CS 615: Design & Analysis of Algorithms Chapter 1: Introduction, Algorithmic Notation and...

CS 615: Design & Analysis of

Algorithms

Chapter 1: Introduction, Algorithmic Notation and

Flowcharts

April 20, 2023 CS 615 Design & Analysis of Algorithms 2

Course Content

1.1. IntroductionIntroduction, , Algorithmic Notation and Flowcharts (Brassard & Bratley, Chap. 3)

2. Efficiency of Algorithms (Brassard & Bratley, Chap 2)

3. Basic Data Structures (Brassard & Bratley, Chap. 5)

4. Sorting (Weiss, Chap. 7)5. Searching (Brassard & Bratley, Chap. 9)6. Graph Algorithms (Weiss, Chap. 9)7. Randomized Algorithms (Weiss, Chap. 10)8. String Searching (Sedgewick, Chap. 19)9. NP Completeness (Sedgewick, Chap. 40)

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Content

Text books, Lectures Assessments

Asymptotic NotationNotation for “the order of”Maximum RuleFlowchartsBasic Flowchart Constructions

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InstructorYusuf Altunel

Email:y.altunel@iku.edu.tr

Web:http://web.iku.edu.tr/~yaltunel

Tel:(212) 498 42 10

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Text BooksMain Resources

Data Structures and Algorithm Analysis in C, 2nd Edition; Mark Allen Weiss; Addison Wesley Longman, 1997Fundamentals of Algorithmics; Gilles Brassard & Paul Bratley; Prentice-Hall, 1996.Data Structures, Algorithms & Software Principles, Thomas A. Standish, Addison Wesley, 1995.

Other ResourcesAlgorithms, Richard Johnsonbaugh and Marcus Schaefer, Pearson, 2004, ISBN 0-02-360692-4. http://condor.depaul.edu/~rjohnson/algorithm/index.htmlAlgorithm Design: Foundations, Analysis, and Internet Examples; Michael T. Goodrich & Roberto Tamassia; Wiley, 2002, ISBN 978-0-471-38365-9. http://ww3.algorithmdesign.net/ Algorithms, Robert Sedgewick, Addison-Wesley 1983, e-book.

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LecturesCourses and labs

Day Hours Location

Theory Thu 11:00-12:45 (2 Hours) Lab 251

Lab Fri 11:00-12:45 (2 Hours) Lab 251

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Follow up the courseUse the web page of the coursehttp://web.iku.edu.tr/~yaltunel/Spring2005/CS615

Use the email group of the courseSend an empty email to subscribe:

CS_615-subscribe@yahoogroups.com To send a message:

CS_615@yahoogroups.comTo access on web:

http://groups.yahoo.com/group/CS_615

April 20, 2023 CS 615 Design & Analysis of Algorithms 8

AssessmentParticipation

%10

Project%30

MidTerm%30

Final%40

BonusGrading: %110%10 Bonus

•Please take care of the rules and regulations of the University.

•Otherwise you might be reported to the faculty, as well as lose all bonus options of this course.

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Project

A real world application with dynamically constructed graph should be implemented until the end of the semester!Details will be announced later!

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Algorithmic Notation and Algorithmic Notation and Flowcharts (Brassard & Flowcharts (Brassard & Bratley Chp: Chapter 3)Bratley Chp: Chapter 3)

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Asymptotatic NotationUsed to express

The time taken by an algorithmWithin a multiplicative constant

PermitsSimplification in measuring other tangible things

Deals withThe behavior of functions in the limits

For sufficiently large parameters

An asymptotically superior algorithm is very often preferable

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Notation for “the order of”f:NR0 be an arbitrary function

from the natural numbersto the nonnegative numbers

The mathematical symbol order of isdenoted by O(f(n))the set of all functions t: NR0 such that

t(n) cf(n) for all nn0

O(f(n))={t: NR0 |(cR+)(nN)[t(n) cf(n)]}Examples

f(n)=n3-3n2-n-8 O(n3)f(n)= n3 O(n3)

Maximum Rule:Let f,g: NR0 be two arbitrary functionsO(f(n),g(n))=O(max(f(n),g(n)))

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Example for Maximum RuleAn algorithm that proceeds in three steps:

InitializationTake time in O(n2)

ProcessingTake time in O(n3)

FinalizationTake time in O(nlogn)

The complete algorithm takes time inO(n2 + n3 + nlogn)= O(max(n2,n3,nlogn))=O(n3)

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Results of Maximum RuleIf t(n) is a complicated function

the most significant term of t(n) gives the order of function discarding its coefficient

Example:f(n)= 12n3- 5n2 + logn + 36

O(f(n))=O(n3)

f(n)= 999999n94 - 345n35 + 1O(f(n))=O(n94)

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Scale of Strength for O-Notation

the relationship between order of functions

O(1) < O(logn) < O(n) < O(nlogn) < O(n2) < O(n3) < O(2n) < O(10n)

O(1)O(logn)

O(n)O(nlogn

)O(n2)O(n3)O(2n)

O(10n)

Higher in order

Mor

e ef

fici

ent

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ExamplesWhat is the order of 18nlog2n + 19n + 3

=O(18nlog2n + 19n + 3)

=O(max (nlogn, n, 3) )=O(nlogn)

What is the order of n4 + 2n + 3nlogn + 3

=O(n4 + 2n + 3nlogn + 3)=O(max (n4, 2n, nlogn , 3) )=O(2n)

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Flowcharts

Process

Process

Decision

Data

Terminator

Display

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Basic Flowchart Constructions

FirstTask

NextTask

Sequence

Cond

ElsePart

ThenPart

F T

Cond

F

T

If Then Else Repeat-Until

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Basic Flowchart Constructions

Cond1

F

T

CondF

T

Selection (Case) While-Do

Cond2

...

T

Condn

F

T

...

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Basic Flowchart Constructions

for (i=1; i<n; i++) {..}for (<initialization>; <condition>; <post statement>) <statement>

initialization

Cond

statement

post statement

T

F

For statement

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Data Flow: Example

End

Cond1

Task2

FT

Start

Task1

Cond2

Task3

Task4

Cond3

FT

TF

StartTask1

if Cond1

thenif Cond2

then Task2

else Task3

else repeatTask4

until Cond3

End

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Example find Maximum

max<numberF

T

Start

get a number

max= infinitive

max=number

More numbers?T

end

Show max

T

F

Startmax= minimumdo

get a number if (max<number)then max = number

while more numbersshow max

End

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End of Chapter 1Introduction, Algorithmic Notation and Flowcharts