This is a brief explanation of a data structure tries

1. TRIES
AN EXCELLENT DATA
STRUCTURE FOR
STRINGS

2. Tries
 Instructor
Md. Shamsujjoha
Senior Lecturer
Department of CSE
East West University
 Presented by:
Md. Naim Khan
Id :2014-2-60-092
Md. Riad Khan
Id :2014-1-60-040
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3. Overview
 History & Definition
 Types of Tries
Standard Tries
Compressed Tries
Suffix Tries
 Conclusion
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4. History
 The term trie comes from retrieval.
 This term was coined by Edward Fredkin, who
pronounce it tri as in the word retrieval.
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5. 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.
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6. 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.
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7. 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.
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8. Standard Tries - Insertion
 Strings ={an, and, any, at}
n
a
d
t
y
Root
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9. 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
o
llla
d y
c
k
p
lllr
Root
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10. 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
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11. 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
$
$ $
$
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12. Standard Tries- Searching
 Search hit: Node where search ends has a $ symbol
 Search - sea
n
a
d
t
y
Root
a t
e
s
$
$$
$
$ $
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13. Standard Tries- Deletion
 Three cases
Word not found…!
Word exists as a stand alone word.
Word exists as a prefix of another word
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14. Standard Tries- Deletion
 Word not found
return false.
 Word exists as a stand alone word
part of any other word
does not a part of any other word
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15. Standard Tries- Deletion
 Part of any other word
 Delete - sea
n
a
d
t
y
Root
a t
e
s
$
$$
$
$ $
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Deleted

16. Standard Tries-Deletion
 Does not a part of any other word
 Delete - set
n
a
d
t
y
Root
t
e
s
$
$
$
$ $
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Deleted

17. Standard Tries- Deletion
 Word exists as a prefix of any other word.
 Delete - an
n
a
d
t
y
Root
a t
e
s
$
$$
$
$ $
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Deleted

18. Compressd Tries
 Tries with nodes of degree at least 2
 Obtained by standard tries by compressing
chains of redundant nodes
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19. Compressed Trie- Example
 In order to understand Compressed Trie we need to
see the Standard Trie Example:
te
s
uie
b
o
llla
d y
c
k
p
lllr
Root
Standard Trie
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20. 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
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21. 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.
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22. Example of Suffix Tries
 Let us consider an example text “soon$″.
Root
s
o
o
n
o
o
n
n
n
$
$
$
$
$
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soon$
oon$
$
n$
on$
Done

23.  After alphabetically ordered the trie will look like
Root
s
o
o
n
o
o
n
n
n
$
$
$
$
$
Example of Suffix Tries

24. 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
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25. References
Web pages
 http://www.mathcs.emory.edu/~cheung/Courses/323/Syll
abus/Text/trie01.html
 http://fbim.fh-
regensburg.de/~saj39122/sal/skript/progr/pr45102/Tries.p
df
 http://www.ideserve.co.in/learn/trie-delete
 http://algs4.cs.princeton.edu/lectures/52Tries.pdf
Book
 Data Structure and Algorithm
by Alfred V. Aho
Jeffery D. Ullman
John E.HopcroftJohn
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26. Questions or Suggestions
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27. Thank you
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Inquiry
riadmrk.khan@gmail.com
naim1248@gmail.com