instructor data structures pasko.org/gip and algorithms

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Data Structures and Algorithms

Instructor:

Dr.Pasko Galina

Sprıng 2009, EUL

Instructor

Education

1983 M. Sc., Moscow Engineering Physics Institute (MEPhI), Russia, Moscow

2005 Dr. Eng., Kanazawa Institute of Technology, Tokyo, Japan

Other interests:

Japanese tea ceremony (sado)

Japanese flower arrangement (ikebana)

Japanese poetry (haiku)

pasko.org/gip

Instructor

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3

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Research/ Education

*Function-based shape modelingand multidimensional modeling

*Visualization *Computer animation

*Digital fabrication (4)*Preservation of cultural heritage

Research Description

Solving actual long-standing

problems in the following computer graphics areas:

(1) Bounded blending operations (2) Space-time blending and

metamorphosis

(3) Trimmed implicit surfaces

pasko.org/gipCourse Evaluation

Assignments – 10%Quizzes – 10%

Attendance – 10% Midterm tests – 30%

Final test - 40%

Course information is at

pasko.org/gip/DSA

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Info

• The course can be given in Fortran, Pascal, C,

C++, Turbo C, Java, Perl, Lisp, Ada, pseudo-

code and many other languages.

• This course is not about any particular

programming language, the lectures are 90%

language independent.

• The assignments will be done in a C

programming language.

Course topics

• Software development

• Linear structures (lists, stacks and queues)

• Nonlinear structures (trees and graphs)

• Elementary sorting and searching methods

• Basics of algorithm analysis


Introduction to

Data Structures and

Algorithms


SequoiaView

Contents

• ACM Computing Classification System

• Basic terminology

•Data and Data Structures

• Algorithms and Turing machine

• History of computing

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The ACM Computing Classification System (1998)

• A. General Literature

• B. Hardware

• C. Computer Systems Organization

• D. Software

• E. Data• F. Theory of Computation

• G. Mathematics of Computing

• H. Information Systems

• I. Computing Methodologies

• J. Computer Applications

• K. Computing Milieux

http://www.acm.org/class/1998/TOP.html

Notion of Data

Etymology

The word data is the

plural of Latin datum,

"something given".

Work of Euclid (300 BC)

was titled Dedomena(in Latin, Data).

Euclid(325BC-265BC)

• Representation of facts, concepts, or

instructions in a formalized manner

suitable for communication,

interpretation, or processing by humans

or by automatic means.

• Any representations such as

characters or analog quantities to which

meaning is or might be assigned.

Notion of Data

UsageNotion of Data

In discussions of problems in mathematics

and engineering, the terms givens and

data are used interchangeably.

Such usage is the origin of data as a

concept in science: data are numbers,

words, images, etc., accepted as they

stand.

Usage in science

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Numerical or other information represented in a form suitable for processing by computer: numbers, characters, images or other outputs from devices to convert physical quantities into symbols.

Usage in computing

Notion of Data

Such data are typically further used by a human or input into a computer, stored and processed there, or transmitted (output) to another human or computer.

Input data Computer Output data

Usage in computing

Notion of Data

Notion of Structure

• Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities.

• The structure of a thing is how the parts of it relate to each other, how it is "put together".

• Both reality and language have structure. One of the goals of science is to create and use language the structure of which accurately parallels the structure of reality.

Notion of Data Structure

Data Structure is a systematic way of

organizing and accessing data

Real world: Filing cabinet

Cyber world : Hierarchical file system

Data structure is also a way of

storing data in a computer so that it

can be used efficiently

Data structure is an actual

implementation of a particular

abstract data type

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Types of Data and Data Type

� Categorical

• Nominal

• Ordinal

• Quantitative

� Measurement

• Continuous data

• Discrete data

• Topology/ structure

data

Data type is an

attribute of a data

which tells what

kind of data it is.

Involves setting constraints on the

datum: what values

it can take and what

operations may be

performed upon it.

Types of Data

• The objects being studied are grouped into categories based on some qualitative trait.

Examples:

�Car color- silver, black, red, blue, etc.

�Opinion of staff about internet connection- good, neutral, bad

�Swimming status- swimmer, non- swimmer

• Commonly are summarized using “percentages” or “proportions”:– 11% of students have a car

Categorical

Categorical Data

• Nominal data - a type of categorical data in

which objects fall into unordered categories,members of some class:

[Tokyo, Moscow, Dubai, Lefke] or [orange, apple, grapefruit]

• Ordinal data - a type of categorical data in

which order is important:

[low, medium, high] or [tiny, small, large, huge]

• Quantitative data - precise numerical values:[ 1; 2.5 ; 0.3E-11 ]

Nominal, Ordinal, Quantitative

graphics.stanford.edu/papers/webviz/

Binary data

• A type of categorical data in which there are only two categories.

• Can either be nominal or ordinal.

• Examples:

Attendance: present or absent

Numbers: 0 or 1

Answers: yes or no

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Measurement data

• The objects being studied are “measured” based on some quantitative trait.

• The resulting data are set of numbers.

• Examples:

� Sugar level

� Weight

� Age

�Time to complete a project

�Number of students late for class

• Measurement data are typically summarized using “averages” or “means”:– Average number of spring semesters students is 200.

Types of Data

• Theoretically, any value within an interval is

possible with a fine enough measuring device.

• Functions: λi = fi (X), where

X = (x1, x2,…, xn), i=1, …, m

xj are independent variables

λi are dependent variables (“parameters”,

attributes)

n>3 multidimensional, multivariate data

m>1 multiparameter data

Measurement Data

Continuous Data

• Only certain values are possible (there are gaps between the possible values).

• Scalar (single integer or real numerical value)

• Scalar array- indexed set of scalar values- 1D (linear) array: samples of y = f(x) - 2D array: image or samples of z = f(x,y)- 3D array: volume data (3D image) or samples

of λ = f(x,y,z)- 4D array: time-dependent volume data or

samples of λ = f(x,y,z,t)- nD array: hypervolume data

Measurement Data

Discrete Data

Discrete data - Gaps between possible values

0 1 2 3 4 5 6 7

0 1000

Continuous data - Theoretically, no gaps

between possible values

Measurement Data

Examples

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Examples

• Discrete:

�Number of crimes reported to police

�Number of times the word is used in the text

�Generally, discrete data are counts.

• Continuous:

�Sugar level

�Age

�Time to complete a project

�Generally, continuous data come from measurements.

Measurement Data

Topology/structure data

• Sequential (text)

• Network

(hypertext,

molecules, Web)

• Hierarchical

(catalogs)

• Relational

(databases)

Measurement Data

infocult.typepad.com/infocult/weblogs/

• Computers are machines that can be programmed to accept data and transform it into useful information

� Computers can do simple operations incredibly fast if you tell them every step to do

RRRR epetition is the m other of educationepetition is the m other of educationepetition is the m other of educationepetition is the m other of education

Nature of a Computer System


• Basic parts of a Computer System are

simple in concept:

– A way (or ways) to get information IN

– A way of storing that information, even temporarily

– A way (or ways) of manipulating that information

– A way (or ways) to get resultant information OUT

! This is the classic definition of a “System”

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Computer consists of only 2 main things:• Storage for data (memory)

• Processor(s) for manipulating data

Types of storage:• Main memory

• External memory: disks, tapes, diskettes, etc.

“Peripheral” input-output devices:

monitor, mouse, keyboard, speakers,

scanners, printers, other drives, etc.


Difference between hardware and software:

Hardware: The physical elements of a

computing system (circuits, wires, disks)

Software is divided into two general

categories: data and programs.


Communication

Application

Operating System

System Programming

Hardware

Data/ Information

Layers of a Computing System

Nature of Software

• What is a program?A set of instructions and data, expressed using

programming language, designed to accomplish

a specific task.

• A program is constructed similar to a Computer System. It needs:

– A way (or ways) to get information IN

– A way of storing that information, even temporarily

– A way (or ways) of manipulating that information

– A way (or ways) to get resultant information OUT

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Nature of a Programming Language

• What is a programming language?- A set of symbols and a grammar for using those

symbols in order to specify the instructions and data.

- Symbols are written using an alphabet (mainly in English)

- Programming languages have inverse evolution of human

languages, but have the same purpose.

• What is that purpose?

• Basic features of a programming language:

� Ways to represent information - data types

� Ways to act on information - operations

Elements of a C Program

Usage in computing

Data Types in C

PRIMARY

1. INT

2. FLOAT

3. CHAR

SECONDARY

1. ARRAY

2. STRUCTURE

3. UNION

4. POINTERS

USER

DEFINED

1. ENUM

2. TYPEDEF

C program is essentially a group of functions which act on data.


• Data are stored in named data structures.

• Variables represent data.

Variables are named data structures:– int age;

– double salary;

– char letter;

• We can build more complicated data structures, but

every data structure has type, and value.

• Named data structure also has name (also called

identifier)

Usage in computing

Declaration of Variables

Every variable used in the program should be declared to the compiler. The declaration does two things:1. Tells the compiler the variables name. 2. Specifies what type of data the variable will hold.

The general format of any declaration

datatype v1, v2, v3, ……….. vn;

Where v1, v2, v3 are variable names. Variables are separated by commas. A declaration statement must end with a semicolon.

Example:

Int sum; Int number, salary; Double average, mean;

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Example:

struct employee {

char *name;

char *address;

float salary;

int idNumber;

}

struct employee john;

john.salary = 112.59;

A structure in C is

an object that

consist of named

members,

possibly of different

types.

The members have

public access.

Data structures and algorithms

• Usually developed hand-in-hand

Example: Pushing and popping from a stack

• The behavior of an algorithm depends on how

the data is structured

Example: Searching a disc vs. searching a tape

Tape: fast-forward, rewind

Disc: select a track

vs.

Notion of algorithm

• Word algorithm comes from the name of the 9th

century Persian mathematician Abu Abdullah

Muhammad bin Musa al-Khwarizmi.

• Word “algorism” originally referred only to the

rules of performing arithmetic using Hindu-

Arabic numerals but evolved via European Latin

translation of al-Khwarizmi's name into algorithm

by 18th century.

• Word evolved to include all definite procedures

for solving problems or performing tasks.

• In mathematics and computer science, an algorithm is a procedure (a finite set of well-defined instructions) for accomplishing some task which, given an initial state, will terminatein a defined end-state.

• Algorithms have steps that repeat (iterate) or require decisions (such as logic or comparison).

• The concept of an algorithm originated as a means of recording procedures for solving mathematical problems such as finding the common divisor of two numbers or multiplying two numbers.

Notion of algorithm

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• Concept of algorithm was formalized in 1936 through Alan Turing's Logical Computing Machine and Alonzo Church’s lambda calculus, which in turn formed foundation of computer science.

• Most algorithms can be implemented by computer programs.

Algorithm

Turing Digital Archive

http://www.turingarchive.org/

Turing, Alan Matheson

(1912-1954)

Turing Machine

• A Turing machine

consists of a

control unit with a

read/write head

that can read and

write symbols on

an infinite tape

Turing Machine

Turing machine consists of:

• Infinite tape divided into cells, one next to the

other. Each cell contains a symbol from some

finite alphabet.

• Head that can read and write symbols on the

tape and move left and right only one step at a

time.

A full-scale Turing machine simulator is supplied by Stanford University's Turing's World software.

• A state register that stores the state of the

Turing machine. The number of different states

is always finite and there is one special start

state.

• An action table that tells the machine what

symbol to write, how to move the head and what

its new state will be, given the symbol it has just

read on the tape and the state it is currently in.

Turing Machine

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The following Turing machine has an alphabet {'0', '1'} with 0 being the blank symbol. It expects a series of 1s on the tape, with the head initially

on the leftmost 1, and doubles the 1s with a 0 in between, i.e., "111"

becomes "1110111". The set of states is {s1, s2, s3, s4, s5} and the start

state is s1. The action table is as follows.

Turing Machine

Action table

Turing Machine

• Why is such a simple machine (model) of any importance?

– It is widely accepted that

anything that is intuitively

computable can be computed

by a Turing machine

– If we can find a problem for

which a Turing-machine solution

can be proven not to exist, then

the problem must be unsolvable

Abacus An early device to record numeric values

Blaise Pascal (1645)The first digital calculator (mechanical device to add, subtract, divide and multiply)

Joseph Jacquard (1801)Jacquard’s Loom, the punched card

Charles Babbage (1823)Analytical Engine

Early History of Computing

Ada Lovelace (1843 )First Programmer, the loop

Alan Turing (1930)Turing Machine, Artificial Intelligence Testing

Harvard Mark I (1944), ENIAC (1946), UNIVAC I (1950), EDVAC (1952)

Mark I was the first large-scale automatic digital computer in the USA.

Early History of Computing

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Vacuum TubesLarge, not very reliable, generated a

lot of heat

Magnetic Drum Memory device that rotated under a read/write head

Card Readers �� Magnetic

Tape DrivesDevelopment of these sequential auxiliary storage devices

First Generation Hardware (1951-1959)

funsan.biomed.mcgill.ca

TransistorReplaced vacuum tube, fast,

small, durable, cheap

Magnetic CoresReplaced magnetic drums,

information available instantly

Magnetic DisksReplaced magnetic tape, data can be accessed directly

Second Generation Hardware (1959-1965)

www.ti.com/corp/docs/press/library/index.shtml

Integrated CircuitsReplaced circuit boards, smaller, cheaper, faster, more reliable.

TransistorsNow used for memory construction

TerminalAn input/output device with a keyboard and screen

Third Generation Hardware (1965-1971)

www.ieicorp.com/micro/micro4.htm

Large-scale IntegrationGreat advances in chip technology

PCs, the Commercial Market, WorkstationsPersonal Computers were developed as new companies

like Apple and Atari came into being. Workstations emerged.

Fourth Generation Hardware (1971-)

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Parallel ComputingComputers rely on interconnected central processing units that increase processing speed.

NetworkingWith the Ethernet small computers could be connected and share resources. A file server connected PCs in the late 1980s.

ARPANET and LANs �� Internet

Parallel Computing and Networking

Machine LanguageComputer programs were written in binary code

Assembly Languages and translatorsPrograms were written in artificial programming languages and were then translated into machine language

Programmer ChangesProgrammers divide into application programmers and systems programmers

First Generation Software (1951-1959)

High Level LanguagesUse English-like statements and made programming easier:

Fortran, COBOL, Lisp.

High-Level

Languages

AssemblyLanguage

MachineLanguage

Second Generation Software (1959-1965)

Third Generation Software (1965-1971)

• Systems Software

– utility programs,

– language translators,

– and the operating system, which decides which programs to run and when.

• Separation between Users and Hardware

Computer programmers now created programs

to be used by people who did not know how to

program

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Programmer / User

Applications Programmer

(uses tools)

User with No

Computer Background

Systems Programmer

(builds tools)

Domain-Specific Programs

Computing as a Tool

Application Package

System Software

High-Level Languages

Assembly Language

Machine Language

Third Generation Software (1965-1971)

Structured ProgrammingPascal, C, C++

New Application Software for UsersSpreadsheets, word processors, database management

systems

Fourth Generation Software (1971-1989)

Windows and UnixThe Windows and Unix operating systemdominate the computing world.

Object-Oriented DesignBased on a hierarchy of data objects (C++, Java)

World Wide WebAllows easy global communication

through the Internet

New UsersToday’s user needs no computer knowledge

Fifth Generation Software (1990- present)

graphics.stanford.edu/papers/webviz/

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References

• Yashavant P. Kanetkar, Data Structures through C, BPB Pub., 1st Ed, Reprinted 2007

• Amit Gupta, Data Structures through C, Galgotia Booksource P. Ltd., 2001.

• Nell Dale “C++ Plus Data Structures”, 4-th ed., John and Bartlett pub., Sudbury, Massachusetts, 2006.

References

• The ACM Computing Classification System [1998 Version], valid in 2006http://www.acm.org/class/1998/

• Turing Machineshttp://plato.stanford.edu/entries/turing-machine/

• On-line encyclopedia Wikipedia www.wikipedia.org

• NIST Dictionary of Algorithms and Data Structureshttp://www.nist.gov/dads/

instructor data structures pasko.org/gip and algorithms

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