5050 Tries
CS Lecture 22
Basic Ideas
Preprocess fixed text rather than pattern Store strings in trees, one character per node Use in search engines, dictionaries, prefixes Fixed alphabet with canonical ordering Might use special char as word terminator
Facts
Prefixes with length i stop in level i # leaves = # strings (words in text) Tree height = length of longest word Tree size O(combined length of all words) Insertion and search as in multi-way ordered trees, O(word length) Word, not substring, matching Could use , e.g., 27-ary trees instead Exclude stop words from trie
Trie Example
Compressed Tries
When there is only one child of a node, a waste of space, so store substrings at nodes Then the tree size is O(s), the number words
Compressed of Tries as Indexes
Tree of all suffixes of a (single) string Used in pattern matching a substring is the prefix of a suffix Changes a linear search for the beginning of the pattern (e.g., KMP) to a tree search
Suffix Tries
Suffix Tries are efficient
In space, O(n) rather than O(n2), because characters only need to appear once
Efficient O(dn) to construct, O(dm) to use
Search Engines
Inverted index (file) has w...