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Jawaharlal Nehru Engineering College

Laboratory Manual

DATA STRUCTURES USING C

For

Second year Students (CSE)

16, Nov 2005 – Rev 00 – Comp Sc – ISO 9000 Tech Document

Author JNEC, Aurangabad

FOREWORD

It is my great pleasure to present this laboratory manual for Second year engineering

students for the subject of Data Structures (Using C).

As a student, many of you may be wondering with some of the questions in your

mind regarding the subject and exactly what has been tried is to answer

through this manual.

As you may be aware that MGM has already been awarded with ISO 9001:2000

certification and it is our endure to technically equip our students taking the

advantage of the procedural aspects of ISO 9001:2000 Certification.

Faculty members are also advised that covering these aspects in initial stage

itself, will greatly relieve them in future as much of the load will be taken care

by the enthusiasm energies of the students once they are conceptually clear.

Dr. S. D. Deshmukh

Principal

LABORATORY MANUAL CONTENTS

This manual is intended for the Second year students of Computer Science and

Engineering in the subject of Data Structures (Using C). This manual typically

contains practical/lab sessions related Data Structures implemented in C covering

various aspects related the subject to enhanced understanding.

Students are advised to thoroughly go through this manual rather than only topics

mentioned in the syllabus as practical aspects are the key to understanding and

conceptual visualization of theoretical aspects covered in the books.

Good Luck for your Enjoyable Laboratory Sessions

Dr. V .B. Musande Mr. Y. R. Tayade

HOD,CSE Asst. Prof., CSE Dept.

MGM’s

Jawaharlal Nehru Engineering College, Aurangabad

Department of Computer Science and Engineering

Vision of CSE Department:

To develop computer engineers with necessary analytical ability and human values who can

creatively design, implement a wide spectrum of computer systems for welfare of the society.

Mission of the CSE Department:

I. Preparing graduates to work on multidisciplinary platforms associated with their

professional position both independently and in a team environment.

II. Preparing graduates for higher education and research in computer science and engineering

enabling them to develop systems for society development.

Programme Educational Objectives:

Graduates will be able to

I. To analyze, design and provide optimal solution for Computer Science & Engineering and

multidisciplinary problems.

II. To pursue higher studies and research by applying knowledge of mathematics and

fundamentals of computer science.

III. To exhibit professionalism, communication skills and adapt to current trends by engaging

in lifelong learning.

Programme Outcomes (POs):

Engineering Graduates will be able to: 1. Engineering knowledge: Apply the knowledge of mathematics, science, engineering

fundamentals, and an engineering specialization to the solution of complex engineering

problems.

2. Problem analysis: Identify, formulate, review research literature, and analyze complex

engineering problems reaching substantiated conclusions using first principles of mathematics,

natural sciences, and engineering sciences.

3. Design/development of solutions: Design solutions for complex engineering problems and

design system components or processes that meet the specified needs with appropriate

consideration for the public health and safety, and the cultural, societal, and environmental

considerations.

4. Conduct investigations of complex problems: Use research-based knowledge and research

methods including design of experiments, analysis and interpretation of data, and synthesis of

the information to provide valid conclusions.

5. Modern tool usage: Create, select, and apply appropriate techniques, resources, and modern

engineering and IT tools including prediction and modeling to complex engineering activities

with an understanding of the limitations.

6. The engineer and society: Apply reasoning informed by the contextual knowledge to assess

societal, health, safety, legal and cultural issues and the consequent responsibilities relevant to

the professional engineering practice.

7. Environment and sustainability: Understand the impact of the professional engineering

solutions in societal and environmental contexts, and demonstrate the knowledge of, and need

for sustainable development.

8. Ethics: Apply ethical principles and commit to professional ethics and responsibilities and

norms of the engineering practice.

9. Individual and team work: Function effectively as an individual, and as a member or leader

in diverse teams, and in multidisciplinary settings.

10. Communication: Communicate effectively on complex engineering activities with the

engineering community and with society at large, such as, being able to comprehend and write

effective reports and design documentation, make effective presentations, and give and receive

clear instructions.

11. Project management and finance: Demonstrate knowledge and understanding of the

engineering and management principles and apply these to one’s own work, as a member and

leader in a team, to manage projects and in multidisciplinary environments.

12. Life-long learning: Recognize the need for, and have the preparation and ability to engage in

independent and life-long learning in the broadest context of technological change.

LAB INDEX

1. Prerequisite for Data Structures implementation

2. Write a C program for implementation of stack using array

3. Write a C program for implementation of queue using array

4. Write a C program for implementation of circular queue using array

5. Design, develop and execute a program in C to evaluate a valid postfix expression

using stack. Assume that the postfix expression is read as a single line consisting of

non-negative single digit operands and binary arithmetic operators. The operators

are +(add), -(subtract), *(multiply), /(divide)

6. Design, develop and execute a program in C to read a sparse matrix of integer values

and make a transpose of it. Use the triple <row, column, value> to represent an element

in sparse matrix.

7. Design, develop and execute a program in C to implement singly linked list where

each node consist of integers. The program should support following functions.

a. Create a singly linked list

b. Insert a new node

c. Delete a node if it is found, otherwise display appropriate message

d. Display the nodes of singly linked list

8. Design, develop and execute a program in C to implement doubly linked list where

each node consist of integers. The program should support following functions.

a. Create a doubly linked list

b. Insert a new node

c. Delete a node if it is found, otherwise display appropriate message

d. Display the nodes of doubly linked list

9. Using array representation for a polynomial, design, develop and execute a program

in C to add two polynomials and then print the resulting polynomial.

10. Write a program in C to construct binary tree and binary tree traversal

11. Design, develop and execute a program in C to create a max heap of integers by

accepting one element at a time and by inserting it immediately in to heap. Use the

array representation of heap. Display the array at the end of insertion phase.

DOs and DON’Ts in Laboratory:

1. Make entry in the Log Book as soon as you enter the Laboratory.

2. All the students should sit according to their roll numbers starting from their left to

right.

3. All the students are supposed to enter the terminal number in the log book.

4. Do not change the terminal on which you are working.

5. All the students are expected to get at least the algorithm of the program/concept to be

implement.

6. Strictly follow the instructions given by the teacher/Lab Instructor.

Instruction for Laboratory Teachers

1. Submission related to whatever lab work has been completed should be done during the

next lab session.

2. The immediate arrangements for printouts related to submission on the day of practical

assignments.

3. Students should be taught for taking the printouts under the observation of lab teacher.

4. The promptness of submission should be encouraged by way of marking and evaluation

patterns that will benefit the sincere students.

1. Lab Exercise

Exercise No 1: ( 2 Hours) – 1 Practical

AIM - Introduction to concepts of Array and Structures in C

Objective- Student should be able to develop the programs using arrays and structures.

• Write a Program to read in one dimensional , calculate the sum and display it

Initialize the array of 10 elements

Read the elements using a loop

Add all the elements

Display the contents of the array and the sum

• Write a Program for addition of two matrices using two dimensional array

• Write a Program to demonstrate the concept of structure and array of structures

• Write a Program to demonstrate passing the structure and array of structures to

a function.

Output

Enter number of students 3

Enter rollno , name and percentage of 3 students

1 Ajay 70 2 Rahul 80 3 Yogesh 90

You entered the student record

1 Ajay 70 2 Rahul 80

3 Yogesh 90

Conclusion

Studied and successfully demonstrated the use arrays and structures.

2. Lab Exercises:


AIM – Write a C program for implementation of stack using array

Objective- Student should be able to develop a program from the logic of stack

Theory:--

A stack is an ordered collection of homogeneous data element where the

insertion and deletion operation take place at one end only. An n-element array can be

used to implement a stack with capacity n. The stack top is indicated by the index top

and it points to the element that was entered into the stack.

Declaration:--

Type Stack = array [1.. stacksize] of integer;

Stacklimit = 0..stacksize;

Algorithm: --

Data Structure: An Array with TOP as the pointer.

Start

Initialize the array of 10 elements and name it as stack

Initialize other variables like top in the beginning of the program

Provide the choice to the users for the different operations on stack like

Push(insert),Pop(delete),Display and Exit

If the choice= push then call the function push()

If the choice= pop then call the function pop()

If the choice= display then call the function display()

If the choice= exit then exit from the program end

Function push()

Check for the overflow condition of the stack

if (TOP>= SIZE) then Print “Stack is full”

If not overflow , increment the value of top

Get the element to be inserted onto the stack from the user

Assign it as the topmost value ,stack[top]

Function pop()

Check for the underflow( empty) condition of the stack

if TOP<0 Print “Stack is Empty”

If not empty ,Output the element to be deleted from the stack Decrement the

value of top.

Function display()

Display all the elements of the stack

Note: Ask the students to list the drawbacks of implementing the Stack using array.

The above program could be repeated using structures and linked lists

Output

Enter the operation to be performed: 1) push 2) pop 3) display 4) exit

1

Enter the number to be Add: 11


1



1



1



2



3

The stack is 11 22 33


4

Conclusion

All the stack operations are successfully performed using the switch case

3. Lab Exercises:


AIM – Write a C program for implementation of queue using array

Objective- Student should be able to develop the program for queue using arrays.

Theory:--

A Queue is an ordered collection of homogeneous data elements where the insertion

and deletion operation take place at two extreme ends.

Declaration:--

Type queue = array [1.. n] of integer;

Var p: queue

Algorithm:--

Data Structure: Q is the array representation of queue structure; two pointers FRONT

and REAR of the queue Q are known.

start

Initialize the array of 10 elements and name it as queue

Initialize other variables like rear and front in the beginning of the program

Give the choice to the users for the different operations on Queue like Insert,

Delete,Display and Exit

If the choice= insert operation call the function qinsert()

If the choice= delete operation call the function qdelete()

If the choice= display operation call the function qdisplay()


Function insert()

Check for the overflow condition of the Queue

If(REAR = N) then Print “Queue is full”

If not overflow , increment the value of rear

REAR = REAR+1

Get the element to be inserted into the queue from the user Q[REAR] = ITEM

Assign it as the last value ,queue[rear]

Function delete()

Check for the underflow( empty) condition of the queue If not empty ,Output the

element to be deleted from the queue Increment the value of front.

Function display()

Display the elements of the queue

Note: Ask the students to list the drawbacks of implementing the Queue using array.


Output

Enter the operation to be performed: 1)Enqueue 2)Dequeue 3)Display 4)Exit

1

Enter the number to be added 11


1



1



1



2

The number to be deleted is 11


3

The queue is 22 33 44

Conclusion

All the queue operations are successfully performed

4. Lab Exercises:


AIM – Write a C program for implementation of circular queue using array

Objective- Student should be able to develop the program for circular queue

Theory:--

A Queue is an ordered collection of homogeneous data elements where the

insertion and deletion operation take place at two extreme ends. And it supports

reinsertion as well as re-deletion at same location.

Declaration:--

Type queue = array [1.. n] of integer;

Var p: queue

Algorithm:--

Data Structure: CQ is the array representation of circular queue structure; two pointers

FRONT and REAR of the queue CQ are known.

start

Initialize the array of 10 elements and name it as queue


Provide the choice to the users for the different operations on Queue like Insert,

Delete, Display and Exit

If the choice= insert operation call the function cqinsert()

If the choice= delete operation call the function cqdelete()

If the choice= display operation call the function cqdisplay()


Function insert()

Check for the overflow condition of the Queue

If(FRONT=(REAR+1)%N) then Print “Queue is full”

If not overflow , increment the value of rear

REAR = (REAR+1) % N

Get the element to be inserted into the queue from the user Q[REAR] = ITEM

Assign it as the last value ,queue[rear]

Function delete()

Check for the underflow (empty) condition of the queue

If not empty ,Output the element to be deleted from the queue

Increment the value of front.

FRONT = (FRONT+1) % N

Function display()

Display the elements of the queue

Note: Ask the students to list the drawbacks of implementing the Queue using array.


Output

1) Insert 2) Delete 3) Display

Enter choice for circular queue 1

Enter any item 14



Enter any item 15



Enter any item 20



14 15 20

Conclusion

All the operations on the circular queue are performed successfully

5. Lab Exercises:


AIM:-- Design, develop and execute a program in C to evaluate a valid postfix

expression using stack. Assume that the postfix expression is read as a single line

consisting of non-negative single digit operands and binary arithmetic operators. The

operators are +(add), -(subtract), *(multiply), /(divide)

Objective- Student should be able to develop the program for evaluation of the postfix expression.

Theory:

Infix Expression : Any expression in the standard form like "2*3-4/5" is an Infix(Inorder)

expression.

Postfix Expression : The Postfix(Postorder) form of the above expression is "23*45/-".

Postfix Evaluation : In normal algebra we use the infix notation like a+b*c. The

corresponding postfix notation is abc*+. The algorithm for the conversion is as follows

Algorithm:--

Start

Declare an array of characters to take an postfix expression Get the postfix

expression from the user.

Scan the Postfix string from left to right.

Initialize an empty stack.

If the scanned character is an operand, add it to the stack.

If the scanned character is an operator, there will be at least two operands in the

stack.

• If the scanned character is an Operator, then we Pop the stack twice to get

our perand1 and operand2.

• Calculate the result with operand1 ,operand2 and the operator Push the

result into the stack.

• Repeat this step till all the characters are scanned.

After all characters are scanned, we will have only one element in the stack.

Pop the stack for final result.

End.

Example:--

Let us see how the above algorithm will be implemented using an example.

Postfix String : 123*+4-

Initially the Stack is empty. Now, the first three characters scanned are 1,2 and 3, which are

operands. Thus they will be pushed into the stack in that order.

Expression

Stack

Next character scanned is "*", which is an operator. Thus, we pop the top two elements

from the stack and perform the "*" operation with the two operands. The second

operand will be the first element that is popped.

Expression

Stack

The value of the expression(2*3) that has been evaluated(6) is pushed into the

stack.

Expression

Stack

Next character scanned is "+", which is an operator. Thus, we pop the top two elements

from the stack and perform the "+" operation with the two operands. The second

operand will be the first element that is popped.

Expression

Stack

The value of the expression(1+6) that has been evaluated(7) is pushed into the

stack.

Expression

Stack

Next character scanned is "4", which is added to the stack.

Expression

Stack

Next character scanned is "-", which is an operator. Thus, we pop the top two elements from

the stack and perform the "-" operation with the two operands. The second operand will be

the first element that is popped.

Expression

Stack

The value of the expression(7-4) that has been evaluated(3) is pushed into the

stack.

Expression

Stack

Now, since all the characters are scanned, the remaining element in the stack (there will

be only one element in the stack) will be returned.

End result :

• Postfix String : 123*+4-

• Result : 3

Output

Enter the Infix Expression: 2+3*4

The Postfix Expression is: 234*+

Do you want to evaluate the Result of Postfix Expression?(Y/N):

Ans= 14

Conclusion

Successful evaluation of the postfix expression is done.

6. Lab Exercises:


AIM:-- Design, develop and execute a program in C to read a sparse matrix of integer

values and make a transpose of it. Use the triple <row, column, value> to represent an

element in sparse matrix.

Objective- Student should be able to develop the program for sparse matrix and its

transpose.

Theory:--

Matrices with a relatively high proportion of zero entries are called Sparse

Matrices. In mathematics a matrix contains m rows and n columns of elements as

illustrated in figure (a). in this figure, the elements are numbers. The first matrix have

5 rows and 3 columns; the second has six rows and six columns. In general, we write

mxn to designate a matrix with m rows and n columns. The total number of elements

in such a matrix is mn. If m = n, the matrix is square and takes m x n x sizeof

(datatype of matrix) bytes to store in memory. But if the matrix is sparse matrix then

storing zero value elements causes inefficient use of memory.

Therefore to use memory efficiently a sparse matrix containing only non zero elements

can be represented by using the triplet <row, column, value >

Figure (a) Two matrices

Structure used for Sparse Matrix: #define MAX_TERMS 101 /* maximum number of terms +1*/

typedef struct

{

int col;

int row;

int value;

} term;

term A[MAX_TERMS];

Operations on Sparse Matrix:

a. Create

b. Transpose

c. Multiplication

Transpose of Sparse Matrix:

Figure (I) shows a sparse matrix represented by array ‘a’ and it’s transpose of a

matrix which is represented in figure (a). thus a[0].row contains the number of rows;

a[0].col contains number of columns; and a[0].value contains total number of nonzero

entries. Positions 1 through 8 store the triples representing the non-zero entries. The

row index is in the field row; the column index is in the field col; the value index is in the

field value. The triples are ordered by row and within rows by columns

row col value row col value

a[0] 6 6 8 b[0] 6 6 8

[1] 0 0 15 [1] 0 0 15

[2] 0 3 22 Transpose [2] 0 4 91

[3] 0 5 -15 [3] 1 1 11

[4] 1 1 11 [4] 2 1 3

[5] 1 2 3 [5] 2 5 28

[6] 2 3 -6 [6] 3 0 22

[7] 4 0 91 [7] 3 2 -6

[8] 5 2 28 [8] 5 0 -15

Figure (I) Sparse matrix and it’s transpose stored as a triples

Algorithm:

for each row i take element <i, j, value> and store

it in element <j, i, value> of the transpose.

Difficulty: where to put <j, i, value>?

(0, 0, 15) ====> (0, 0, 15)

(0, 3, 22) ====> (3, 0, 22)

(0, 5, -15) ====> (5, 0, -15)

(1, 1, 11) ====> (1, 1, 11)

Move elements down very often.

For all elements in column j, place element <i,

j, value> in element <j, i, value>

Function for transpose of sparse matrix:

void transpose (term a[], term b[])

/* b is set to the transpose of a */

{

int n, i, j, currentb;

n = a[0].value; /* total number of elements */

b[0].row = a[0].col; /* rows in b = columns in a */

b[0].col = a[0].row; /*columns in b = rows in a */

b[0].value = n;

if (n > 0) {/*non zero matrix */

currentb = 1;

for (i = 0; i < a[0].col; i++)

/* transpose by columns in a */

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

/* find elements from the current column */

if (a[j].col == i) {

/* element is in current column, add it to b */

b[currentb].row = a[j].col;

b[currentb].col = a[j].row;

b[currentb].value = a[j].value;

}

}

}

Output

Enter the matrix elements of size 3 by 3

1 0 6 0 0 8 0 5 0

Given matrix is

1 0 6

0 0 8

0 5 0

Sparse Matrix is

[0] 3 3 4

[1] 0 0 1

[2] 0 2 6

[3] 1 2 8

[4] 2 1 5

Transpose is

[0] 3 3 4

[1] 0 0 1

[2] 2 0 6

[3] 2 1 8

[4] 1 2 5

Conclusion

Successful conversion of given matrix into the sparse matrix and its transpose.

7. Lab Exercises:

Exercise No 7: (2 Hours) – 2 Practical

AIM :-- Program for implementing Singly Linked List

Objective- Student should be able to develop the program for linked list creation and operations on it

Theory :--

Linked list is a chain of structures or records called nodes. Each node has at

least two members, one of which points to the next item or node in the list! These are

defined as Single Linked Lists because they only point to the next item, and not the

previous. Those that do point to both are called Doubly Linked Lists. Unlike arrays

there is no upper limit on the amount of memory reserved. A singly linked list is the

simplest of linked lists. Each node of a singly linked list has data elements and a single

link (pointer) that points to the next node of the list (or) NULL if it is the last node of

the list. Addition/ Deletion of a node to the singly linked list involve the creation/

deletion of the node and adjusting the node pointers accordingly. Some operations

include

Traversing a list

Insertion of a node into a list.

Deletion of a node from the list.

Searching for an element in a list.

Merging two linked list into a larger list.

Linked list can be developed using the user defined data types. i.e Structure struct

list

{

int data; struct

list * next;

};

Node Structure:

Operations on Linked List:

Fig: Insertion

Fig: Deletion

Algorithm:--

Start

Initialize the structure of the node


Give the choice to the users for the different operations on Queue like Insert, Delete,

Display and Exit

If the choice = insert operation call the function insert()

If the choice = delete operation call the function delete()

http://upload.wikimedia.org/wikipedia/commons/5/51/C_language_linked_list_link.png

If the choice = display operation call the function display()

If the choice = exit then exit from the program

end

INSERT-Singly List

new = GETNODE(NODE)

If (new = NULL) then

a. Print “Memory is insufficient : Insertion is not possible” b.

Exit.

Else

• Ask the user where to insert the item at beginning, at end or besides some node

and get the data for new node as x

• If the node is to be inserted besides some node,find the node. Lets call it as key

ptr= start

While(ptr.data<>key)and(ptr.next<> NULL) do

o ptr = ptr1.next

End while

If (ptr.next = NULL) then o Print “Key is not

available in the list” o Exit

Else o new.next = ptr.next o new.data= x o

ptr.next= new

End if

• If the node is to be inserted at the beginning

new.next = start

new.data= x

start= new

• If the node is to be inserted at the end

ptr= start

While (ptr.next<> NULL) do

ptr = ptr1.next

• End while

• If (ptr.next = NULL) then

new.next = NULL

new.data= x

ptr.link= new

• End if

DELETE-Singly List

Ask the user which item to delete .Find the item. The item may be at beginning, at end

or between some nodes

If the node is to be deleted is besides some node. Lets call it as key

• ptr= start

• While(ptr.data<>key)and(ptr.next<> NULL) do

ptr = ptr1.NEXT

• Endwhile


Print “Key is not available in the list”

Exit

Else

prevnode.next = ptr.next

free(ptr)

Endif

If the node to be deleted is at the beginning

• ptr = start

• temp=ptr.next

• start=temp

• free(ptr)

If the node to be deleted is at the end

• ptr= start

• While (ptr.next<> NULL) do

ptr = ptr1.next

• Endwhile


prevnode.next = NULL

free(ptr)

Endif

DISPLAY-Singly List

ptr=start

While (ptr.next<> NULL) do

ptr = ptr1.next

print ptr.data

Endwhile

Output:

Singly Linked List:

1. Create or Append List

2. Insert in Beginning

3. Insert in Middle

4. Remove from the List

5. Count

6. Display

7. Quit

Enter your Choice: 1

Enter any number: 12

Enter more(y/n): y


Enter more(y/n): n

Singly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


Enter the Data to be inserted at Beginning: 11

Singly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


Enter the Position to be Inserted: 2

Enter the Data: 14

Singly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


Enter the Data to be Deleted: 12

Singly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


The Number of Nodes: 3 28

Singly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


11 14 13

Conclusion

All the Singly Linked List operations are performed.

8. Lab Exercises:


AIM - Design, develop and execute a program in C to implement doubly linked list

where each node consist of integers. The program should support following functions.

Create a doubly linked list

Insert a new node

Delete a node if it is found, otherwise display appropriate message Display the

nodes of doubly linked list

Objective- Student should be able to develop the program for creation of doubly linked

list and operations on it

Theory :--

In computer science, a doubly-linked list is a linked data structure that consists

of a set of data records, each having two special link fields that contain references to

the previous and to the next record in the sequence.

Structure Declaration: struct

list

{

int data;

struct list * next, * prev;

};

Node Structure:

prev data next

3

Operations on Linked List:--

a) Insertion in doubly linked list:

b) Deletion in doubly linked list:

Output

Doubly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit



Enter more(y/n): y


Enter more(y/n): n

Doubly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


Enter the Data to be inserted at Beginning: 11

Doubly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


Enter the Position to be Inserted: 2

Enter the Data: 14

Doubly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


Enter the Data to be Deleted: 12

Doubly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


The Number of Nodes: 3 28

Doubly Linked List:



3. Insert in Middle


5. Count

6. Display

7. Quit


11 14 13

Conclusion

All the Doubly Linked List operations are performed.

9. Lab Exercises:


AIM:-- Using array representation for a polynomial, design, develop and execute a

program in C to add two polynomials and then print the resulting polynomial.

Objective- Student should be able to develop the program for operations on two polynomials

Theory:--

Assume that there are two polynomials A and B. Te polynomial storing the

addition result is stored in one large array C and i, j and k represents the pointers to

the polynomials and arrays respectively. Following algorithm carry out the addition of

these two polynomials

Consider two polynomials

A(X) = -7X5 + 4X2 + X

B(X) = 3X4 + 5X3 + 6X2 + 10X - 14

A(X) + B(X) = -7X5 + 3X4 + 5X3 + 10X2 + 11X - 14

Polynomial Addition using array representation

Algorithm:

Set i to point to first term in A

Set j to point to first term in B

Set k to point to first term in C

Read n1=no. of terms in A and n2= no. of terms in B While i < n1 and j < n2

• If exponent at i’th position of A = exponent at j’th position of B then C at

C at k’th position = coeff of A at i’th position + coeff of B at j’th position

Increment i, j, k to point to next position in A, B, C

• Else

if exponent position i > exponent position j in B then

Copy coeff at i’th position from A to coeff at k’th position in C

Copy the exponent pointed by i into exponent field at position k in C

Increment i, k

else

Copy coeff at j’th position from B to coeff at k’th position in C

Copy the exponent pointed by j into exponent field at position k in C

Increment j, k

While i < n1

(a) Copy coeff at i'th position of the coeff field into coeff at k’th position in C

(b) Copy exponent pointed by i into exponent field at k’th position in C

(c) i and k are incremented by to point to the next position in arrays A and C

While j < n2

(d) Copy coeff at j'th position of the coeff field into coeff at k’th position in C

(e) Copy exponent pointed by j into exponent field at k’th position in C

(f) j and k are incremented by to point to the next position in arrays B and C

Display C [complete array as the addition of two polynomials A

and B]

Exit

Output

Enter the first polynomial::

Enter the coefficient :5

Enter the power :3

Continue??? (Y/N) :Y


Enter the power :2

Continue??? (Y/N) :

First polynomial is ::

5x^3 + 3x^2

Enter the second polynomial::


Enter the power :3

Continue??? (Y/N) :

Second polynomial is ::

7x^3

Addition of the two polynomials::12x^3 + 3x^2

Conclusion

Thus the addition of two polynomial equations has been implemented successfully in C program.

10. Lab Exercises:


AIM:-- Write a program in C to construct binary tree and binary tree traversal

Objective- Student should be able to develop the program for creation of binary search tree and traversal operations on it

Theory:--

A binary tree is made of nodes, where each node contains a "left" pointer, a

"right" pointer, and a data element. The "root" pointer points to the topmost node in the

tree. The left and right pointers recursively point to smaller "subtrees" on either side. A

null pointer represents a binary tree with no elements -- the empty tree. The formal

recursive definition is: a binary tree is either empty (represented by a null pointer), or

is made of a single node, where the left and right pointers (recursive definition ahead)

each point to a binary tree.

Tree Structure:

Structure declaration of a node: struct

node

{

int data; struct node* left; struct node* right;

}

Algorithm for Creation of Binary tree

Initialize root= NULL

Create node as

• s= new node

• s.data=x

• s.left=NULL

• s.right=NULL

If root =NULL then root=s i.e the node is first node

If leaf nodes are to be inserted then call function insert(root,s)

Insert function( root, s)

If root.data<s.data then

If (root.left=NULL) then root.left=s

Else insert(root.left,s)

Else

If (root.right=NULL) then root.right=s

Else insert(root.right,s)

Algorithm preorder

Let T be an ordered binary tree with root R

If T has only R then R is the preorder traversal

Else

• Let T1, T2 be the left and right subtrees at R

• Visit R

• Traverse T1 in preorder

• Traverse T2 in preorder

Algorithm postorder


If T has only R then R is the inorder traversal

Else


• Traverse T1 in inorder

• Visit R

• Traverse T2 in inorder

Algorithm inorder


If T has only R then R is the postorder traversal

Else


• Traverse T1 in postorder

• Traverse T2 in postorder

• Visit R

Output

Enter the root node:30

1.Insertion 2.Preorder 3.Inorder 4.Postorder 5.Quit

Enter your choice 1

Enter the element to insert 10

10 is inserted at the left


Enter your choice 1

Enter the element to insert 40

40 is inserted at the right


Enter your choice 2

The preorder elements are 30 10 40


Enter your choice 4

The postorder elements are

10 40 30


Enter your choice 3

The inorder elements are

10 30 40


Enter your choice 5

Conclusion

Thus the expression tree has been implemented successfully in C program.

11. Lab Exercises:


AIM:-- Design, develop and execute a program in C to create a max heap of integers by

accepting one element at a time and by inserting it immediately in to heap. Use the

array representation of heap. Display the array at the end of insertion phase.

Objective- Student should be able to develop the program for creation of max heap tree

Theory:--

There are two type of heap MAX heap and MIN heap. MAX heap is a complete

binary tree in which root node value is greater than its left child value and right child

value. Similarly MIN heap is a complete binary tree in which root node value is less

than its left child value and right child value.

Operations on heap:

a) Insertion in MAX heap

b) Deletion in MAX heap

a) Insertion in MAX heap:

Suppose H is a heap with N elements, and suppose an ITEM of information is given, and

then ITEM can be inserted into heap H as follows:

• First adjoin ITEM at the end of H so that H is still a complete tree, but not

necessarily a heap.

• Then let ITEM rise to its “appropriate place” in H so that H is finally heap.

9

8 4

5 6

After Insertion of node 7 above tree will be:

Algorithm:

INSHEAP (TREE, N, ITEM)

A heap H with N elements is stored in array TREE, and an ITEM of information is

given. This procedure inserts ITEM as a new element of H. PTR gives the location of

ITEM, and PAR denotes the location of parent of ITEM.

[Add new node H and initialize PTR]

Set N := N+1 and PTR := N.

[Find location to insert ITEM.]

Repeat Step 3 to 6 while PTR > 1

Set PAR := (PTR/2). Location of parent node

If ITEM <= TREE[PAR], then:

Set TREE[PTR] := ITEM, and Return.

[End of if structure]

Set TREE[PTR] := TREE[PAR]. [Moves the node down.]

Set PTR := PAR. [Updates PTR.]

[End of step two loop]

[Assign ITEM as the root of H.]

Set TREE[1] := ITEM

Return

9

8 7

5 6 4

b) Deletion in MAX heap

A heap H with N elements is stored in array TREE. This procedure assigns the

root TREE[1] of H to variable ITEM and then reheaps the remaining elements. The

variable LAST saves the value of the original last node of H. The pointers PTR, LEFT,

RIGHT gives the location of LAST and its left and right children as LAST sinks in the

tree.

After Deletion of 9 above tree will be

Algorithm:

DELHEAP (TREE, N, TIEM)

Set ITEM := TREE[1]. [Removes the root of H.]

Set LAST := TREE[N] and N := N-1. [Removes the last node of H.]

Set PTR := 1, LEFT := 2 and RIGHT := 3 [Initialize pointers]

8

4 6

8

9

8 4

5 6

Repeat step 5 to 7 while RIGHT <=N:

If LAST >= TREE[LEFT] and LAST >= TREE[LIGHT], then

Set TREE[PTR] := LAST and Return

[End of If structure.]

If TREE[RIGHT] <= TREE[LEFT] then:

Set TREE[PTR] := TREE[LEFT] and PR := LEFT Else:

Set TREE[PTR] := TREE[RIGHT] and PR := RIGHT

[End of If structure.]

Set LEFT := 2*PTR and RIGHT := LEFT + 1

[End of step 4 loop.]

If LEFT = N and if LASST < TREE[LEFT], then: Set PTR := LEFT

Set TREE[PTR] := LAST

Return

Output

Array representation of heap:

97 88 95 66 55 95 48 66 35 48 55 62 77 25 38 18 40 30 26 24

Enter item to be inserted into heap 70

Array representation of heap:

97 88 95 66 70 95 48 66 35 55 55 62 77 25 38 18 40 30 26 24 48

After deletion of root

95 88 95 66 70 77 48 66 35 55 55 62 48 25 38 18 40 30 26 24

Conclusion

Successfully created the max-heap tree from given elements.

Conduction of Viva-Voce Examinations:

Teacher should oral exams of the students with full preparation. Normally, the

objective questions with guess are to be avoided. To make it meaningful, the questions

should be such that depth of the students in the subject is tested Oral examinations

are to be conducted in co-cordial environment amongst the teachers taking the

examination. Teachers taking such examinations should not have ill thoughts about

each other and courtesies should be offered to each other in case of difference of

opinion, which should be critically suppressed in front of the students.

Define data structure and it’s types

What is the difference between linear and non linear data structure

How to declare the pointer.

How to declare the structure.

What is mean by array

How polynomial is represented using array

How polynomial addition takes place by using array

How polynomial addition takes place by using structure

What is the difference between structure and array

What is the mean by dynamic array

What is the difference between static variable and dynamic variable

What is the difference between static array and dynamic array

How the memory is utilized in structure and union

Define two dimensional array

Define multi dimensional array

What is performance analysis

Define algorithm

What is the criteria for algorithm specification

Define space and time complexity

What is performance measurement

Definition of Stack

What are the different operations on the stack.

Applications of the stack.

What is dynamic stack

Define PUSH operation

Define POP operation.

What is the drawback of stack

Define multiple stack

Definition of Queue

How to use queue in program

Explain the operations on the Queue

Types of Queue

Application of Queue.

Disadvantage of queue

Define circular queue

What is dynamic circular queue

What is the difference between stack and queue

Difference between simple queue and circular queue

How to insert node in the linked list.

Define the Header.

How to delete the node at the last position in the linked list.

How polynomial is represented using singly linked list

How polynomial is represented using circular linked list

How polynomial is represented using doubly linked list

How polynomial addition takes place by using linked list

Define BINARY tree

Define BST

What is the difference between binary tree and BST

What is AVL tree

Define Red-Black tree

What is selection tree

Difference between winner tree and looser tree

Define Splay tree

What is heap and it’s types

Difference between Min heap and Max heap

Tree representation methods

How to represent binary tree in memory location

Advantages and Disadvantages of binary tree.

Operations on binary tree.

Traversals of the binary tree

Evaluation and marking system:

Basic honesty in the evaluation and marking system is absolutely essential and

in the process impartial nature of the evaluator is required in the examination system

to become popular amongst the students. It is a wrong approach or concept to award

the students by way of easy marking to get cheap popularity among the students to

which they do not deserve. It is a primary responsibility of the teacher that right

students who are really putting up lot of hard work with right kind of intelligence are

correctly awarded.

The marking patterns should be justifiable to the students without any ambiguity and

teacher should see that `students are faced with unjust circumstances.

The assessment is done according to the directives of the Principal/ Vice-Principal/ Dean

Academics.

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