Google·Software Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Apr 2026Remote

Summary

Google SWE coding round with a pretty gnarly 2D geometry problem. Not your typical sliding window or hashmap question, this one had me second-guessing my whole approach for a while.

Questions Asked (1)

Design a class that accepts 2D points one at a time and, after each insertion, returns and removes a valid triplet of points where all pairwise Euclidean distances are below a given threshold. If no such triplet exists, return empty.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

I stared at this for a solid minute before saying anything.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., threshold, point distribution, expected frequency of triplets) and then propose a solution using a spatial data structure like a grid or k-d tree to efficiently find nearby points. After each insertion, search for a triplet among the new point and its neighbors, remove it if found, and update the data structure accordingly. Discuss trade-offs between different data structures and algorithms, and consider edge cases like duplicate points and dynamic threshold changes.

Pro tip: Emphasize that the problem is essentially dynamic clique detection in a unit disk graph; mentioning this shows depth. Also, proactively discuss how to handle deletions and maintain the data structure's integrity, as this is often overlooked.

1. Clarify Requirements and Constraints

Ask about the threshold value, expected number of points, frequency of triplet removal, and whether points can be duplicated. This ensures you design the right solution for the scale and use case.

2. Choose a Spatial Data Structure

Select a data structure like a uniform grid, k-d tree, or ball tree to efficiently query nearby points within the threshold distance. Justify your choice based on expected point distribution and update frequency.

3. Design Insertion and Triplet Search

On insertion, add the point to the data structure and search for a triplet involving the new point and its neighbors. Use a clique-finding approach (e.g., check all pairs among neighbors) to find a valid triplet.

4. Handle Removal and Data Structure Updates

If a triplet is found, remove those points from the data structure and return them. Ensure the data structure remains balanced and efficient after deletions.

5. Analyze Complexity and Trade-offs

Discuss time and space complexity for insertion, search, and deletion. Compare alternative approaches (e.g., brute force vs. spatial indexing) and explain why your solution is optimal for the given constraints.

Key Points to Mention

Use of spatial indexing (e.g., grid, k-d tree) to reduce search space for nearby points.
Triplet condition: all pairwise distances < threshold, equivalent to finding a triangle in a unit disk graph.
Handling of deletions: updating the spatial index and ensuring no stale references.
Edge cases: duplicate points, points exactly at threshold distance, and empty results.
Complexity analysis: average vs. worst-case time for insertion and triplet search.
Potential for concurrency if multiple insertions occur simultaneously (if relevant to system design).

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