Data Structure and Algorithm Design · Data Structure 10 A data structure is a logical representation to understand physical representation. “Clever”ways to organize information

Lecture 1 to Lecture 8

Theory

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020

University of Salahaddin-HawlerCollege of EngineeringSoftware and Informatics Engineering DepartmentFirst Year Class

Lecture 1

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020


Objectives

3

The students in this course will learn how the data structures are

built

The course, intended to clarify the concepts used to build data inside

computer and how different searching and sorting techniques are

applied to it.

Finally, the student will be introduced to different techniques of

building algorithms.

Syllabus

4

The following topics will be covered:

o Introduction to the course and data

structure concepts and mechanisms

o Asymptotic Complexity

o Abstract Data Type Stack

Queue

Linked List

o Pointer and heap memory.

o Tree Data Structure

o Sorting Algorithms

oSearching Algorithms

oGraph Theory and its

algorithms

References

5

Data Structurs, Algorithms and Application in C++ by S. Sahni,

any edition

Data Structure and Programming Design in C++ by Krurse and

Ryba, Prentice Hall, any edition.

Algorithms and Data Structures by Kurt Mehlhorn and Peter

Sanders, any edition.

Advanced Data Structures by Prof. Erik Demaine, Notes

Collection.

Fundamentals of Data Structures by Ellis Horowitz and Sartaj

Sahni

Course Overview

6

Introduction to many of the basic data structures used in computer

software

Understand the data structures

Analyze the algorithms that use them

Know when to apply them

Practice design and analysis of data structures.

Practice using these data structures by writing programs.

Goals

7

You will understand

what the tools are for storing and processing common data types

which tools are appropriate for which

So that you will be able to

Justify your design decisions via formal reasoning

Communicate ideas about programs clearly and precisely

Terminology

8

Abstract Data Type (ADT)

Mathematical description of an object with set of operations on the

object. Like stack, queue,…

Data Type

A data type is a well-defined collection of data with a well-defined

set of operations on it.

Data Types versus Data Structure

9

Algorithm

A high level, language independent, description of a step-by-step

process

Data structure

A specific family of algorithms for implementing an abstract data

type.

Implementation of data structure

A specific implementation in a specific language

Data Structure

10

A data structure is a logical representation to understand physical

representation.

“Clever” ways to organize information in order to enable efficient

computation

A data structure is a particular way of storing and organizing data in

a computer so that it can be used efficiently.

Data Structure Continue

11

Data structures organize data

more efficient programs.

More powerful computers

more complex applications.

More complex applications demand more calculations.

Complex computing tasks are unlike our everyday experience.

Data Structure Features

12

Ideal data structure:

“fast”, “elegant”, memory efficient

Generates tensions:

time vs. space

performance vs. elegance

generality vs. simplicity

one operation‟s performance vs. another‟s

Organizing Data

13

Any organization for a collection of records can be searched,

processed in any order, or modified.

The choice of data structure and algorithm can make the difference

between a program running in a few seconds or many days.

Efficiency

14

A solution is said to be efficient if it solves the problem within its

resource constraints.

Space

Time

The cost of a solution is the amount of resources that the solution

consumes.

Introduction to C++ Programming Language

15

To be able to write effective programs, one needs to know a few

things:

Mastery of the tools-of-the-trade (programming language,

development environment etc.)

The ability to analyze a “real world” problem and to construct a

model for it suitable for programming.

Careful design of an algorithm and user-interface for the program

at hand.

Knowing the techniques that have made other programmers more

effective.

Variables

16

A variable is a placeholder used for storing data.

The type of data may be numerical, string, character and any other type that the

language supports

The data in a variable is called its value and it can be changed or deleted.

In order to uniquely identify and keep track of a variable, we need to give each

variable a name; this is called declaring a variable.

For example: int books; double myWeight;

The books variable is declared of type integer, and the variable myWeight is of

type double, its value can be a number with a fraction like 1.3. declaration

statements end with simi colon)

Assignment Statements

17

Values can be assigned or stored in variables with assignment statements:

books=34;

An assignment statement is an order, to the computer, to assign the value on

the right-hand side of the equal sign to the variable on the left-hand side. The

sign (=) is called the assignment operator. (Assignment statements end with a

semicolon.)

The value on the right-hand side can also be another variable or expression:

books1=books2;

In an assignment statement, first the value on the right-hand side is evaluated

and then its result is stored or assigned to the variable on the left-hand side.

Performing Output

18

The values of variables, numerical values and strings of text, maybe output to the

screen using cout as in:

int books=0;

cout<<books<<endl;

cout<<72<<endl;

cout<<“This is the output”<<endl;

In the first output statement, the value of variable books will be output on the

screen, which is 0; In the second, the numerical value 72 will be output to the

screen, and in the last statement, the string “This is the output” will be output to

the screen.

Performing Output Continue

19

Typically, you would want a newline to appear after some output to the screen; to

force a newline the C++ keyword endl is appended at the end of the line. A second

method for forcing a newline is using the escape character \n as in:

cout<<“Hello everyone \n”;

But this is only possible when the output is a text of string.

You can also combine a number of outputs in a single output statement as in

cout<<“iam“<<18<<“yearsold”<<endl;

To force a blank line on the screen use either

cout<<endl; or cout<<“\n”;

The double arrow signs (<<) are called the insertion operators.

Lecture 2

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020


Performing Input

21

In C++, cin is used to input values into variables.

int price;

cout<<“Enter the price:”;

cin>>price;

cout<<“The price you entered is $“<<price<<endl;

In this program extract, first an integer is declared, then the user is asked to

enter / type a value for price. This value is then input in the variable price

using cin. A message is also output to the screen notifying the user of the

input value.

Performing Input Continue

22

To have more than one input value entered at the keyboard:

int price1, price2; //(two variables of type int)

cout<<“Enter two prices:”<<endl;

cin>>price1>>price2;

Or you could have two separate cin statements. After each input, the

computer waits for user to input some value. Then the user must type a

space or a tab or a newline to separate the two input values.

A cin statement sets the value of a variable equal to values typed at the

keyboard.

Basic Data Types Continue

23

Notice that character values are placed inside single quotes. While the string data

type where the string of text is placed inside double quotes as in:

char a;

cin>>a;

cout<<“Ths is a character value :”<<a<<“\n While

this is string of text.”<<endl;

So, in C++ the character „A‟ is treated differently from “A” since the first is

considered a character and the second a string.

Values of type bool are called boolean expressions and include only two values:

true or false. Boolean expressions are used in branching and looping statement

Simple C++ Program

24

E.x1: we will write our first complete C++ program.

1.#include<iostream>

using namespace std;

2.int main()

3. {

4. int hours=0;

5. cout<<“How many hours/ week do you practice C++?”;

6. cin>>hours;

7. cout<<“You practice“<<hours<<“per week.”<<endl;

8. return 0;

9. }

Simple C++ Program Continue

25

Line 1:

This include statement directs the C++ compiler to include the

iostream.h library file with the program. This library contains

input/ouput function definitions of the C++ language cin and cout.

Line 2:

Every C++ program must have a function called main. This function has

a body consisting of program statements to be executed in sequence by

the computer.


26

Lines 3, 9:

Every main function starts with an open bracket { and ends with a

close bracket }.

Line 4:

in this line we declare and initialize a variable of type int.

Lines 5:

Here, we are just outputting some text to the screen.

Line 6:

We capture the user input value and store it in a variable.


27

Line7:

In this line, we output some text and at he value of the variable hours.

Line8:

Here, at the end of the program, were turn control to the operating

system and declare that the program has finished its execution.

Important Note

The important thing to remember is that all C++ programs must have

a function called main and that program execution begins and ends

inside this method.

Arithmetic Operator

28

The main C++ arithmetic operator are the following:

+ for addition

- for subtraction

* for multiplication

/ for division

% for division with remainder

Arithmetic Operator Continue

29

Division Operator (/)

If both operands are of type int, the result is of type int. If one, or both operands

are of type double, the result will be of type double.

Remainder Operator(%)

The % operator can be used with operands of type int to recover the information

lost when you use / to do division with operands of type int; for example:

cout<<“11 divided by 3 is “<<11/3<<endl;

cout<<“with a remainder of “<<11%3<<endl;

Output:??????

Precedence Rules

30

You can specify the order of operations in C++ using parentheses as illustrated in

the following expressions:

1: (x+y)*z; the computer first adds x to y and then multiplies the result by z.

2: x+(y*z); the computer first multiplies y by z and then adds the result to x.

If you omit the parentheses, the computer will follow the C++ rules of precedence.

So, if you wrote x+y*z, the computer would multiply y by z and add the result to

x. Because * has higher precedence than +. (the same is true for / and %)

Constants

31

Constants in a C++ program is as follows:

const int ENGINEERING_AVERAGE=90;

if (student_grade>= ENGINEERING_AVERAGE)

cout<<“Engineering Student”<<endl;

else

cout<<“Science Student”<<endl;

This could be a large program and there could be many places where the

constant engineering_average is used. To change eng.average for next year, we

only need to change the value at one place. It‟s common to use capital letters

for constants.

If-Else Statements

32

The general form of the C++ if-else-statement is as follows:

if(Boolean-expression)

yes-statement

else

no-statement

When program execution reaches the if-else-statement only one of the two

statements is executed .If the Boolean-expression is true then the yes-

statement is executed, if the Boolean-expression is false then the no-statement

is executed.

If-Else Statements Continue

33

The table below is the full list of comparison operators in C++:


34

E.x2: Suppose your program asks the user about the amount of time per week he/

she spends on practicing C++. And you want the program to decide whether or not

this is enough. Assume that 4hours/week of practice is enough. Any thing less is

not good enough.

#include <iostream.h>

main()

{

int hours_per_week=0;

cout<<“How many hours/week do you practice C++?”;

cin>> hours_per_week;

if (hours_per_week>=4)

cout<<“That‟s good ”<<endl;

else

cout<<“That‟s not good enough”<<endl;

return 0;

{


35

You may want to execute more than one statement inside an if-else statement.

To do this, enclose the statements inside brackets { }. For example:

if (grade >=50)

{

cout<<“ The student has passed”<<endl;

passed-students +=1;

}

else

{

cout<<“Student has failed”<<endl;

failed-students +=1;

}

A list of statements enclosed inside brackets is called a compound statement.

If Statements

36

The C++ if-statement like Java if-statement test a condition and if the condition is

satisfied the program does something, otherwise it does not do anything.

You can do this by omitting the else part from the if-else-statement. For example:

if (grade>=50)

cout<<“The student has passed.”<<endl;

cout<<“……”<<endl;

So, if the Boolean expression is not satisfied, the cout statement will not be

executed and program execution will go to the second cout line.

Nesting If-Else Statements

37

by nesting if-else statements, you have a three- or four-way branch so that your

program can choose between more than two alternative actions.

E.x3/ Suppose we want to write a game-playing program in which the user

must guess the value of some number.

cout<<“Guess the number: “;

cin>>guess;

if (guess >50)

cout<<“No, too high”;

else if (guess==50)

cout<<“Correct!”<<endl;

else

cout<<“No, too low”<<endl;

Lecture 3

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020

University of Salahaddin-HawlerCollege of EngineeringSoftware and Informatics Engineering DepartmentFirstYear Class

Loops

39

C++ has a number of ways to create loops. One of them is called a (1-while-

statement or while-loop).

E.x:


main()

{

int num_of_greetings=0;

cout<<“How many greetings do you want?”;

cin>>num_of_greetings;

while (num_of_greetings> 0)

{

cout<<“Hello “;

num_of_greetings=num_of_greetings-1;

}

return 0;

}

Loops Continue

40

The section between the brackets { and } is called the body of the while-loop.

It is the action that is repeated a number of times. Each repetition of the loop

is called an iteration of the loop.

If the user enters 0 at the keyboard, the loop body is executed zero times, that

is, it is not executed at all. Because, the Boolean-exp is not satisfied and

program execution proceeds with the following line after the while-loop.

You should be sure that the loop ends at some point. Otherwise, the loop will

run forever. In this example, we decrease a variable value after each iteration.

We decrease it by one after each iteration. This is called decrementing.

Loops Continue

41

2-The do-while loop statement is similar to the while-loop statement, except that

the loop body is executed at least once. The syntax of do-while loop statements is

as follows:

do

{

Statement_1;

Statement_2;

…

Statement_n;

} while (Boolean-expression);

Loop body is executed once first, then the Boolean expression is checked for

additional iterations of the loop body.

Loops Continue

42

E.x6/ An example involving a do-while loop statement:


main()

{

int num_of_greetings=0;

cout<<“How many greetings do you want?”;

cin>>num_of_greetings;

do

{

cout<<“Hello “;

num_of_greetings=num_of_greetings-1;

} while (num_of_greetings> 0)

return 0;

}

Loops Continue

43

3-For Loop

In performing numerical calculations, it is common to do a calculation with the

number one, then with the number two and so forth until some last value is

reached.

For example to add one through ten you want the computer to perform the

following statement ten times with the value of n equal to1 the first time and with

n increased by one each subsequent time.

sum=sum+n

Loops Continue

44

The following is one way to accomplish this with a while statement:

sum=0;

n=1;

while (n<=10)

{

sum=sum + n;

n++;

}

Although awhile-loop is OK here, this kind of situation is just what the for-loop

was designed for. The following for-loop will neatly accomplish the same thing:

sum=0;

for ( n=1; n <= 10; n++)

sum=sum + n;

E.x9/ Write a program to sum the numbers from 1 to 10.

Increment and Decrement Operators

45

The C++ language has two more unary operators ++ and --. The ++ operator is

called the increment operator and – the decrement operator. They are usually use

in variables of type int. The operator ++ increases a variable‟s value by one and –

decreases a variable value by one.

int count=5;

count++;

cout<<“Count is changed to“<<count<<endl;

count--;

cout<<“Count is changed to“<<count<<endl;

Functions and Procedural Abstraction

46

A natural way to solve large problems is to break them down into a series

of smaller sub-problems, which can be solved more-or-less independently

sub-programs and then combined to arrive at a complete solution; in C++

sub-programs are called functions.

There are pre-defined functions that we can use in our programs; we even

don‟t need to know how the are defined as long as we know how to use

them.

You can have user-defined functions too. You can define your own

functions to do specific tasks.

Functions Continue

47

E.x11/Write a function to return area of a rectangle, test your function in a

complete C++ program


int area(intlength, intwidth);//function declaration

main()

{

int this_length, this_width, rectangle_area;

cout<<“Enter the length followed by width:”;

cin>>this_length>>this_width;

//function call

rectangle_area=area(this_length, this_width);

Functions Continue

48

cout<<“The rectangle area is“<<rectangle_area<<endl;

return 0;

}

int area(intlength, intwidth)//start of function definition

{

int number;

number= length * width;

return number;//function returning a value

}

Void Function

49

In C++ a function that returns no value is called a void function.

E.x/

void myFunction(int num);

main()

{

int x=0;

myFunction(x); //function call

retrun 0;

}

void myFunction(int num)

{

num++;

cout<<“ one plus your number is “<<num<<endl;

}

Array

50

In C++ the array elements are stored in contiguous memory locations. The lowest

address refers to the first element and the highest address refers to the last element.

For example, to store a list of exam marks for students we can use an array as in:

int mark[5];

This array is of type integer and it can hold 5 variables of type integer. Mark is the

name of this array.

Array elements are numbered from 0. That is, the index of the first Element in the

array is 0 and the index of the last element is one less than the size of the array. ( in

this example, first element has index 0 and last element has index 4)

Array Continue

51

You can initialize arrays in this way:

int mark[5]={87,67,90,89,100};

int mark[]={87,67,90,89,100};

To access array elements we use the array name plus the index of the required

element.

Array Continue

52

E.x/Write a C++ program to output the numbers from 1 to 5.


main()

{

int number[5];

for (int i=0; i<5; i++)

{

number[i]=i;//initialize the array

cout<<i;

cout<<"\t"<<(number[i] * number[i])<<endl;

}

return 0;

}

Array Continue

53

To calculate the address of any element of one dimensional array we use this

syntax:

Location (A[i]) = Base address + (i*size)

i: is address of the current element.

size: is the size of the array type.

Ex.17/ If base address=800, calculate the address of(short A[2])?

Location (A[2]) = BA + i*sizeof(A[2])

So:

Location (A[2]) = 800 + 2*2

=804

Two Dimensional Array

54

In C++ arrays of arrays are called multi dimensional arrays.

The most common form of a multidimensional array is a two-dimensional array

which is similar to a rectangular structure divided in to rows and columns. This

type of two-dimensional array is called a matrix.

Consider the two-dimensional array matrix:

int matrix[2][3]={{2,2,2}, //two rows, three columns

{2,2,2}

This is an array(size2) of two arrays(size3). So the size of this two dimensional

array is 2*3 which is equal to 6.

Two Dimensional Array Continue

55

E.x/ Write a C++ program to add 2 matrixes using a function.

main()

{

int array1[4][2]={ {0,1}, {0,1}, {0,1}, {0,1}};

int array2[4][2]={ {1,1}, {1,1},{2,2},{2,2}};

addMatrixes(array1, array2);

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

{

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

cout<<array1[i][j]<<" ";

}

return 0;

}


56

void addMatrixes(int a[][2],int b[][2])

{

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

{

for(intj=0; j<2; j++)

a[i][j]=a[i][j]+ b[i][j];//adding

}// to display the result on the screen

}


57

Multi-dimensional arrays are mainly used to perform matrix operations and

numerical analysis calculations, you can do all matrix operations like matrix

addition, multiplication, matrix transformations using two-dimensional arrays.

The base type of a multi-dimensional array can be any type; but for numerical

calculations the type is usually int or double..

Lecture 4

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020



59

To calculate the address in two dimensional array there are two methods:

1.Row-wisemethod.

2.Column-wisemethod.

In row-wise method can arrive to any location of array in memory through rows

until arrive to row that is contain the location of element.

While in column-wise method can arrive to any location of array in memory

through columns until arrive to column that is contain the location of element.


60

Row-wise method: char a[r][c];

Locationa[i][j]=BA+(i*c+j)*size

Where:

i: is the current row.

c: is total no. of columns.

j: is current column.


E.x17: short a[3][4]; BA=400, Find the location of a[0][0] and location a[1][1]?

Location a[0][0]=400+(0*4+0)*2

=400

Locationa[1][1]=400+(1*4+1)*2

=410


61

Column-wise method: char a[r][c];

Location a[i][j]=BA+(j*r+i)*size

Where:

i: is the current row.

r: is total no. of row.

j: is current column.


E.x18/ short a[3][4]; BA=400, Find the location of a[1][1]?

Location a[1][1]=400+(1*3+1)*2

=408

Structure

62

In C++ composite data types are declared using structures.

For example, you can represent a point as a data type whose type is a structure

consisting of two values of type int.

struct point

{

int x;

int y;

};

Structure Continue

63

To declare a variable of this new type, you follow the same method as we did for

basic data types:

point firstPoint;

The variables inside the structure are called member variables and their values the

structure‟s member values.

Member variables are specified by giving the name of the structure variable

followed by a dot and then the member name. For example to initialize the

variable “point” from last slide:

firstPoint.x=0;

firstPoint.y=0;

Structure Continue

64

But it is more common to initialize structures as in:

firstPoint={0,0};

To assign one structure variable to another variable of the same type:

Point firstPoint, secondPoint;

firstPoint={1,2};

secondPoint=firstPoint;

To compare structures with each other:

if(firstPoint==secondPoint) //illegal

if((firstPoint.x==secondPoint.x)

&& (firstPoint.y==secondPoint.y)) //OK

Structure Continue

65

E.x/ Write a C++ program to find distance between any two points using your own

structure:

#include<iostream.h>

#include<math.h>

struct point

{

double x;

int y;

};

Structure Continue

66

main()

{

point firstPoint={4,9};

point secondPoint={5,10};

double distance=0.0;

distance=sqrt(((secondPoint.x–firstPoint.x)*

(secondPoint.x–firstPoint.x))+

((secondPoint.y–firstPoint.y)*

(secondPoint.y–firstPoint.y)))

cout<<“the distance between

points(4,9)and(5,10)is“<<distance<<endl;

return0;

}

Structure Mapping Function

67

The information used to calculate the Structure Mapping Function SMF is the

address of any element in the structure.

1.Data type of each member.

2.Data length of each member.

3.Offset from the base of the structure.

Example:

struct Dept

{

short Room;

char name[10];

float size;

};

Calculate the size of structure.

Structure Mapping Function Continue

68

Structure Mapping Function Continue

69

E.x: Dept B[10]; Base Address=400, find the location of B[3]?

Location(B[i])=Base Address+ size o f structure * i

Location(B[3])=400+16*3

=448

Lecture 5

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020


Asymptotic Complexity

71

Finding the exact complexity, [f(n)= number of basic operations], of an algorithm

is difficult.

This “approximate“ measure of efficiency is called asymptotic complexity.

Thus the asymptotic complexity measure does not give the exact number of

operations of an algorithm, but it shows how that number grows with the size of

the input.

Asymptotic Complexity Continue

72

This gives us a measure that will work for different operating systems, compilers

and CPUs.

The most commonly used notation for specifying asymptotic complexity is the

big-O notation.

Asymptotic Complexity Continue

73

Some Big-O complexity classes in order of magnitude from smallest to highest:

Big-O Examples

74

Rules of big-O

75

For large values of input n, the constants and terms with lower degree of n are

ignored.

Multiplicative Constants Rule: Ignoring constant factors.

O(cf(n))=O(f(n)), where c is a constant;

Example:

O(20n3)=O(n3)

Addition Rule: Ignoring smaller terms.

If O(f(n))<O(h(n)) then O(f(n)+h(n))=O(h(n)).

Example:

O(n2logn+n3)=O(n3)

Multiplication Rule:O(f(n)*h(n))=O(f(n))*O(h(n))

Example:

O((n3+2n2+3nlogn+7)(8n2+5n+2))=O(n5)

Determine Complexity of Code Structures

76

Loops: for, while, and do-while:

Complexity is determined by the number of iterations in the loop times the

complexity of the body of the loop.

Examples:

for(int i=0;i<n; i++) O(n)

sum=sum-i;

for(int i=0; i<n*n; i++) O(n2)

sum=sum+i;

i=1;

while(i<n) Olog(n)

{

sum=sum+i;

i=i*2;

}

Determine Complexity of Code Structures Continue

77

Nested Loops: Complexity of inner loop* complexity of outer loop.

Examples:

sum=0

for(int i=0; i<n; i++)

for(int j=0; j<n; j++) O(n2)

sum+=i*j;

i=1;

while(i<=n){

j=1;

while(j<=n){

statements of constant complexity

j=j*2; O(nlogn)

}

i=i+1;

}


78

Sequence of statements: Use Addition rule

O(s1; s2; s3; … sk) = O(s1) + O(s2) + O(s3) + … + O(sk)

= O(max(s1, s2, s3, . . . , sk))

Example:

for (int j = 0; j < n * n; j++)

sum = sum + j;

for (int k = 0; k < n; k++)

sum = sum -l;

System.out.print("sum is now ” + sum);

Complexity is O(n2) + O(n) +O(1) = O(n2)


79

If Statement: Take the complexity of the most expensive case :


80

Sometimes if-else statements must carefully be checked:

O(if-else) = Max[O(Condition), O(if), O(else)

Abstract Data Type

81

An Abstract Data Type ADT Abstract Data Type(ADT): a definition for a data

type in terms of a set of values and a set of operations on that data type.

ADT: A mathematical description of an object and the set of operations on the

object. Like Stack, queue, linked list,….

An ADT specifies:

1.Data stored.

2.Operations on the data.

3.Error conditions associated with operations.

Stack

82

A stack data structure could use an array, a linked list, or any thing that can hold

data, stores arbitrary objects, in which data is added and removed at only one end

called the top. It supports the following main operations:

push(object o): inserts element o.

pop(): removes and returns the last inserted element.

top(): returns a reference to the last inserted element without removing it.

isEmpty(): returns a Boolean value indicating whether no elements are stored.

size(): returns the number of elements stored.

isFull(): checks weather stack is full or not.

Stack Continue

83

To add(push) an item to the stack, it must be placed on the top of the stack.

To remove(pop) an item from the stack, it must be removed from the top of the

stack too.

Thus, the last element that is pushed in to the stack, is the first element to be

popped out from the stack. i.e. ,Last In First Out(LIFO)

Stack Continue

84

Stack Applications

85

Reversing a sequence of string.

Checking palindrome sequences.

Store the return address when use the CALL interrupt.

Converting expression from infix to prefix or prefix to infix and evaluation the

expression which found in any form above.

Page-visited history in a Web browser

Undo sequence in a text editor

)Lecture 6 (Stack

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020


Stack

87

ئ م كات تان باش قوتابيان

يوادارم ت وذروست باش به

ژی شمم پراتيک تان بۆ دادەويمئةم واو ي ش جوان بخويىه بو رو

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Stack

88

A stack data structure could use an array, a linked list, or any thing that can hold

data, stores arbitrary objects, in which data is added and removed at only one end

called the top. It supports the following main operations:

push(object o): inserts element o.

pop(): removes and returns the last inserted element.

top(): returns a reference to the last inserted element without removing it.

isEmpty(): returns a Boolean value indicating whether no elements are stored.

size(): returns the number of elements stored.

isFull(): checks weather stack is full or not.

Stack Continue

89

To add(push) an item to the stack, it must be placed on the top of the stack.

To remove(pop) an item from the stack, it must be removed from the top of the

stack too.

Thus, the last element that is pushed in to the stack, is the first element to be

popped out from the stack. i.e. ,Last In First Out(LIFO)

Stack Continue

90

Stack Applications

91

Reversing a sequence of string.

Checking palindrome sequences.

Store the return address when use the CALL interrupt.

Converting expression from infix to prefix or prefix to infix and evaluation the

expression which found in any form above.

Page-visited history in a Web browser

Undo sequence in a text editor

Exception

92

Attempting the execution of an operation of ADT may some times cause an error

condition, called an exception.

Exceptions are said to be “thrown” by an operation that can not be executed.

In the Stack ADT, operations pop can not be performed if the stack is empty.

Attempting the execution of pop on an empty stack throws an

EmptyStackException

Stack Implementation

93

Stack is an order collection of items, it may be declared as array or structure

containing two objects.

As array we can define the stack as follows:

int stack[max_size_of_stack];

int top;

Note that stack variable can be of any data type (integer, float, etc.) while top must

be of type integer always.

Stack Algorithms

94

A simple way of implementing the stack uses an array.

We add elements from left to right.

A variable keeps track of the index of the top element.

1.Num_Of_Elements algorithm: Used to returns number of the elements in the

stack

Num_Of_Elements():

return top + 1

Stack Algorithms Continue

95

2.Stack full algorithm: This algorithm is use to check if stack is full or not, it is

called from push algorithm.

isFull()

if top=maxsize-1 then

return true


96

3. Stack empty algorithm:

This algorithm is used to check if stack is empty or not, it is called from pop

algorithm.

isEmpty()

if top=-1 then

return true


97

4. PUSH algorithm:

The array storing the stack elements may become full, a push operation will then

throw a FullStackException

PUSH(item)

if isFull() then

begin

print or throws FullStackException

exit

end

else

begin

top ← top + 1

S[top] ← item

end


98

5. POP algorithm: To return elements from the stack

POP()

if isEmpty() then

begin

print or throw EmptyStackException

exit

end

else

begin

return S[top]

top ← top − 1

end


99

6.Clear_Stack: This algorithm is used to make the stack empty.

clear()

top=-1

Performance and Limitations

100

Performance

Let n be the number of elements in the stack.

The space used is O(n).

Each operation runs in time O(1).

Limitations

The maximum size of the stack must be defined a priori, and can not be

changed.

Trying to push a new element in to a full stack causes an implementation-

specific exception

Convert Infix to Postfix

101

1. Infix: A+B Here arithmetic operator in the middle.

2. Postfix: AB+ Here arithmetic operator at the end.

3. Prefix: +AB Here arithmetic operator at the begin.

In computer the compiler covert infix expression top postfix expression by using a

stack.

Algorithm of converting infix expression to postfix expression by using single

stack.

1. We use single stack to store the operator signal.

2. Check arithmetic expression character by character from left to right.

Convert Infix to Postfix Continue

102

3. Character may be:

1. If character is operand (a to z) then output string.

2. If character is left bracket “(“ then push in stack

3. if character is operator ( +,-,*,/) then pop all operators from stack that have

priority greater or equal than new operator to the output string then push

new operator to the stack.

4. if character is right bracket “)‟, pop all operators from stack until left

bracket to the output string , ignore left and right brackets do not add to the

output string.`


103

4. If you finished the arithmetic expression then popped all operators from stack to

the output string. The final shape of output string is postfix expression.

The order of precedence:

Exponentiation ^

* ,/

+ ,-

Equivalent(=,<,<=,>,>=.!=)

NOT

AND,%

OR


104

E.x/ Convert infix to postfix: (6 – 2) * (5+4)

O/P StringStackI/PStep No.

((1

6(62

6( --3

6 2( -24

6 2 -null)5

6 2 -**6

6 2 -* ((7

6 2 - 5* (58

6 2 - 5* ( ++9

6 2 – 5 4* ( +410

6 2 – 5 4 +*)11

6 2 – 5 4 + *nullnull12


105

E.x/ Convert Infix to Postfix

Queue Lecture 7

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020


107



م ان شاءهللا ژی شمم پراتيک تان بۆ دادەويئةم واو ي ش جوان بخويىه بو رو

https://drive.google.com/open?id=1yFOC9jfmchIbHM5qQwOa3TWO6Q3CsDWM




















Queue

108

The Queue ADT stores arbitrary objects.

Queues are linear data structures in which we add elements to one end and remove

them from the other end.

The first item to be en-queued is the first to be de-queued. Queue is therefore

called a First In First Out (FIFO) structure.

Main queue operations:

No_Elements(): returns the number of elements stored.

isEmpty(): returns a Boolean indicating whether no elements are stored.

isFull(): return false or true if queue is full or not.

Queue Continue

109

Enqueue (Object o): inserts an element at the end of the queue.

Dequeue(): removes and returns the element at the front of the queue.

Clear(): reset the queue

In queue there are two index for two end of queue one for addition called rear and other

is front for deletion.

Notes:

At the beginning Front=Rear=-1, in C++.

If Front=Rear=-1 then queue is empty.

If Rear=(maxsize-1) then the queue is full.

110

‌QueueisFullisEmptyNo_Of_Elements

(Rear-Front)

FrontRearCase

Falsetrue-1 - (-1)= 0-1-1

AFalseFalse0 - (-1)= 1-10enqueue(A)

ABFalseFalse1 - (-1)= 2-11enqueue(B)

ABCFalseFalse2 - (-1)= 3-12enqueue(C)

BCFalseFalse2 - 0 = 202dequeue()

CFalseFalse2 - 1 = 112dequeue()

CDTrueFalse3 - 1 = 213enqueue(D)

DTrueFalse3 - 2 = 123dequeue()

DTrueFalse3 - 2 = 123enqueue(E)

TrueTrue3 - 3 = 033dequeue()

TrueTrue3 - 3 = 033enqueue(F)

TrueTrue3 - 3 = 033dequeue()

Applications of Queue

111

Waiting lines: Queues are commonly used in systems where waiting line has to be

maintained for obtaining access to a resource. For example, an operating system

may keep a queue of processes that are waiting to run on the CPU.

Access to shared resources (e.g., printer).

Multi programming.

Exceptions

112

Attempting the execution of dequeue or front on an empty queue throws an

EmptyQueueException.

Attempting the execution of enqueue on an full queue throws an

FullQueueException.

Queue Algorithms Continue

113

Note:

Max_Size: Size of the queue.

front: end of deletion.

rear: end for addition.

Q: Queue.


114

1.No. of elements in the queue algorithm: return number of the elements in the

queue

No_Element()

return rear-front

2. Queue is empty algorithm: check if the queue is empty or not

isEmpty()

return (rear=-1 or rear==front)

3. Queue is full algorithm: check if the queue is full or not:

isfull()

return rear=Max_Size-1


115

4. Enqueue algorithm: Adding an element to queue

enqueue(item)

begin

if isFull()

over flow exit

else

rear ←(rear + 1)

Q[rear] ←item

end


116

5. Dequeue Algorithm: Deleting an element from queue, throws an exception if

the queue is empty.

dequeue()

begin

if isEmpty()

empty queue exit

else

front←(front + 1)

item ←Q[front]

return item

end


117

6. Clear queue algorithm: Reinitialize or reset the queue

clear()

begin

set Front to-1

set Rear to-1

end

Circular Queue Lecture8

Lecturer

Kanar Shukr Muhamad

Data Structure

and

Algorithm Design

2019-2020


119



واوي روي ا , پراتيکم بۆتان دائةم واو ي ش جوان بخويىه

١٠/٤/٢٠٢٠گرتن كوتا كاتي وه ر

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Circular Queue

120

Circular Queue is a linear data structure in which the operations are performed

based on FIFO (First In First Out) principle and the last position is connected

back to the first position to make a circle. It is also called ‘Ring Buffer’

In a normal Queue, we can insert elements until queue becomes full. But once

queue becomes full, we can not insert the next element even if there is a space

in front of queue

Circular queue avoids the wastage of space in a regular queue.

Circular Queue

121

As you can see in the above image, after a bit of enqueueing and dequeueing,

the size of the queue has been reduced.

The indexes 0 and 1 can only be used after the queue is reset.

Circular Queue solves this by the process of circular increment i.e. when we

try to increment any variable and we reach the end of queue, we start from the

beginning of queue.

122

Circular ‌QueueisFullisEmptyFrontRearCase

Falsetrue-1-1

AFalseFalse00enqueue(A)

BAFalseFalse01enqueue(B)

CBAFalseFalse02enqueue(C)

CBFalseFalse12dequeue()

DCBFalseFalse13enqueue(D)

DCFalseFalse23dequeue()

DCEFalseFalse20enqueue(E)

DEFalseFalse30dequeue()

DFEFalseFalse31enqueue(F)

DGFEFalseFalse32enqueue(G)

DGFETrueFalse32enqueue(H)

Circular Queue Algorithms

123

1. Circular Queue is_empty algorithm: check if the circular queue is empty or not

isEmpty()

return (front == -1)

2. Circular Queue is full algorithm: check if the queue is full or not:

isfull()

if((front==0 && rear==SIZE-1) || (front==rear+1))

“Queue is full.”

Case1:

Case2:

Rear=3Front=0

DCBA

Front=2Rear=1

DCFE

Circular Queue Algorithms Continue

124

3. Enqueue algorithm: Adding an element to queue

enqueue(item)

beign

if isFull()

{over flow exit}

else

if(rear == -1)

{ rear = 0; front = 0; }//it becomes 1st element

else if(rear == SIZE-1)

rear = 0;//return back there is a space

else

rear++;//store it regularly

queue[rear] = item;

end

Circular Queue Algorithms Continue

125

4. Dequeue Algorithm: Deleting an element from queue, throws an exception if

the queue is empty.

dequeue()

begin

if isEmpty()

“empty queue” exit

else{

item = queue[front];

if(front == rear)

{front = -1;rear = -1;}// We have just one element

else if(front == SIZE-1)

front = 0;//return back

else

front++;} //delete regularly

end

Data Structure and Algorithm Design · Data Structure 10 A data structure is a logical representation to understand physical representation. “Clever”ways to organize information

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