1. Lecture 12 : Trie Data Structure Bong-Soo Sohn Assistant Professor School of Computer Science and Engineering Chung-Ang University

2. Problem Store this collection of words in a memory efficient way : {abacus, abode, dreaded, dust, dusty, planar, east}

3. Arrays aabcus aobde deradde dsut dsuty = 6 slots = 5 slots = 7 slots = 4 slots = 5 slots

4. Idea Take advantage of the common letters in the words Reduce redundancy Use same letter for more than one word

5. Trie Store characters (digits) in each node, not keys. Path from root to a node is associated with a key Use characters of the key to guide the search process All the descendants of a node have a common prefix of the string associated with that node retrievalFrom retrieval, but pronounced “try”

6. Example u d en l h st o g l i e m go shed shell sun time she Make sure the word “she” is not found… …unless it has been explicitly inserted!

7. example A trie for keys "t", "to", "te", "tea", "ten", "i", "in", and "inn".

8. Advantages Looking up keys is faster. O(m) time. A BST takes O(log n) time m : length of key, n : # of elements In the worst case, log(n) will approach m Tries can require less space when they contain a large number of short strings Longest prefix matching is possible finding the key sharing the longest possible prefix of characters all unique Fast search/insert/delete

9. Drawbacks Tries can be slower in some cases. Especially when the tree is accessed from disk It is not easy to represent all keys as strings Floating point numbers (1.0, +1.0, 1 …) Inefficient when a key is too long

10. Applications Can replace a hash table Only take O(m), m : length of key No collision No need to provide hash function Can provide an alphabetical ordering of keys Dictionary IP routing Routing : process of selecting paths in a network along which to send network traffic when given a destination address, find next place(place) to go. Internet router table is a collection of rules of the form (P, NH), P : prefix, NH : next hop