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

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

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

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

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

7. 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 log 2 (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