The add operations are straightforward enough but the referral one trips you up because updating the referrer's revenue means their position in any sorted structure changes.
Start by clarifying the requirements and constraints, such as the expected number of operations, the range of revenues, and whether the query threshold is inclusive. Then propose a data structure that supports efficient insertion, update, and threshold-based top-k queries, discussing trade-offs between different approaches. Finally, analyze the time and space complexity of each operation and consider optimizations for the given constraints.
Pro tip: Mention that the referral operation requires updating the referrer's revenue, which may change its position in the ordering; thus, the data structure must support efficient updates. Also, consider using a balanced BST augmented with subtree sizes to handle top-k queries efficiently.
Ask about the expected number of operations, the range of revenue values, whether revenues can be negative, and if the threshold is inclusive. Also, clarify if the query should return the customers in sorted order or just any k customers.
Propose using a balanced binary search tree (e.g., AVL or Red-Black tree) where each node stores a customer and is keyed by revenue, augmented with subtree sizes to support order statistics. Alternatively, consider a Fenwick tree over compressed revenue values if revenues are bounded.
For addCustomer: insert a new node with the given revenue and return its id. For addReferral: insert the new customer and update the referrer's revenue by adding the new customer's revenue, which may require deleting and reinserting the referrer's node. For query: find the first node with revenue > threshold, then retrieve the next k nodes in order.
For a balanced BST with subtree sizes, each operation takes O(log n) time on average, where n is the number of customers. The query operation takes O(log n + k) time. Space complexity is O(n). If using a Fenwick tree, operations are O(log M) where M is the number of distinct revenue values.
Compare the BST approach with alternatives like a skip list or a segment tree. Discuss how to handle duplicate revenues (e.g., by storing a list of customers per revenue or using a tie-breaker). Mention that if k is small, a heap-based approach might be simpler but less efficient for arbitrary k.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.