Lexicographic Search:Tries

1. Lexicographic Search:Tries • All of the searching methods we have seen so far compare entire keys during the search • Idea: Why not consider a key to be a sequence of characters (letters or digits, for example) and use these characters to determine a multiway branch at each step • If the keys are alphabetic names (names), we make a 29-way branch at each step. • If the keys are natural numbers in base 10, we make a 10 way branch at each step • Similar to a thumb index in a dictionary • Called Retrieval -- pronounced like “try”

2. 0 Tries - Example • Assume that we have the following keys in a trie: • 0, 10, 11, 100, 101, 110, 2, 21 • Notice that the rootdoes not store actual data 0 1 2 3 4 5 6 7 8 9 2 10 11 21 110 100 101

3. 0 110 Tries - Search • Search 110: 0 1 2 3 4 5 6 7 8 9 2 10 11 21 110 100 101

4. 0 2195 Tries - Insertion • Insert 2195 into the following trie: 0 1 2 3 4 5 6 7 8 9 2 10 11 21 110 100 101

5. 0 2195 Tries - Deletion • Delete 10 from the following trie: 0 1 2 3 4 5 6 7 8 9 2 10 11 21 110 100 101

6. 0 2195 Tries - Deletion • Delete 110 from the following trie: 0 1 2 3 4 5 6 7 8 9 2 21 110 100 101

7. Tries: Summary • # of steps requires to search a trie (or to insert into it) is proportional to the number of characters making up a key • E.g., if we have numbers in the range 0 – 999999, then we have at most 6 steps (comparisons) to reach a key • If the number of chars is small relative to the logarithm 2 of the number of keys, a trie may be superior to a binary search tree • E.g., if keys consist of all 999999 numbers in the range 0-999999, we have at most 6 steps to reach a key, whereas a binary search tree would take log2(999999) ~ 20 steps (key comparisons) • The best solution may be to combine the methods • A trie can be used in the fist few chars of the key, and then another method can be used for the remainder of the key