I knew LRU cold but LFU tripped me up for a minute because the tie-breaking rule means you need to track both frequency AND insertion/access order within each frequency bucket.
Start by clarifying the requirements and edge cases, then propose a design using a combination of a hash map and a doubly linked list of frequency buckets. Explain how each operation achieves O(1) by maintaining pointers and updating frequency lists, and finally discuss trade-offs and potential optimizations.
Pro tip: Mention that LFU with tie-breaking by recency is equivalent to LRU within each frequency level, so you can reuse an LRU structure per frequency. This shows deep understanding and simplifies the implementation.
Ask about cache capacity, behavior when capacity is 0, handling of duplicate keys, and whether get updates frequency. Confirm that tie-breaking is by least recently used among least frequently used.
Propose using a hash map for O(1) key lookup, a doubly linked list for each frequency to maintain recency order, and a min-frequency pointer to track the lowest frequency for eviction.
Explain get: if key exists, update its frequency (move to next frequency list) and return value. Explain put: if key exists, update value and frequency; if new, insert with frequency 1, and if capacity exceeded, evict from min-frequency list's tail (least recently used).
Argue that both operations are O(1) due to constant-time hash lookups and pointer manipulations. Discuss trade-offs: memory overhead vs. speed, and compare with other eviction policies like LRU.
Address edge cases: capacity 0, updating existing key, and frequency overflow. Mention possible optimizations like using a single linked list with frequency buckets or a heap (but heap would not be O(1)).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.