Took me a few minutes to really internalize the recursive part.
Start by clarifying requirements and constraints, then propose a data model that supports efficient updates and queries. Discuss the trade-offs between different approaches for maintaining aggregate revenues and answering top-K queries, and outline an implementation plan with complexity analysis.
Pro tip: Mention that in a real system, you'd likely use a combination of in-memory data structures and periodic persistence, and highlight the importance of handling cycles in the referral graph to avoid infinite loops.
Ask about expected scale, update/query frequency, and whether the referral graph can have cycles. Confirm that aggregate revenue is computed recursively and that ties are broken by customer ID.
Propose storing customers in a hash map for O(1) access, with each customer having direct revenue, a list of referees, and a cached aggregate revenue. Consider maintaining a reverse index from referrer to referees for efficient updates.
For insert, update the customer's direct revenue and, if a referrer is given, link them. Propagate the revenue change up the referral chain to update aggregate revenues, using memoization or a topological order to avoid redundant computations.
For top-K query, filter customers by aggregate revenue threshold, then sort by revenue descending and ID ascending. Use a heap for efficient top-K selection if K is small relative to the number of customers.
Discuss time and space complexity for both operations. For updates, propagation cost depends on depth of referral tree; for queries, sorting is O(N log N) or O(N log K) with a heap. Mention potential optimizations like lazy propagation or segment trees.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.