CX 103: Introduction to Computers

Lecture 23



 
 


 
 

Second Exam: Tomorrow

Focus of Exam

JavaScript

Fire in the Valley: Chapters 5 - 8

Closed Books & Notes, but

can bring 1 sheet of scribblings
 
 


 
 


 
 

Volunteer Opportunity

Design a Web Page for

The Middlebury Fire Department

Jennie Diggins

Volunteer Coordinator

Community Service Office

Middlebury College

802-443-3099
 
 

Searching Arrays

Linear Search

Verbal Description:

Compare Target with first element in the array

If identical, stop.

Otherwise move to the next element

Repeat

 Recursive Approach (Basic Idea)

LinearSearch(Low,High)

if (Target == TheArray[Low] ) STOP;

else LinearSearch(Low+1, Search)

(Need to clean up to handle what happens if Low = High and Target not yet found)
 
 




LINEAR SEARCH



INITIAL STEP



 
 
 
 

AFTER 1 STEP

AFTER 2 STEPS
 
 

Binary Search



Verbal Description:

Is Target >= Middle Element of current List?

If "Yes" then throw away bottom half of list

If "No" then throw away top half of list

Repeat until list has one element.

Is Target = remaining element?


function Binary(Low,High)

{ (provide escape clause when High = Low+1) else

Middle = Math.floor( (Low + High)/2 );

if ( Target >= TheArray[Middle] )

        Low = Middle;

else High = Middle;

Binary(Low, High);

BINARY SEARCH


INITIAL STEP
 
 
 

AFTER 1 STEP
 
 

AFTER 2 STEPS
 
 

AFTER 3 STEPS
 
 

Example: Is Homer in the List?

List is:
 
1) Andrew 9) Colin 17) Kennan 25) Rebecca
2) Annalise 10) DavidM 18) Liz 26) RyanB
3) Beth 11) DavidR 19) Louisa 27) RyanP
4) Bob 12) DavidS 20) Matt 28) Ted
5) Brendan 13) Eliza 21) Megan 29) Tejas
6) Casey 14) John 22) Missy 30) Trevor
7) CharlesM 15) Jordan 23) Nathaniel 31) Tyler
8) CharlesR 16) Kate 24) Rada 32) Veljko

Step 1: Could Target be in second half of the list?

Is Homer >= Name[17]?

Is Homer >= Kennan?

No
 
 
 
 

List is:
 
1) Andrew 9) Colin
2) Annalise 10) DavidM
3) Beth 11) DavidR
4) Bob 12) DavidS
5) Brendan 13) Eliza
6) Casey 14) John
7) CharlesM 15) Jordan
8) CharlesR 16) Kate

 

Step 2: Could Target be in second half of the list?

Is Homer >= Name[9]?

Is Homer >= Colin?

Yes

List is:
 
9) Colin
10) DavidM
11) DavidR
12) DavidS
 
13) Eliza
14) John
15) Jordan
16) Kate

 

Step 3: Could Target be in second half of the list?

Is Homer >= Name[13]?

Is Homer >= Eliza?

Yes
 
 

List is:
 
13) Eliza
14) John
 
15) Jordan
16) Kate

Step 4: Could Target be in second half of the list?

Is Homer >= Name[15]?

Is Homer >= Jordan?

NO

List is:
 
13) Eliza
 
14) John

Step 5: Could Target be in second half of the list?

Is Homer >= Name[14]?

Is Homer >= John?

NO

List is:
 
13) Eliza

Step 6: Is Target the remaining element?

Is Homer = Name[13]?

Is Homer = Eliza?


Example: Is Ted in the List?

List is:
 
1) Andrew 9) Colin 17) Kennan 25) Rebecca
2) Annalise 10) DavidM 18) Liz 26) RyanB
3) Beth 11) DavidR 19) Louisa 27) RyanP
4) Bob 12) DavidS 20) Matt 28) Ted
5) Brendan 13) Eliza 21) Megan 29) Tejas
6) Casey 14) John 22) Missy 30) Trevor
7) CharlesM 15) Jordan 23) Nathaniel 31) Tyler
8) CharlesR 16) Kate 24) Rada 32) Veljko

Step 1: Could Target be in second half of the list?

Is Ted >= Name[17]?

Is Ted >= Kennan?

Yes
 
 
 
 

List is:
 
17) Kennan 25) Rebecca
18) Liz 26) RyanB
19) Louisa 27) RyanP
20) Matt 28) Ted
21) Megan 29) Tejas
22) Missy 30) Trevor
23) Nathaniel 31) Tyler
24) Rada 32) Veljko

 

Step 2: Could Target be in second half of the list?

Is Ted >= Name[25]?

Is Ted >= Rebecca?

Yes

List is:
 
25) Rebecca
26) RyanB
27) RyanP
28) Ted
 
29) Tejas
30) Trevor
31) Tyler
32) Veljko

 

Step 3: Could Target be in second half of the list?

Is Ted >= Name[29]?

Is Ted >= Tejas?

No
 
 

List is:
 
25) Rebecca
26) RyanB
 
27) RyanP
28) Ted

Step 4: Could Target be in second half of the list?

Is Ted >= Name[27]?

Is Ted >= RyanP?

Yes

List is:
 
27) RyanP
 
28) Ted

Step 5: Could Target be in second half of the list?

Is Ted >= Name[27]?

Is Ted >= Ted?

NO

List is:
 
28) Ted

Step 6: Is Target the remaining element?

Is Ted = Name[28]?

Is Ted = Ted?

Does Binary Search Work?

Is it Efficient?
 
 

If it takes 6 steps to search a list of

32 names, how many steps does it take to search a list of 64 names?
 
 

Each doubling of the list size only increases the number of comparisons by 1.

With n comparisons, we can search an ordered list of 2^n elements.
 
Array size Number of steps
1000 10
1,000,000 20
1,000,000,000 30

BinarySearch.html

BinarySearch2.html

BinarySearch3.html
 
 

Multiple-Subscripted Arrays

Arrays and Computer Dating Services
 
  #1 #2 #3 #4 #5 #6 #7 #8 #9 #10
Andrew Yes No No Yes Yes Yes Yes No No No
Annalise Yes Yes Yes No No Yes No No Yes Yes
Beth Yes Yes No No Yes No Yes Yes Yes Yes
Bob No Yes Yes Yes No No No Yes No No
Brendan Yes No Yes Yes Yes No No Yes Yes Yes
Casey Yes No Yes Yes No Yes Yes No Yes Yes
Charles M Yes No No Yes Yes No Yes Yes No Yes
Charles R No Yes No Yes Yes No No Yes No No
Colin Yes Yes Yes No No No Yes Yes Yes Yes
David M Yes No Yes Yes No Yes No Yes Yes No
David R No No No No No Yes Yes Yes Yes No
David S Yes No No Yes No Yes No No No Yes
Eliza Yes Yes No Yes Yes No No Yes Yes Yes
John No Yes No Yes Yes No Yes No No Yes
Jordan Yes Yes No Yes Yes No Yes No Yes No
Kate Yes No No No No No Yes Yes No Yes
Kennan Yes Yes No No No No No Yes No Yes
Liz No Yes No Yes Yes No No No Yes Yes
Louisa Yes No No Yes No No Yes Yes No No
Matt No Yes No No Yes Yes No Yes Yes No
Megan Yes No No Yes Yes Yes Yes No Yes No
Missy No No No Yes No No No Yes No No
Nathaniel Yes No No No Yes No No Yes No Yes
Rada No No Yes Yes Yes No Yes Yes Yes Yes
Rebecca No Yes No Yes No No No Yes No Yes
Ryan B Yes No Yes Yes Yes Yes No No Yes No
Ryan P Yes Yes No No Yes No No No Yes Yes
Ted Yes No Yes Yes No Yes Yes Yes Yes Yes
Tejas Yes No Yes Yes No No Yes Yes Yes No
Trevor No Yes No Yes No Yes Yes No No Yes
Tyler No Yes No No No No Yes Yes Yes No
Veljko No Yes Yes Yes No No Yes No No Yes
                     

 


 
 
 
Casey Yes No Yes Yes No Yes Yes No Yes Yes
Eliza Yes Yes No Yes Yes No No Yes Yes Yes 4

 
 
Casey Yes No Yes Yes No Yes Yes No Yes Yes
Louisa Yes No No Yes No No Yes Yes No No 5
Brendan Yes No Yes Yes Yes No No Yes Yes Yes
Casey Yes No Yes Yes No Yes Yes No Yes Yes 6

 
 
 

Array of 32 students

Each student is represented by an array of 11 elements
 
 


An Array of Arrays

<HTML>

<HEAD>

<TITLE>Presidents</TITLE>

<SCRIPT LANGUAGE = "Javascript">

var President = new Array(5);

for (i = 0; i <= 4; i = i + 1)

President[i] = new Array(3);

President[0] [0] = "Name"

President[0] [1] = "Home State"

President[0] [2] = "Year Elected"

President[1] [0] = "Ronald Reagan"

President[1] [1] = "California"

President[1] [2] = "1980, 1988"

President[2] [0] = "George Bush"

President[2] [1] = "Maine"

President[2] [2] = "1988"

President[3] [0] = "Bill Clinton"

President[3] [1] = "Arkansas"

President[3] [2] = "1992, 1996"

President[4] [0] = "George W. Bush"

President[4] [1] = "Texas"

President[4] [2] = "2000"

document.writeln("<TABLE BORDER = '2' WIDTH = '100%' > ") ;

for (i = 0; i <= 4; i = i + 1)

{ for (j=0; j<=2; j=j+1)

document.writeln("<TD><H1>" + President[i][j] + "</TD>");

document.writeln("<TR>");

}

document.writeln(" </TABLE> ");

</SCRIPT>

</HEAD>

<BODY BGCOLOR = "cadetblue">

</BODY>

</HTML>

Presidents.html