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I knew a hashmap alone wouldn't cut it the moment they said O(1) for both max and min.
Start by clarifying the operations and constraints, then propose a hybrid data structure combining a hash map for O(1) key access and a doubly linked list of frequency buckets to maintain order. Explain how increment and decrement adjust the key's position between buckets, and how get-max-key and get-min-key retrieve from the ends of the list.
Pro tip: Mention that this is essentially an LFU cache design, and highlight that the O(1) average time relies on hash map operations and constant-time list manipulations. Also, discuss edge cases like when multiple keys share the same frequency and how to handle them.
Ask if keys are integers or strings, if frequencies can be negative, and if we need to handle concurrent access. Confirm that all operations must be O(1) average time.
Use a hash map to store key -> node, where each node contains the key and its frequency. Use a doubly linked list of buckets, each bucket representing a frequency and containing a set of keys with that frequency.
For increment: move key to the next higher frequency bucket, creating it if necessary. For decrement: move to the next lower bucket, removing empty buckets. For get-max-key and get-min-key: return any key from the highest or lowest frequency bucket respectively.
Explain that each operation involves O(1) hash map lookups and O(1) pointer updates in the linked list. Discuss edge cases: multiple keys with same frequency, decrementing to zero, and empty structure.
Mention how to adapt for ML engineering (e.g., tracking feature frequencies) and trade-offs like memory overhead vs. speed. Optionally, compare with alternative approaches like balanced BSTs (O(log n)).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.