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Anthropic·Software Engineer·Technical Phone Screen·Senior

Senior
May 2026

Summary

Anthropic coding round focused on a single meaty data structures problem. The question had multiple layers and they clearly wanted to see you think through the design before writing anything.

Questions Asked (1)

Q1

Given a stream of numeric data points grouped into clusters, design a system that supports adding a value to a cluster and efficiently querying both the mode (most frequent value, ties broken by smallest) and the median for any cluster. Walk through your data structures and the complexity of each operation.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs
Author's notes

I jumped straight to the median heap setup and nearly forgot the mode entirely for the first few minutes.

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AI HintsAI Generated

Suggested Approach

Start by clarifying requirements: operations include adding a value to a cluster, and querying mode and median per cluster. Propose a design using a hash map from cluster ID to a data structure that maintains both frequency counts and order statistics, such as a balanced BST augmented with subtree sizes and a frequency map. Discuss trade-offs between different approaches (e.g., heaps, order-statistic trees, skip lists) and analyze time and space complexity for each operation.

Pro tip: Mention that the mode query requires tracking the maximum frequency and handling ties by smallest value, which can be done by maintaining a separate structure or by augmenting the BST nodes with frequency and subtree max frequency. Also, note that median can be found using order statistics, and if the cluster size is large, consider approximate methods or streaming algorithms if exactness is not required.

1. Clarify Requirements and Assumptions

Confirm that clusters are identified by an ID, values are numeric, and operations are add and query. Ask about expected data volume, update frequency, and whether exact mode/median are required.

2. Choose Core Data Structures

Propose a hash map mapping cluster ID to a per-cluster structure. For each cluster, use a balanced BST (e.g., red-black tree) keyed by value, with each node storing the frequency count and subtree size. Additionally, maintain a frequency map (value -> count) and a variable tracking the current mode (value and frequency).

3. Detail Operations and Complexity

For add: update the BST (insert or increment frequency), update the frequency map, and update the mode if the new frequency exceeds the current max or ties with a smaller value. For mode query: return the stored mode. For median query: use order statistics on the BST to find the k-th smallest element (k = (n+1)/2 for odd, average of two for even). Analyze time complexity: add O(log n), mode O(1), median O(log n).

4. Discuss Trade-offs and Alternatives

Compare with alternatives like using two heaps for median (but mode becomes harder) or a skip list for simpler implementation. Discuss space complexity O(n) per cluster. Mention that if clusters are many and small, simpler structures like sorted arrays might suffice.

5. Summarize and Conclude

Recap the design, emphasizing efficiency and correctness. Mention potential extensions like handling deletions or approximate queries for very large streams.

Key Points to Mention

  • Use of balanced BST augmented with subtree sizes for order statistics (median).
  • Maintaining a frequency map and a mode tracker for O(1) mode query.
  • Tie-breaking for mode: smallest value among highest frequency.
  • Time complexity: add O(log n), mode O(1), median O(log n).
  • Space complexity: O(n) per cluster, overall O(total data points).
  • Trade-offs: exact vs approximate, and alternative structures like skip lists or heaps.

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