Data structure tries
27
TRIES AN EXCELLENT DATA STRUCTURE FOR STRINGS
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Transcript of 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
