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I knew a hashmap alone wouldn't cut it for the max/min ops.
Start by clarifying the requirements and constraints, then propose a design using a hash map for key-to-count lookup and a doubly linked list of buckets to group keys by count, enabling O(1) access to max and min. Explain how each operation updates the data structures in constant time, and discuss handling edge cases like decrementing to zero.
Pro tip: Mention that this is a classic problem (often called 'All O(1) Data Structure') and that the bucket approach is optimal; also note that using a balanced BST would give O(log n), so the linked list of buckets is key to achieving O(1).
Ask about expected key types, whether counts can be negative, and if operations need to be thread-safe. Confirm that average O(1) is acceptable and that any max/min key is fine.
Suggest a hash map mapping keys to their count and a node in a doubly linked list of buckets, where each bucket represents a count and contains a set of keys with that count.
Explain how increment moves a key to the next bucket (creating it if needed), decrement moves it to the previous bucket (removing if count becomes zero), and how max/min are obtained from the head/tail of the bucket list.
Discuss cases like incrementing a new key, decrementing a key with count 1, and maintaining empty buckets. Analyze time and space complexity, emphasizing O(1) average time per operation.
Recap the design, highlighting how each operation achieves O(1), and ask if the interviewer wants to dive deeper into any part or consider alternative approaches.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.