The add and executeNext parts came pretty naturally, heap with a sequence counter for tie-breaking.
Start by clarifying the requirements and constraints, then propose a data structure that combines a hash map for O(1) ID lookup and a balanced binary search tree (or heap with lazy deletion) for O(log n) priority-based ordering. Explain how you would handle ties by creation time and ensure all operations meet the O(log n) complexity, discussing trade-offs between different approaches.
Pro tip: Mention that in real systems, you might use a heap with lazy deletion to avoid the overhead of removing from the middle of a heap, but be prepared to discuss why a balanced BST is more straightforward for O(log n) removal by ID. Also, consider concurrency if tasks are added/removed from multiple threads.
Ask about expected number of tasks, concurrency needs, and whether priorities are static or can change. Confirm that all operations must be O(log n) and that ties are broken by earliest creation time.
Propose a hash map (ID -> task) for O(1) lookup and a balanced BST (e.g., red-black tree) ordered by (priority, timestamp) for O(log n) insertion, deletion, and retrieval of the highest-priority task.
Detail how add inserts into both structures, remove deletes from both using the ID, and executeNext finds and removes the minimum (or maximum) element from the BST, ensuring ties are broken by timestamp.
Explain that all operations are O(log n) due to the BST, and discuss alternatives like a heap with lazy deletion (which may not guarantee O(log n) for remove by ID) or a skip list.
Address empty structure, duplicate IDs, and concurrency. Mention possible extensions like updating priority or timestamp, and how the design would adapt.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.