data structure tries

TRIES

AN EXCELLENT DATA STRUCTURE FOR

STRINGS

Tries Instructor Md. Shamsujjoha Senior Lecturer Department of CSE East West University

Presented by:Md. Naim KhanId :2014-2-60-092Md. Riad KhanId :2014-1-60-040

Slide 2

Overview

History & Definition Types of Tries Standard Tries Compressed Tries Suffix Tries Conclusion

Slide 3

History

The term trie comes from retrieval. This term was coined by Edward Fredkin, who

pronounce it tri as in the word retrieval.

Slide 4

Definition of Tries

A data structure for representing a collection of strings.

In computer science, a trie, also called digital tree and sometimes radix tree or prefix tree.

Tries support fast pattern matching.

Slide 5

Properties of a tries

A multi-way tree. Each node has from 1 to n children. Each edge of the tree is labeled with a

character. Each leaf nodes corresponds to the stored

string, which is a concatenation of characters on a path from the root to this node.

Slide 6

Standard Trie The standard trie for a set of strings S is an

ordered tree such that:

*Each node but the root is labeled with a character.

*The children of a node are alphabetically ordered.

*The paths from the external nodes to the root yield the strings of S.

Slide 7

Standard Tries - Insertion Strings ={an, and, any, at}

n

a

d

t

y

Root

Slide 8

Example of Standard tries Example: Standard trie for the set of strings

S = { bear, bell, bid, bull, buy, sell, stock, stop }

te

s

uie

b

ollla d yc

k

plllr

Root

Slide 9

Handling keys(strings) When a key(string) is a prefix of another key. How can we know that “an” is a word? Example: an, and

n

a

d

t

y

Root

Slide 10

Handling keys(strings) We add a special termination symbol “$’’ We append the “$’’ to each keyword Strings={ an, and, any, at}

n

a

d

t

y

Root

$

$ $

$

Slide 11

Standard Tries- Searching Search hit: Node where search ends has a $

symbol Search - sea

n

a

d

t

y

Root

a t

e

s

$

$$

$

$ $Slide 12

Standard Tries- Deletion

Three cases

Word not found…! Word exists as a stand alone word.

Word exists as a prefix of another word

Slide 13

Standard Tries- Deletion Word not found return false. Word exists as a stand alone word part of any other word does not a part of any other word

Slide 14

Standard Tries- Deletion Part of any other word Delete - sea

n

a

d

t

y

Root

a t

e

s

$

$$

$

$ $

Slide 15

Deleted

Standard Tries-Deletion Does not a part of any other word Delete - set

n

a

d

t

y

Root

t

e

s

$

$

$

$ $

Slide 16

Deleted

Standard Tries- Deletion Word exists as a prefix of any other word. Delete - an

n

a

d

t

y

Root

a t

e

s

$

$$

$

$ $

Slide 17

Deleted

Compressd Tries

Tries with nodes of degree at least 2 Obtained by standard tries by

compressing chains of redundant nodes

Slide 18

Compressed Trie- Example In order to understand Compressed Trie we

need to see the Standard Trie Example:

te

s

uie

b

ollla d yc

k

plllr

Root Standard Trie

Slide 19

Compressed Tries Example Compressed Tries: S = { bear, bell, bid, bull, buy, sell, stock,

stop }

b s

e u toid ell

llar ll y ck p

Root Compressed Trie

Slide 20

Suffix Tries

A suffix trie is a compressed trie for all the suffixes of a text.

Suffix trie are a space-efficient data structure to store a string that allows many kinds of queries to be answered quickly.

Slide 21

Example of Suffix Tries Let us consider an example text “soon$″.

Root

s

o

o

n

o

o

n

n

n

$ $

$

$

$

Slide 22

soon$

oon$

$

n$

on$

Done

After alphabetically ordered the trie will look like

Root

s

o

o

n

o

o

n

n

n

$$

$

$

$

Example of Suffix Tries

Understanding Requirements

Insertion is faster as compared to the Hash Table

Lookup is much more faster than Hash Table implementations

There are no collision of different keys in tries

Slide 23

References Web pages http://www.mathcs.emory.edu/~cheung/Cours

es/323/Syllabus/Text/trie01.html http://fbim.fh-regensburg.de/~saj39122/sal/sk

ript/progr/pr45102/Tries.pdf http://www.ideserve.co.in/learn/trie-delete http://algs4.cs.princeton.edu/lectures/52Tries.

pdfBook Data Structure and Algorithm by Alfred V. Aho Jeffery D. Ullman   John E.HopcroftJohn Slide

24

Questions or Suggestions

Slide 25

Thank you

Slide 26

Inquiryriadmrk.khan@gmail.com

naim1248@gmail.com