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. 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

8. 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; }

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

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

11. 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
. . .

12. 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

13. 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

14. Analysis
If a word of length M can be made from N different characters (like 26 in the alphabet) then the number of possible nodes in the data structure is M^N A trie to store words 20 character long in an alphabet of 52 chars (upper and lower) is 20^52

15. Analysis
Note that if we store 26 character words and limit us to lower case we get 26^26 possible nodes… This is slightly worse than 26 ! 26 * 26 * 26 * … * 26 Is worse than 26 * 25 * 24 * … * 2 * 1

16. Analysis
How bad is N! ? Lets compare let N = 20 2^N is 2^20 is about a million N! is 20! is e+18 2,432,902,000,000,000,000 2,432,902,000,000 * a million 2.4 trillion millions

17. So what?
A trie made to hold 20 character words… Made from 20 lower case characters Worst case find operation is O(20) or O(N) Worst case space… O(N!) So -- its very fast to use -- Impossible (very impractical) to build in time and space

18. Beyond this is just templates
END
Beyond this is just templates