My first instinct was a heap and I was pretty confident about it.
Clarify the problem: high-frequency tag counting likely means maintaining counts of tags in a sliding window and efficiently retrieving the top-k or max-frequency tags. Use a monotonic queue to maintain a deque of candidate tags in decreasing order of frequency, updating counts as the window slides. Then explain how to handle increments/decrements and query the top tag in O(1) amortized time.
Pro tip: Emphasize that a monotonic queue alone isn't enough for arbitrary frequency updates; you often need a hash map for counts and a bucket or heap for ordering. Discussing this trade-off shows you understand the data structure's limitations and can design a hybrid solution.
Ask whether the window size is fixed or variable, whether we need top-1 or top-k, and the expected frequency of updates and queries. This determines if a monotonic queue is appropriate or if a more complex structure is needed.
Propose a hash map to store tag frequencies and a monotonic deque to maintain tags in decreasing order of frequency. Explain that the deque will store tags whose frequencies are non-increasing from front to back.
For each incoming tag, increment its count in the map. Then, while the deque's back has a frequency less than or equal to the new count, pop it. Push the tag to the back. For sliding window, also handle decrements and remove tags that fall out of the window.
The front of the deque gives the current max-frequency tag. Discuss how to handle ties, empty deque, and stale entries (tags whose counts have changed but remain in the deque).
State that each tag is pushed and popped at most once per window slide, giving O(1) amortized time per update. Mention that the monotonic queue works well for max queries but not for arbitrary order statistics, and suggest alternatives like heaps or balanced trees if needed.
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