This looked like a coding question but it was really a system design problem crammed into a class implementation.
Start by clarifying requirements and constraints, then propose a data structure that efficiently supports both operations. For the store operation, maintain levels in a stack-like structure with capacity tracking; for retrieve, use a max-heap per level to find the heaviest item, and lazily remove expired items. Discuss trade-offs between different data structures and consider edge cases.
Pro tip: Demonstrate awareness of real-world constraints by discussing how to handle expiration efficiently—e.g., using lazy deletion with periodic cleanup to avoid O(n) scans on every operation. Also, mention that you would confirm the definition of 'at least half full' (by count or weight) and whether levels are fixed capacity.
Ask questions to understand the exact behavior: What is the capacity of each level? Is 'half full' based on item count or total weight? How are expiration times handled? Are there concurrency requirements? This ensures you design the right solution.
Propose a list of levels, each with a capacity and a max-heap (or balanced BST) keyed by weight for efficient retrieval. For expiration, consider storing items with timestamps and using lazy deletion or a separate min-heap by expiration time.
Iterate from the topmost level downwards to find the first level with available capacity. Insert the item into that level's heap and update the level's current size. If no level has space, either reject or create a new level (depending on requirements).
Starting from the topmost level, remove expired items (lazily or eagerly), then check if the level is at least half full. If so, extract the heaviest item from that level's heap and return it. If not, move to the next level. If no level qualifies, return null or an error.
Discuss time and space complexity: store is O(L) where L is number of levels (or O(log n) if using a balanced tree for levels), retrieve is O(L + log n) due to heap operations and expiration checks. Mention alternatives like using a segment tree for level fullness or a global heap with level filtering.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.