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)


Content

Text books, Lectures Assessments

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


InstructorYusuf Altunel

Email:[email protected]

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

Tel:(212) 498 42 10


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.


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


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:

[email protected] To send a message:

[email protected] access on web:

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


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.


Project

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


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


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


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)))


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)


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)


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


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)


Flowcharts

Process

Process

Decision

Data

Terminator

Display


Basic Flowchart Constructions

FirstTask

NextTask

Sequence

Cond

ElsePart

ThenPart

F T

Cond

F

T

If Then Else Repeat-Until



Cond1

F

T

CondF

T

Selection (Case) While-Do

Cond2

...

T

Condn

F

T

...



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

initialization

Cond

statement

post statement

T

F

For statement


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


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


End of Chapter 1Introduction, Algorithmic Notation and Flowcharts

cs 615: design & analysis of algorithms chapter 1: introduction, algorithmic notation and...

Documents

algorithm analysis

htmlalgorithm design

flowcharts cs

graph algorithms weiss

randomized algorithms

algorithms software

algorithmic notation

sorting weiss