David Stotts Computer Science Department - PowerPoint Presentation

Slide1

David StottsComputer Science DepartmentUNC Chapel Hill

Data Structures

and Analysis

(COMP 410)

Design Problem

Type aheadLike 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 typedKeep typing more chars, the choices narrow and changeDesign a data structure that will let you do thisDescribe the time complexity of using it… searching it as typing is done, generating alternatives, etc.

Real Problem

Discuss an approach with your neighborIn 5-10 mins we will discuss ideas as a class

Take some time

Let’s not use node to store a whole wordUse child link to represent a char typedPath is then the word

Basic idea

e

t

a

tea

a

to

o

a

s

n

an

as

w

e

n

<root>

new

a

r

tar

Basic idea…

e

t

a

tea

a

to

o

a

s

ant

t

n

an

as

w

e

n

<root>

t

new

a

r

tar

This tree encodes (stores) these words:

tar, tan, tea, to, ton, toe, a, an, ant, as, net, nest, new, no

n

tan

ton

n

toe

e

o

no

s

net

nest

t

TriePronounced “try” or “tree”, both waysOr “trie tree” tree-tree, try-treeComes from “ re TRIE val ”Used for prefix-based retrieval of strings formed over an alphabet

This has a name

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

Representation

node { string

val = null; node[26] child = new [null,null,…,null]; boolean isWord = false;}

Representation

val:

child:

isWord: false

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

Representation

val

:

child:

isWord

: false

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

val

: “a”

child:

isWord

:

true

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

val

: “b”

child:

isWord

:

false

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

val

: “be”

child:

isWord

:

true

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

val

:

child:

isWord

: false

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

val

: “a”

child:

isWord

:

true

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

val

: “b”

child:

isWord

:

false

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

val

: “be”

child:

isWord

:

true

. . .

0 1 2 3 4 5 6 7 . . . 22 23 24 25

a

b

e

be

<root>

a

Representation

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

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 wordsLength of the longest path in the tree is length of the longest word stored in the tree

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 isM^N A trie to store words 20 character long in an alphabet of 52 chars (upper and lower) is20^52

Analysis

Note that if we store 26 character words and limit us to lower case we get26^26 possible nodes…This is slightly worse than 26 !26 * 26 * 26 * … * 26Is worse than26 * 25 * 24 * … * 2 * 1

Analysis

How bad is N! ?Lets compare let N = 202^N is 2^20 is about a millionN! is 20! is 2.432902e+182,432,902,000,000,000,0002,432,902,000,000 * a million2.4 trillion millions

Analysis

A trie made to hold 20 character words… Made from 20 lower case charactersWorst 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

So what?

Beyond this is just templates

END