I went straight to a Trie and explained how each node could cache its top 3 sentences so you don't have to re-scan everything on each keystroke.
Start by clarifying requirements and constraints, then propose a trie where each node stores a min-heap or sorted list of the top 3 sentences for its prefix. Explain how to maintain these lists efficiently during insertions and updates, and discuss trade-offs between update cost and query speed.
Pro tip: Emphasize that storing only the top 3 per node bounds memory and update time, and mention that you can lazily recompute or use a heap to merge child results if needed. This shows you understand the balance between precomputation and on-demand computation.
Ask about expected scale (number of sentences, query rate), update frequency, and whether the top-3 list must be exact or approximate. Confirm that ranking is by frequency descending, then lexicographically ascending.
Propose a trie where each node represents a prefix and stores a list of up to 3 (sentence, frequency) pairs. Explain that each node's list contains the top sentences among all sentences that pass through that node.
When adding a sentence or incrementing its frequency, traverse the trie and update the top-3 list at each node along the path. Use a min-heap or sorted insertion to maintain the top 3 efficiently.
Discuss strategies to keep updates O(L * log 3) or O(L) per operation, such as comparing the new frequency against the minimum in the node's list and replacing if necessary. Mention that since k=3 is constant, operations are effectively O(L).
Compare precomputing top-3 at each node (fast queries, slower updates) versus computing on demand by merging children (slower queries, simpler updates). Also mention memory overhead and potential optimizations like caching or lazy propagation.
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