Why pair a trie with a top-k heap instead of just returning all candidates?
A trie node holds millions of descendants in real dictionaries. A top-k heap (min-heap of size k) tracks the k best words by frequency/popularity. Autocomplete returns the heap top-k instantly without scanning all descendants. Cost: O(k log k) extraction, where k is typically 5–10.
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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