Lecture 12 : Trie Data Structure Bong-Soo Sohn Assistant Professor School of Computer Science and Engineering Chung-Ang University.
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Transcript Lecture 12 : Trie Data Structure Bong-Soo Sohn Assistant Professor School of Computer Science and Engineering Chung-Ang University.
Lecture 12 : Trie Data Structure
Bong-Soo Sohn
Assistant Professor
School of Computer Science and Engineering
Chung-Ang University
Problem
Store this collection of words in a memory
efficient way :
{abacus, abode, dreaded, dust, dusty, planar,
east}
Arrays
a
b
a
c
u
a
b
o
d
e
d
r
e
a
d
d
u
s
t
d
u
s
t
= 6 slots
s
= 5 slots
e
d
= 7 slots
= 4 slots
y
= 5 slots
Idea
Take advantage of the common letters in
the words
Reduce redundancy
Use same letter for more than one word
Trie
Store characters (digits) in each node, not keys.
Path from root to a node is associated with a
key
Use characters of the key to guide the search
process
All the descendants of a node have a common
prefix of the string associated with that node
From retrieval, but pronounced “try”
Example
g
s
o
h
t
i
u
go
Make sure the word
“she” is not found…
she
e
m
n
sun
d
l
e
…unless it has been
explicitly inserted! shed
time
l
shell
example
A trie for keys "t", "to", "te", "tea", "ten",
"i", "in", and "inn".
Advantages
Looking up keys is faster. O(m) time.
A BST takes O(log n) time
m : length of key , n : # of elements
In the worst case, log(n) will approach m
Tries can require less space when they contain a
large number of short strings
Longest prefix matching is possible
finding the key sharing the longest possible prefix of
characters all unique
Fast search/insert/delete
Drawbacks
Tries can be slower in some cases.
Especially when the tree is accessed from disk
It is not easy to represent all keys as strings
Floating point numbers (1.0 , +1.0, 1 …)
Inefficient when a key is too long
Applications
Can replace a hash table
Only take O(m) , m : length of key
No collision
No need to provide hash function
Can provide an alphabetical ordering of keys
Dictionary
IP routing
Routing : process of selecting paths in a network along which to
send network traffic
when given a destination address, find next place(place) to go.
Internet router table is a collection of rules of the form (P, NH),
P : prefix, NH : next hop