a coding round that pushed the classic packing problem into 2D territory. The geometric twist was unexpected and the discussion about scaling to higher dimensions felt like it could've gone on forever.

Questions Asked (1)

You have a stream of items, each with a 2D size vector. Identify all triple-packs where the maximum pairwise Euclidean distance among the three items falls below a given threshold. How do you do this efficiently?

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I knew the 1D version well enough, so my first instinct was to just sort by x and use binary search to filter candidates within the threshold range on that axis.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: the stream may be infinite, so we need an online algorithm that processes each item once and reports triple-packs whose maximum pairwise distance is below a threshold. Then propose a spatial indexing approach (e.g., grid or KD-tree) to efficiently find neighbors within the threshold, and for each new item, find pairs of existing items that are within threshold of each other and of the new item, forming valid triple-packs.

Pro tip: Mention that the maximum pairwise distance condition is equivalent to all three pairwise distances being below the threshold, which simplifies the search to finding cliques of size 3 in the threshold graph. Also, discuss the trade-off between memory and accuracy if using approximate methods like LSH for high-dimensional data.

1. Clarify requirements and constraints

Ask about the dimensionality, expected stream rate, memory limits, and whether exact or approximate results are acceptable. Confirm that the threshold is fixed and that we need to output triple-packs as they are found.

2. Choose a spatial indexing strategy

Select an index such as a grid (for low dimensions) or a KD-tree/ball tree (for moderate dimensions) to efficiently query neighbors within the threshold. For high dimensions, consider LSH or random projections.

3. Process each new item

For each incoming item, query the index to find all existing items within the threshold distance. Then, among those neighbors, find pairs that are also within threshold of each other (using the index or a precomputed neighbor list).

4. Emit triple-packs and update index

For each valid pair of neighbors that are within threshold of each other, output the triple-pack (new item + pair). Then insert the new item into the index for future queries.

5. Analyze complexity and trade-offs

Discuss time and space complexity: query time depends on the index, and the number of triple-packs can be large. Mention pruning strategies (e.g., only consider neighbors within threshold/2) and potential approximations.

Key Points to Mention

Equivalence of max pairwise distance < threshold to all three pairwise distances < threshold.
Use of spatial data structures (grid, KD-tree, ball tree) for efficient range queries.
Handling streaming data: incremental insertion and querying, possibly with sliding window if only recent items matter.
Complexity analysis: worst-case O(n^2) for dense clusters, but average-case better with indexing.
Approximation techniques (LSH, random projections) for high-dimensional data to trade accuracy for speed.
Memory management: storing all items may be infeasible; consider discarding items that cannot form future triple-packs (e.g., if no neighbors within threshold).

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