Why does a naive database query like LIKE 'car%' get slower as the dictionary grows?
The query must scan every row or index entry, comparing the prefix against each one. That's O(N) per keystroke, where N is the full dictionary. A trie answers the same question in O(p), the prefix length, because it jumps directly to the 'car' subtree.
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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