Tries are a data structure for storing strings that allow for fast pattern matching. A trie is a tree where each edge represents a character and each path from the root node to a leaf spells out a key. Standard tries insert strings by adding nodes for each character. Compressed tries reduce redundant nodes by compressing chains. Suffix tries store all suffixes of a text in a compressed trie to enable quick string queries. Tries support faster insertion and lookup compared to hash tables, with no collisions between keys.

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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16
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