Can a trie be built incrementally as new words are added to a system?
Yes. Insertion is O(p) per word. A trie is a mutable structure, not a static lookup table. If you're updating frequencies for ranking, track them alongside the trie and rebuild the top-k heaps incrementally; that's faster than full recomputation.
Answered in
Tries: Why Autocomplete Doesn't Scan Every WordA trie finds all words with a prefix in O(p) time, independent of dictionary size. Radix compression and top-k heaps make autocomplete instant.
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