Anthropic·Software Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Coding interview at Anthropic for a software engineering role, focused entirely on a tricky streaming data problem that combined two classic data structure questions into one. The design pressure was real and the follow-up complexity caught me a bit off guard.

Questions Asked (1)

Given a continuous stream of integers, design a data structure that supports two queries at any time: returning the current mode (most frequent value, with ties broken by smallest value) and returning the current median (lower middle element when count is even).

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

Two problems duct-taped together, which I did not see coming.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., stream size, update/query frequency, memory limits) and then propose a hybrid data structure that maintains both mode and median efficiently. For mode, use a hash map for frequencies plus a balanced BST or heap to track the most frequent; for median, use two heaps (max-heap for lower half, min-heap for upper half). Discuss trade-offs between update and query times, and consider if approximate solutions are acceptable.

Pro tip: Mention that you would first implement a simple solution (e.g., recompute mode and median on each query) to establish correctness, then optimize based on expected query/update patterns. This shows pragmatic engineering thinking.

1. Clarify Requirements and Constraints

Ask about the expected number of elements, frequency of queries vs updates, memory limits, and whether exact answers are required. This guides the choice of data structures.

2. Design for Mode

Use a hash map to count frequencies and a balanced BST (or heap with lazy deletion) to maintain the current mode. For ties, ensure the BST is keyed by (frequency, value) so the smallest value is easily accessible.

3. Design for Median

Maintain two heaps: a max-heap for the lower half and a min-heap for the upper half. Balance them after each insertion so the median is the top of the max-heap (for even count, lower middle).

4. Integrate and Optimize

Combine both structures, ensuring updates are O(log n) and queries are O(1). Discuss potential optimizations like using a single balanced BST for both if possible, or approximate methods for very large streams.

5. Analyze Trade-offs and Edge Cases

Compare time/space complexity of your solution with alternatives. Discuss handling of duplicates, negative numbers, and dynamic tie-breaking. Mention scalability and potential distributed approaches if needed.

Key Points to Mention

Time complexity: O(log n) update, O(1) query for both mode and median.
Space complexity: O(n) for storing frequencies and heaps.
Use of balanced BST (e.g., TreeMap in Java) for mode with tie-breaking by value.
Two-heap approach for median, ensuring lower middle element for even counts.
Handling ties in mode: smallest value wins, so order by (frequency, value).
Trade-offs: exact vs approximate solutions, memory vs speed, and potential use of order-statistic trees.

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