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I knew the high-level idea but the O(1) constraint is where it gets painful.
Start by clarifying the requirements: O(1) get and put, LFU eviction, and LRU tiebreaking. Then propose a design using two hash maps and a frequency-indexed doubly linked list structure, explaining how each operation maintains O(1) time. Finally, walk through the implementation details and edge cases.
Pro tip: Mention that you would use a min-frequency pointer to avoid scanning for the lowest frequency, and emphasize that the LRU tiebreaking is naturally handled by maintaining insertion order within each frequency list.
Confirm that get and put must be O(1), eviction is based on least frequency, and ties are broken by LRU order. Ask about cache capacity and whether updates count as usage.
Propose a combination of a key-to-node hash map, a frequency-to-doubly-linked-list hash map, and a min-frequency variable. Each node stores key, value, frequency, and pointers for the list.
Detail how get retrieves the node, updates its frequency, and moves it to the appropriate frequency list. For put, handle insertion, update, and eviction when capacity is exceeded, ensuring O(1) by manipulating list pointers and hash maps.
Discuss how LRU tiebreaking is achieved by adding new nodes to the tail of the frequency list and evicting from the head. Cover cases like updating an existing key, evicting the last item, and maintaining min-frequency correctly.
Confirm that all operations are O(1) time and O(capacity) space. Walk through a small example to validate the design and mention potential optimizations or alternative approaches.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.