I went with a doubly linked list to preserve arrival order plus a hashmap from user to node for O(1) deletes.
Start by clarifying the requirements and constraints, then propose a data structure that balances the three operations. A common approach is to combine a hash map for O(1) removal by name with a balanced binary search tree (e.g., TreeMap) keyed by arrival order to efficiently find the first fitting party. Discuss trade-offs and possible optimizations.
Pro tip: Mention that the found user stays on the waitlist, so you must not remove them during the search; this implies the search operation should be read-only. Also, consider using a segment tree or Fenwick tree over party sizes to achieve O(log n) search if the waitlist is large.
Ask about expected number of operations, whether party sizes are bounded, and if the waitlist order is strictly by arrival time. Confirm that the found user remains on the waitlist.
Use a hash map (name -> node) for O(1) removal and a balanced BST (e.g., TreeMap) keyed by arrival order to maintain the queue. Each node stores party size.
To find the first fitting party, traverse the BST in arrival order (in-order) and check party size <= capacity. This is O(n) worst-case, but can be optimized with a segment tree over party sizes to O(log n).
Add: O(log n) for BST insertion + O(1) for hash map. Remove: O(log n) for BST deletion + O(1) for hash map. Search: O(n) with naive BST, O(log n) with segment tree.
Compare naive BST vs. segment tree vs. bucket by party size. Mention that if party sizes are small, an array of queues per size can give O(1) search but may not preserve global arrival order.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.