Decagon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Decagon SWE interview had me extending a sliding-window score tracker with percentile queries. The problem builds on a previous round's work, which felt clever in retrospect but was a lot to hold in your head at once.

Questions Asked (1)

You have a sliding-window conversation score tracker from a prior round. Now add a method that, given a percentile p and a rank n, returns the score of the n-th conversation at that percentile among all conversations currently in the active window. How do you define percentile here, and what data structure supports this efficiently?

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

The percentile definition part tripped me up more than the implementation.

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AI HintsAI Generated

Suggested Approach

First, clarify the percentile definition (e.g., nearest-rank method) and how rank n maps to a percentile. Then, propose a data structure like an order-statistic tree or two heaps that supports efficient insertion, deletion, and percentile queries in O(log n) time.

Pro tip: Discuss the trade-offs between different data structures and mention that the choice depends on the frequency of updates versus queries. Also, consider edge cases like empty window or invalid percentile/rank.

1. Clarify Requirements

Define what percentile means in this context (e.g., nearest-rank, linear interpolation) and how rank n relates to percentile p. Confirm whether n is 1-indexed and if p is between 0 and 100.

2. Choose Data Structure

Select a data structure that maintains order statistics, such as an order-statistic tree (balanced BST with subtree sizes) or a Fenwick tree over compressed scores, to support efficient rank queries.

3. Handle Sliding Window

Integrate the data structure with the sliding window: when a conversation enters or leaves the window, update the structure accordingly (insert/delete).

4. Implement Percentile Query

For a given percentile p and rank n, compute the target rank (e.g., ceil(p/100 * window_size)) and then find the n-th conversation at that percentile using the order-statistic operations.

5. Analyze Complexity

State the time complexity for updates and queries (e.g., O(log n) per operation) and discuss space complexity. Mention potential optimizations or alternative approaches.

Key Points to Mention

Definition of percentile (nearest-rank vs. interpolation) and its implications
Order-statistic tree or Fenwick tree for efficient rank queries
Handling duplicates and ties in scores
Sliding window update strategy (insertion and deletion)
Time and space complexity trade-offs
Edge cases: empty window, invalid p or n, and dynamic window size

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