Topic 25 Tries In 1959 Edward Fredkin recommended

Topic 25 Tries “In 1959, (Edward) Fredkin recommended that BBN (Bolt, Beranek and Newman, now BBN Technologies) purchase the very first PDP-1 to support research projects at BBN. The PDP-1 came with no software whatsoever. Fredkin wrote a PDP-1 assembler called FRAP (Free of Rules Assembly Program); ” Tries were first described by René de la Briandais in File searching using variable length keys.

Clicker 1 8 How would you pronounce “Trie” A. “tree” B. “tri – ee” C. “try” D. “tiara” E. something else CS 314 Tries 2

Tries aka Prefix Trees 8 Pronunciation: 8 From retrieval 8 Name coined by Computer Scientist Edward Fredkin 8 Retrieval so “tree” 8… but that is very confusing so most people pronounce it “try” CS 314 Tries 3

Predictive Text and Auto. Complete 8 Search engines and texting applications guess what you want after typing only a few characters CS 314 Tries 4

Auto. Complete 8 So do other programs such as IDEs CS 314 Tries 5

Searching a Dictionary 8 How? 8 Could search a set for all values that start with the given prefix. 8 Naively O(N) (search the whole data structure). 8 Could improve if possible to do a binary search for prefix and then localize search to that location. 8 May be more difficult if prefix is not actually in the set or dictionary CS 314 Tries 6

Tries 8 A general tree 8 Root node (or possible a list of root nodes) 8 Nodes can have many children – not a binary tree 8 In simplest form each node stores a character and a data structure (list? ) to refer to its children 8 Stores all the words or phrases in a dictionary. 8 How? CS 314 Tries 7

René de la Briandais Original Paper CS 314 Tries 8

? ? Picture of a Dinosaur CS 314 Tries 9

Can CS 314 Tries 10

Candy CS 314 Tries 11

Fox CS 314 Tries 12

Clicker 2 8 Is “fast” in the dictionary represented by this Trie? A. No B. Yes C. It depends CS 314 Tries 13

Clicker 3 8 Is “fist” in the dictionary represented by this Trie? A. No B. Yes C. It depends CS 314 Tries 14

Tries 8 Another example of a Trie 8 Each node stores: – A char – A boolean indicating if the string ending at that node is a word – A list of children CS 314 Tries 15

Predictive Text and Auto. Complete 8 As characters are entered we descend the Trie 8… and from the current node … 8… we can descend to terminators and leaves to see all possible words based on current prefix 8 b, e, e -> bee, been, bees CS 314 Tries 16

8 Stores words and phrases. Tries – other values possible, but typically Strings 8 The whole word or phrase is not actually stored in a single node. 8… rather the path in the tree represents the word.

Implementing a Trie CS 314 Tries 18

TNode Class 8 Basic implementation uses a Linked. List of TNode objects for children 8 Other options? – Array. List? – Something more exotic? CS 314 Tries 19

Basic Operations 8 Adding a word to the Trie 8 Getting all words with given prefix 8 Demo in IDE CS 314 Tries 20

Compressed Tries 8 Some words, especially long ones, lead to a chain of nodes with single child, followed by single child: s b e a r i l l d u o y y e t l o l c k p

Compressed Trie 8 Reduce number of nodes, by having nodes store Strings 8 A chain of single child followed by single child (followed by single child … ) is compressed to a single node with that String 8 Does not have to be a chain that terminates in a leaf node – Can be an internal chain of nodes CS 314 Tries 22

Original, Uncompressed s b e a r CS 314 i l l d u y s e t l o l y c p k Tries 23

Compressed Version s b e ar id ll ell u sy to ck p y 8 fewer nodes compared to uncompressed version s–t–o–c-k CS 314 Tries 24

Data Structures 8 Data structures we have studied – arrays, array based lists, linked lists, maps, sets, stacks, queues, trees, binary search trees, graphs, hash tables, red-black trees, priority queues, heaps, tries 8 Most program languages have some built in data structures, native or library 8 Must be familiar with performance of data structures – best learned by implementing them yourself CS 314 Heaps 25

Data Structures 8 We have not covered every data structure Heaps http: //en. wikipedia. org/wiki/List_of_data_structures

Data Structures 8 deque, b-trees, quad-trees, binary space partition trees, skip list, sparse matrix, union-find data structure, Bloom filters, AVL trees, 2 -3 -4 trees, and more! 8 Must be able to learn new and apply new data structures CS 314 Heaps 27