The base version felt manageable, just a dict of queues keyed by party size.
Start by clarifying requirements and constraints, then design a data structure that efficiently supports both FIFO per size group and global oldest-first allocation. For the follow-up, propose a solution that balances time complexity and implementation simplicity, such as a segment tree over party sizes or a heap with lazy deletion, and analyze trade-offs.
Pro tip: Demonstrate awareness of real-world constraints like table capacity distribution and party size distribution, and discuss how they affect data structure choice. Also, mention that you would start with a simple solution and optimize based on expected load.
Ask about expected number of parties, table sizes, frequency of operations, and whether parties can be split or combined. Confirm that FIFO per size group means within each party size, order is preserved.
Propose using a queue per party size for FIFO, and a mapping from table capacity to available tables. For allocation, iterate over sizes that fit the table and pick the oldest party.
Introduce a global ordering mechanism, such as a segment tree over party sizes storing the oldest timestamp, or a min-heap of all waiting parties with lazy deletion when parties are seated out of order.
Compare time complexities: naive O(k) per allocation vs. segment tree O(log n) vs. heap O(log n) with lazy deletion. Discuss space and implementation complexity.
Consider empty waitlist, no fitting table, multiple tables opening simultaneously, and thread safety if concurrent. Mention testing strategy.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.