1. Data Structures and Analysis (COMP 410)
David Stotts
Computer Science Department
UNC Chapel Hill

2. Design Problem

3. Real Problem Type ahead
Like on google search, phone typing…
you type a few chars and the program fills in a list of possible choices for you… based on the prefix you have typed
Keep typing more chars, the choices narrow and change
Design a data structure that will let you do this
Describe the time complexity of using it…
searching it as typing is done,
generating alternatives, etc.

4. Take some time
Discuss an approach with your neighbor In 5-10 mins we will discuss ideas as a class

5. Let’s not use node to store a whole word Use child link to represent a char typed Path is then the word
Basic idea t
<root> n a a a e r o s e n
tar to as an a w
tea
new

6. Basic idea… This tree encodes (stores) these words:
tar, tan, tea, to, ton, toe, a, an, ant, as, net, nest, new, no t
<root> n a a n e
tan a o o r s n e no
tar to as an a n w t s e t
tea
ton
ant
new t
net
toe
nest

7. Representation How many children at each node?
As many as there are chars you can type
Let’s say 26 for this example
node { string val = null;
node[26] child = new [null,null,…,null];
boolean isWord = false; }

8. Representation
node { string val = null; node[26] child = new [null,null,…,null]; boolean isWord = false; }
val:
isWord: false
. . .
child:

9. Representation . . . . . . . . . . . . val: isWord: false child:
val: “b”
child:
isWord: false
. . .
val: “a”
child:
isWord: true
. . .
val: “be”
child:
isWord: true
. . .

10. Representation . . . . . . . . . . . . val: isWord: false child: b a a b e be
<root>
val: “b”
child:
isWord: false
. . .
val: “a”
child:
isWord: true
. . .
val: “be”
child:
isWord: true
. . .

11. Analysis
Big Oh time complexity is always expressed in terms of some problem size Here the problem size is not the number of words encoded in the tree, like we say for BST Rather we choose M, the length of a word being inserted or searched for

12. Analysis
The worst case time needed to find a word of length M is… O(M)
This is true if the tree contains 10 words or 10 million words
Length of the longest path in the tree is length of the longest word stored in the tree

13. This has a name Trie Pronounced “try” or “tree”, both ways
Or “trie tree” tree-tree, try-tree
Comes from “ re TRIE val ”
Used for prefix-based retrieval of strings formed over an alphabet

14. Beyond this is just templates
END
Beyond this is just templates