Trie

1
Trie

• Irena Pevac
• CS501

2
Dictionary ADT

• Dictionary ADT is set of elements with the
  following basic operations
• insertion
• deletion
• lookup

3
Implementing Dictionary ADT

• Dictionary can be implemented with
• array
• sorted array
• linked list
• trie
• leftmost child - right - sibling
• binary search trees
• hash tables

4
Trie

• Trie is used to model dictionary ADT.
• We use tree where each node except the root has
  one character and a boolean value true or false.
• String of characters represented by a node n with
  boolean value true is the sequence of characters
  along the path from the root to n.

5
Example

• Construct a trie for the dictionary consisting of
  the following few words
• boot, root, bee, be, bond, boss, rose

6
Trie
7
Implementation of Trie

• For dictionary that contains words in English
  language we use a tree with nodes having one
  letter, one boolean and 26 references to at most
  26 children. The letter field of the root is
  irrelevant. Here we assume that only uppercase or
  only lowercase letters are used.
• Nodes in a trie in general have a branching
  factor equal to the number of different
  characters in the alphabet from which the words
  are formed.

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Cost of Basic Operations

• Insert O(1)
• Delete O(1)
• Lookup O(1)