Lecture 12 : Trie Data Structure

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Lecture 12 Trie Data Structure

• Bong-Soo Sohn
• Assistant Professor
• School of Computer Science and Engineering
• Chung-Ang University

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Problem

• Store this collection of words in a memory
  efficient way
• abacus, abode, dreaded, dust, dusty, planar,
  east

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Arrays
a
a
b
c
u
s
6 slots
a
o
b
d
e
5 slots
d
e
r
a
d
d
e
7 slots
d
s
u
t
4 slots
d
s
u
t
y
5 slots
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Idea

• Take advantage of the common letters in the words
• Reduce redundancy
• Use same letter for more than one word

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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

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Example
g
s
t
i
o
u
h
go
m
e
n
she
Make sure the word she is not found unless
it has been explicitly inserted!
sun
d
l
e
shed
time
l
shell
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example

• A trie for keys "t", "to", "te", "tea", "ten",
  "i", "in", and "inn".

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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

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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

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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