Data-Structure-using-C-Rajesh-Pandey.pdf

Data Structure Using C
Mr. Rajesh Pandey
Asst. Professor
Shobhit Institute of Engineering & Technology
(Deemed-to-be-University), Meerut
Email: rajesh@shobhituniversity.ac.in
Mobile: 7417970699

CONTENTS
1. Introduction to Data Structure and Algorithm
2. Array.
3. Stack.
4. Infix, Prefix and Postfix expression
5. Queue
6. Pointers.
7. Linked list
8. Tree traversal
9. Binary search tree

1. Introduction to Data Structure and
Algorithm
➢ Data Structure: Definition.
➢ Data Structure: Types.
➢ Need of Data Structure.
➢ Application of Data Structure.
➢ Algorithm: Definition
➢ Characteristics of Algorithm

Data Structure: Definition
• A data structure is a special way of organizing and
storing data in a computer so that it can be used
efficiently.
• Array, Linked List, Stack, Queue, Tree, Graph etc
are all data structures that stores the data in a
special way so that we can access and use the
data efficiently.
• Each of these mentioned data structures has a
different special way of organizing data so we
choose the data structure based on the
requirement.

Data Structure: Types
• We have two types of data structures:
1. Linear Data Structure
2. Non-linear Data Structure
• Linear data structures: Elements of Linear data structure
are accessed in a sequential manner, however the elements
can be stored in these data structure in any order. Examples
of linear data structure are: LinkedList, Stack, Queue and
Array.
• Non-linear data structures: Elements of non-linear data
structures are stores and accessed in non-linear order.
Examples of non-linear data structure are: Tree and Graph

Why Data Structures are needed?
• With increasing complexities in computer algorithms, the
amount of data usage is increasing, this can affect the
performance of the application and can create some areas
of concern:
➢To handle very large data,
➢To achieve high-speed processing.
➢Data Search: Getting a particular record
from database should be quick and with optimum use of
resources.
➢Multiple requests: To handle simultanous requests from
multiple users

Advantages of Data Structures
• Efficient Memory use: With efficient use of data
structure memory usage can be optimized,
for e.g we can use linked list vs arrays when we are
not sure about the size of data. When there is no
more use of memory, it can be released.
• Reusability: Data structures can be reused, i.e.
once we have implemented a particular data
structure, we can use it at any other place.
Implementation of data structures can be compiled
into libraries which can be used by different clients.

Algorithm
• Algorithm is a step by step procedure, which defines a set of
instructions to be executed in certain order to get the
desired output.
• An algorithm are generally analyzed on two factors − time
and space. That is, how much execution time and how
much extra space required by the algorithm.

Characteristics of Algorithm
Effectiveness

An algorithm must have the following characteristics:
1.Clear and Unambiguous: Algorithm should be clear and
unambiguous. Each of its steps should be clear in all aspects
and must lead to only one meaning.
2.Well-Defined Inputs: If an algorithm says to take inputs, it
should be well-defined inputs.
3.Well-Defined Outputs: The algorithm must clearly define
what output will be yielded and it should be well-defined as
well.
4.Finite-ness: The algorithm must be finite, i.e. it should not
end up in an infinite loops or similar.

5. Effectiveness: It is measured in terms of time and space.
An algorithm must require minimum memory space and
should have minimum execution time for its successful
execution.
6. Language Independent: The Algorithm designed must be
language-independent, i.e. it must be just plain instructions
that can be implemented in any language, and yet the
output will be same, as expected.

2. Arrays
➢ Array: Definition.
➢ Advantages & Disadvantages of Array
➢ Application of Arrays.
➢ Basic Operations on Array.
✓ Insertion & Traversal of Array
✓ Deletion from Array
✓ Searching in Array
• Sequential Search
• Binary Search
➢ Two Dimensional Array

Arrays in ‘C’
• An array is defined as finite ordered collection of
homogenous data, stored in contiguous memory locations.
Here the words,
➢finite means data range must be defined.
➢ordered means data must be stored in continuous
memory addresses.
➢homogenous means data must be of similar data type.
• Following are the important terms to understand the concept
of Array.
➢ Element − Each item stored in an array is called an element.
➢ Index − Each location of an element in an array has a numerical
index, which is used to identify the element.

Advantages & Disadvantages of Array
• Advantages :
➢It is used to represent multiple data items of
same type by using only single name.
➢It can be used to implement other data structures
like stacks, queues, trees, graphs etc.
➢2D arrays are used to represent matrices.
➢It is easy to understand and implement.

Advantages & Disadvantages of Array
• Disadvantages :
➢We must know in advance that how many elements are
to be stored in array.
➢Array is static structure. It means that array is of fixed
size. The memory which is allocated to array can not be
increased or reduced.
➢Since array is of fixed size, if we allocate more memory
than requirement then the memory space will be wasted.
And if we allocate less memory than requirement, then it
will create problem.
➢Insertion and deletion are quite difficult in an array as the
elements are stored in consecutive memory locations
and the shifting operation is costly.

Applications of Array
• Arrays can be used for sorting data elements.
Different sorting techniques like Bubble sort,
Insertion sort, Selection sort etc use arrays to store
and sort elements easily.
• Arrays can be used for performing matrix
operations. Many databases, small and large,
consist of one-dimensional and two-dimensional
arrays whose elements are records.
• Arrays can be used for CPU scheduling.
• Lastly, arrays are also used to implement other
data structures like Stacks, Queues, Heaps, Hash
tables etc

Basic Operations
• Following are the basic operations supported by an
array.
➢Traverse − print all the array elements one by
one.
➢Insertion − Adds an element at the given index.
➢Deletion − Deletes an element at the given
index.
➢Search − Searches an element using the given
index or by the value.
➢Update − Updates an element at the given
index.

Insertion & Traversal Operation
void main()
{
int arr[4];
int i, j;
printf("Enter array element");
for(i = 0; i < 4; i++)
{
scanf("%d", &arr[i]); //Run time array initialization
}
for(j = 0; j < 4; j++)
{
printf("%dn", arr[j]);
}
}

Deletion Operation
main() {
int arr[] = {1,3,5,7,8};
int k = 3, n = 5; // 3rd element has to be deleted.
int i , j ;
printf("The original array elements are :n");
for(i = 0; i<n; i++)
{
printf("arr[%d] = %d n", i, arr[i]);
}
j = k ;
while( j < n)
{
arr[ j -1 ] = arr[ j ];
j = j + 1;
}
n = n – 1 ;
printf("The array elements after deletion :n");
for(i = 0; i<n; i++) {
printf(“arr[%d] = %d n", i, arr[i]);
}
}
OUTPUT
The original array elements are:
arr[0] = 1
Arr[1] = 3
Arr[2] = 5
Arr[3] = 7
Arr[4] = 8
The array elements after deletion:
arr[0] = 1
Arr[1] = 3
Arr[2] = 7
Arr[3] = 8

Searching in Array
What is Searching?
• Searching is the process of finding the position of a given
value in a list of values.
• It decides whether a search key is present in the data or not.
Searching Techniques:
• To search an element in a given array, it can be done in
following ways:
.
1. Sequential/Linear Search
2. Binary Search

Sequential Search
• Sequential search is also called as Linear Search.
• Sequential search starts at the beginning of the list and
checks every element of the list.
• It is a basic and simple search algorithm.
• Sequential search compares the element with all the other
elements given in the list. If the element is matched, it
returns the value index, else it outputs “value not present”.

Binary Search
• Binary Search is used for searching an element in a sorted
array.
• Binary search works on the principle of divide and conquer.
• This searching technique looks for a particular element by
comparing the middle most element of the collection.
• It is useful when there are large number of elements in an
array.
• The above array is sorted in ascending order. As we know
binary search is applied on sorted lists only for fast
searching.

Binary Search
• For example:
• Binary searching starts with middle element. If the middle element is equal to the element
that we are searching then return true. If the middle element is less than then move to the
right of the list or if the middle element is greater then move to the left of the list. Repeat
this, till you find an element.

Two Dimensional Array
#include<stdio.h>
int main(){
/* 2D array declaration*/
int abc[5][4];
/*Counter variables for the loop*/
int i, j;
for(i=0; i<5; i++) {
for(j=0;j<4;j++) {
printf("Enter value for abc[%d][%d]:", i, j);
scanf("%d", &abc[i][j]);
}
}
return 0;
}
• i =0
J=0 to 3

#include<stdio.h>
int main(){
int disp[2][3];
int i, j;
for(i=0; i<2; i++) {
for(j=0;j<3;j++) {
printf("Enter value for disp[%d][%d]:", i, j);
scanf("%d", &disp[i][j]);
}
}
//Displaying array elements
printf("Two Dimensional array elements:n");
for(i=0; i<2; i++) {
for(j=0;j<3;j++) {
printf("%d", disp[i][j]);
if(j==2){
printf("n");
}
}
}
return 0;
}

#include<stdio.h>
int main(){
int disp[2][3];
int i, j;
for(i=0; i<2; i++) {
for(j=0;j<3;j++) {
printf("Enter value for disp[%d][%d]:", i, j);
scanf("%d", &disp[i][j]);
}
}
//Displaying array elements
printf("Two Dimensional array elements:n");
for(i=0; i<2; i++) {
for(j=0;j<3;j++) {
printf("%d ", disp[i][j]);
if(j==2){
printf("n");
}
}
}
return 0;
}
i= 1, J=0
Enter value for disp[0][0]:1
Two Dimensional array elements:
1 2 3
4 5 6

3. Stack
➢ Stack: Definition.
➢ Application of Stack
➢ Implementation of Stack
➢ Basic Operation on Stack
➢ PUSH Operation (Insertion)
➢ POP Operation (Deletion)

Stack
What is Stack?
• Stack is an ordered list of the same type of elements.
• It is a linear list where all insertions and deletions are
permitted only at one end of the list.
• Stack is a LIFO (Last In First Out) structure.
• In a stack, when an element is added, it goes to the top of
the stack.
Definition:
“Stack is a collection of similar data items in which both
insertion and deletion operations are performed based on
LIFO principle”.

Applications of stack
• Balancing of symbols
• Infix to Postfix /Prefix conversion
• Redo-undo features at many places like editors,
photoshop.
• Forward and backward feature in web browsers.
• Used in many algorithms like Tower of Hanoi, tree
traversals, stock span problem, histogram problem.
• Other applications can be Backtracking, Knight tour
problem, rat in a maze, N queen problem.

Implemention of Stack
• Empty stack: Top = -1 & for full stack: Top = Max_Size - 1

Stack Overflow & Underflow Condition
• Stack Overflow : When the stack is full and user
still try to push an element in, the condition is called
stack overflow/ stack full.
TOP = Max_Size – 1
• Stack Underflow : When the stack is empty and
an user try to pop element from the stack, the
condition is called stack underflow/ stack empty.
TOP = -1

Stack Overflow & Underflow Condition

Basic Operations
• a stack is used for the following two primary
operations −
➢push() − Pushing (storing) an element on the stack.
➢pop() − Removing (accessing) an element from the
stack.

Push Operation
• The process of putting a new data element onto stack is known as a
Push Operation. Push operation involves a series of steps −
Step 1 − Checks if the stack is full.
Step 2 − If the stack is full, output “Stack Overflow”.
Step 3 − If the stack is not full, increments top to point next empty space.
Step 4 − Adds data element to the stack location, where top is pointing.
Step 5 − Returns success.

POP Operation
• A Pop operation may involve the following steps −
Step 1 − Checks if the stack is empty.
Step 2 − If the stack is empty, produces an error and exit.
Step 3 − If the stack is not empty, accesses the data element at which top is pointing.
Step 4 − Decreases the value of top by 1.
Step 5 − Returns success.

Program to Implement Stack
#include <stdio.h>
#include <conio.h>
void push();
void pop();
void display();
int stack[10], top=-1, element;
void main()
{
int ch;
do
{
printf("nnnn 1. Insertn 2. Deleten 3. Displayn 4. Exitn");
printf("n Enter Your Choice: ");
scanf("%d", &ch);
switch(ch)
{
case 1: push();
break;
case 2: pop();
break;
case 3: display();
break;
case 4: exit ();
default: printf("nn Invalid entry. Please try again...n");
}
}
while(ch!=4);
getch();
}

void push()
{
if(top == 9)
printf("nn Stack is Full.");
else
{
printf("nn Enter Element: ");
scanf("%d", &element);
top++;
stack[top] = element;
printf("nn Element Inserted = %d", element);
}
}

void display()
{
int i;
if(top == -1)
printf("nn Stack is Empty.");
else
{
for(i=top; i>=0; i--)
printf("n%d", stack[i]);
}
}

void pop()
{
if(top == -1)
printf("nn Stack is Empty.");
else
{
element = stack[top];
top--;
printf("nn Element Deleted = %d", element);
}
}

4. Infix, Prefix and Postfix
expression
➢ Polish notations.
➢ Infix, Postfix, Prefix form.
➢ Conversion without stack.
➢ Conversion with stack.

Infix, Prefix & Postfix Notaions
• An arithmetic expression can be represented in
various forms such as Infix, Postfix and Prefix.
• Infix notation is also called as Polish notation and
postfix is known as Reverse polish notation.
Infix Expression Prefix Expression Postfix Expression
A + B + A B A B +

Conversion from infix to postfix form
Example: Convert the expression (A + B) / (C - D) to
postfix form.
Solution : (A + B) / (C - D)
(AB+) / (CD-)
Now, Put X = (AB+) and Y = (CD-)
X / Y
XY/
Put the value of X and Y, we get
AB+CD-/

Exercise: Convert the
expression A * B + C / D
to postfix form.

Example: Convert the expression A * B + C / D to postfix
form.
Solution : A * B + C / D
A * B + CD/
A * B + Y [ Put Y = CD/]
AB* + Y
X + Y [ Put X = AB*]
XY+
Put the value of X and Y, we get
AB*CD/+

Infix to postfix Conversion Using Stack
Algorithm:
1. Scan the input string (infix notation) from left to right.
2. If the symbol scanned is an operand, it may be immediately appended to the
postfix string.
3. If the next symbol is an operator,
➢ Pop and append to the postfix string every operator on the stack that
▪ is above the most recently scanned left parenthesis, and
▪ has precedence higher than or is a right-associative operator of equal
precedence to that of the new operator symbol.
➢ Push the new operator onto the stack.
4. When a left parenthesis is seen, it must be pushed onto the stack.
5. When a right parenthesis is seen, all operators down to the most recently
scanned left parenthesis must be popped and appended to the postfix string.
Furthermore, this pair of parentheses must be discarded.
6. When the infix string is completely scanned, the stack may still contain some
operators. All the remaining operators should be popped and appended to the
postfix string.

Example 1: Suppose we are converting 3*3/(4-1)+6*2 expression into postfix form.
Following table shows the evaluation of Infix to Postfix:
Expression Stack Output
3 Empty 3
* * 3
3 * 33
/ / 33*
( /( 33*
4 /( 33*4
- /(- 33*4
1 /(- 33*41
) - 33*41-
+ + 33*41-/
6 + 33*41-/6
* +* 33*41-/62
2 +* 33*41-/62
Empty 33*41-/62*+

Example 2: Suppose we are
converting 5 * (6 + 2) – (12/4)
expression into postfix form using
stack.

Example 2: Suppose we are converting 5 * (6 + 2) – (12/4) expression into postfix
form.
Following table shows the evaluation of Infix to Postfix:

Evaluation of a postfix Expression
Using Stack
Algorithm :
1. Scan the postfix expression from left to right.
2. If an operand is encountered, push it on stack.
3. If an operator ‘op’ is encountered,
▪ Pop two elements of stack, where A is the top element and B is
the next top element.
▪ Evaluate B op A.
▪ Push the result on stack.
4. The evaluated value is equal to the value at the top
of stack.

Evaluation of a postfix Expression Using Stack
Example :
Infix : (5+3) * (8-2)
= 48
Postfix : 5,3,+,8,2,-,*
= 48

5. QUEUE
➢ What is Queue ?
➢ Applications of Queue.
➢ Queue Representation.
➢ Types of Queue:
➢Simple Queue
➢Circular Queue
➢Priority Queue
➢Double Ended Queue
➢Program to implement a queue using Array

What is Queue ?
• Queue is a linear data structure where the first element is inserted from
one end called REAR and deleted from the other end called as FRONT.
• Front points to the beginning of the queue and Rear points to
the end of the queue.
• Queue follows the FIFO (First - In - First Out) structure.
• According to its FIFO structure, element inserted first will also be
removed first.
• In a queue, one end is always used to insert data (enqueue) and the
other is used to delete data (dequeue), because queue is open at both
its ends.
• The enqueue() and dequeue() are two important functions used in a
queue.
REAR FRONT

What is Queue ?
• A real-world example of queue can be a single-lane one-
way road, where the vehicle enters first, exits first. More
real-world examples can be seen as queues at the ticket
windows and bus-stops.

Applications of Queue
Due to the fact that queue performs actions on first in first out
basis which is quite fair for the ordering of actions. There are
various applications of queues discussed as below.
1.Queues are widely used as waiting lists for a single shared
resource like printer, disk, CPU.
2.Queues are used in asynchronous transfer of data (where
data is not being transferred at the same rate between two
processes) for eg. pipes, file IO, sockets.
3.Queues are used as buffers in most of the applications like
MP3 media player, CD player, etc.
4.Queue are used to maintain the play list in media players in
order to add and remove the songs from the play-list.
5.Queues are used in operating systems for handling
interrupts.

Array Representation of Queue
• We can easily represent queue by using linear arrays. There are two variables
i.e. front and rear, that are implemented in the case of every queue. Front and
rear variables point to the position from where insertions and deletions are
performed in a queue. Initially, the value of front and rear is -1 which represents
an empty queue. Array representation of a queue containing 5 elements along
with the respective values of front and rear, is shown in the following figure.
• The above figure shows the queue of characters forming the English
word "HELLO". Since, No deletion is performed in the queue till now, therefore
the value of front remains 0 .

• However, the value of rear increases by one every time an insertion is
performed in the queue. After inserting one more element into the queue shown
in the previous figure, the queue will look something like following.
• The value of rear will become 5 while the value of front remains same.

• After deleting an element, the value of front will increase
from 0 to 1. however, the queue will look something like
following.

Types of Queue
• There are four types of Queue:
1. Simple Queue
2. Circular Queue
3. Priority Queue
4. Double Ended Queue

Types of Queue
1. Simple Queue :
➢ As is clear from the name itself, simple queue lets us perform
the operations simply. i.e., the insertion and deletions are
performed likewise. Insertion occurs at the rear (end) of the
queue and deletions are performed at the front (beginning) of
the queue list.
➢ Initially, the value of front and rear is -1 which represents an
empty queue.

Types of Queue
2. Circular Queue :
• In a circular queue, all nodes are treated as circular. Last node is connected
back to the first node.
• Circular queue is also called as Ring Buffer.
• Circular queue contains a collection of data which allows insertion of data at
the end of the queue and deletion of data at the beginning of the queue.

Types of Queue
3. Priority Queue :
• Priority queue contains data items which have some preset priority. While
removing an element from a priority queue, the data item with the highest
priority is removed first.
• In a priority queue, insertion is performed in the order of arrival and deletion
is performed based on the priority.

Types of Queue
4. Double Ended Queue (Deque) :
• Double ended queue allows insertion and deletion from both the ends i.e.
elements can be added or removed from rear as well as front end.
• There are two variations in Deque:
➢ Input-Restricted Deque
➢ Output-Restricted Deque.

Types of Queue
Input Restricted Double Ended Queue
• In input restricted double-ended queue, the insertion operation is performed
at only one end and deletion operation is performed at both the ends.
Output Restricted Double Ended Queue
• In output restricted double ended queue, the deletion operation is performed
at only one end and insertion operation is performed at both the ends.

Program to implement a queue using Array
#include <stdio.h>
int queue_array[50];
int rear = - 1, front = - 1;
main()
{
int choice;
while (1)
{
printf("1.Insert n");
printf("2.Deleten");
printf("3.Display n");
printf("4.Exit n");
printf("Enter your choice : ");
scanf("%d", &choice);
switch (choice)
{
case 1: insert();
break;
case 2: delete();
break;
case 3: display();
break;
case 4: exit(1);
default: printf("Inavlid choice n");
} /*End of switch*/
} /*End of while*/
} /*End of main()*/

insert()
{
int add_item;
if (rear == 49)
printf("Queue Overflow n");
else
{
if (front == - 1)
/*If queue is initially empty */
front = 0;
printf("Inset the element in queue : ");
scanf("%d", &add_item);
rear = rear + 1;
queue_array[rear] = add_item;
}
} /*End of insert()*/

delete()
{
if (front == - 1 || front > rear)
{
printf("Queue Underflow n");
return ;
}
else
{
printf("Deleted Element is : %dn",
queue_array[front]);
front = front + 1;
}
} /*End of delete() */

display()
{
int i;
if (front == - 1)
printf("Queue is empty n");
else
{
printf("Queue is : n");
for (i = front; i <= rear; i++)
printf("%d ", queue_array[i]);
printf("n");
}
} /*End of display() */

6. Pointers
➢ Address in C.
➢ Pointer Syntax.
➢ Assigning Addresses to pointers.
➢ Changing the value pointed by pointers
➢ Working of pointers.

Pointers in C programming
“Pointers are powerful features
of C and C++ programming.
Before we learn pointers, let's
learn about addresses in C
programming.”

Address in C
• If you have a variable var in your program, &var
will give you its address in the memory.
• We have used address numerous times while
using the scanf() function:
scanf (“ %d” , &var) ;
• Here, the value entered by the user is stored in
the address of var variable. Let's take a working
example.
Note :
&= ampersand ‘address of’ operator
&a = address of a printf(“%d”, &a)

Address in C
include <stdio.h>
int main()
{ int var = 5;
printf("var: %dn", var); // Notice the use of & before var
printf("address of var: %d", &var);
return 0;
}
Output:
var: 5
address of var: 266768
Note: You will probably get a different address when you run the above code.

Pointer Syntax
• Pointers (pointer variables) are special variables that are
used to store addresses rather than values.
• Pointer Syntax
➢ Here is how we can declare pointers.
int *p; // we have declared a pointer p of int type.
➢ You can also declare pointers in these ways.
Int *p1; or int * p2;
➢ Let's take another example of declaring pointers.
Int *p1, p2 ; // Here, we have declared a pointer p1 and a normal variable p2.

Assigning addresses to Pointers
• Let's take an example.
int *pc, c ;
c = 5 ; 222 999
pc = &c ; c (*pc) pc
Here, 5 is assigned to the c variable. And, the address of c
is assigned to the pc pointer.
Note:
• In the above example, pc is a pointer, not *pc. You cannot and
should not do something like *pc = &c ;
• & is ‘address of’ operator. For e.g &a means address of a.
• * is ‘value at address’ operator. For e.g *a means value at
address stored in a.
5 222

Changing Value Pointed by Pointers
• Let's take an example.
int* pc, c;
c = 5;
pc = &c;
c = 1;
printf("%d", c); // Output: 1
printf("%d", *pc); // Ouptut: 1
➢ We have assigned the address of c to the pc pointer.
➢ Then, we changed the value of c to 1. Since pc and the address
of c is the same, *pc gives us 1.
• Let's take another example.
int* pc, c;
c = 5;
pc = &c;
*pc = 1;
printf("%d", *pc); // Ouptut: 1
printf("%d", c); // Output: 1
➢ We have assigned the address of c to the pc pointer.
➢ Then, we changed *pc to 1. Since pc and the address of c is the
same, c will be equal to 1.

Changing Value Pointed by Pointers
• Let's take one more example.
int* pc, c, d;
c = 5;
d = -15;
pc = &c;
printf("%d", *pc); // Output: 5
pc = &d;
printf("%d", *pc); // Ouptut: -15
➢ Initially, the address of c is assigned to the pc pointer using pc =
&c; . Since c is 5, *pc gives us 5.
➢ Then, the address of d is assigned to the pc pointer using pc =
&d; . Since d is -15, *pc gives us -15.

Working of Pointers
#include <stdio.h>
int main()
{
int* pc, c;
c = 22;
printf("Address of c: %dn", &c);
printf("Value of c: %dnn", c); // 22
pc = &c;
printf("Address of pointer pc: %dn", pc);
printf("Content of pointer pc: %dnn", *pc); //
22
c = 11;
printf("Address of pointer pc: %dn", pc);
printf("Content of pointer pc: %dnn", *pc); //
11
*pc = 2;
printf("Address of c: %dn", &c);
printf("Value of c: %dnn", c); // 2
return 0;
}
Address of c: 2686784
Value of c: 22
Address of pointer pc: 2686784
Content of pointer pc: 22
Address of pointer pc: 2686784
Content of pointer pc: 11
Address of c: 2686784
Value of c: 2

Common mistakes when working with
pointers
Suppose, you want pointer pc to point to the address of c, then
int c, *pc;
// pc is address but c is not
pc = c; // Error
// &c is address but *pc is not
*pc = &c; // Error
// both &c and pc are addresses
pc = &c;
// both c and *pc values
*pc = c;

7. Linked List
➢ Linked list: Definition.
➢ Advantages & disadvantages of linked list.
➢ Types of linked list.

Linked List: Definition
• Linked list is a linear data structure. It is a collection of data
elements, called nodes pointing to the next node by means of a
pointer.
• In linked list, each node consists of its own data and the address of
the next node and forms a chain.
• The above figure shows the sequence of linked list which contains
data items connected together via links. It can be visualized as a
chain of nodes, where every node points to the next node.
• Linked list is a dynamic data structure.

Advantages & Disadvantages
Advantages :
• Linked list is dynamic in nature which allocates the
memory when required.
• There is no need to define an initial size
• Insert and delete operation can be easily implemented in
linked list.
Disadvantages :
• Linked list has to access each node sequentially; no
element can be accessed randomly.
• In linked list, the memory is wasted as pointer requires
extra memory for storage.

Types of Linked List
• Following are the types of Linked List
1. Singly Linked List
2. Doubly Linked List
3. Circular Linked List
4. Doubly Circular Linked List

Singly Linked List
• Each node has a single link to another node is called
Singly Linked List.
• Singly Linked List does not store any pointer to the
previous node.
• Each node stores the contents of the node and a
reference/address to the next node in the list.
• It has two successive nodes linked together in linear way
and contains address of the next node to be followed.
• It has successor and predecessor. First node does not
have predecessor while last node does not have
successor. Last node have successor reference as NULL.

Singly Linked List
• It has only single link for the next node.
• In this type of linked list, only forward sequential
movement is possible, no direct access is
allowed.

Doubly Linked List
• Doubly linked list is a sequence of elements in which every node has
link to its previous node and next node.
• Traversing can be done in both directions and displays the contents
in the whole list.
• In the above figure, Link1 field stores the address of the previous
node and Link2 field stores the address of the next node. The Data
Item field stores the actual value of that node. If we insert a data into
the linked list, it will be look like as follows:

Doubly Linked List
Advantages of Doubly Linked List
• Doubly linked list can be traversed in both forward and backward
directions.
• To delete a node in singly linked list, the previous node is required,
while in doubly linked list, we can get the previous node using
previous pointer.
• It is very convenient than singly linked list. Doubly linked list maintains
the links for bidirectional traversing.
Disadvantages of Doubly Linked List
• In doubly linked list, each node requires extra space for previous
pointer.
• All operations such as Insert, Delete, Traverse etc. require extra
previous pointer to be maintained.

Circular Linked List
• Circular linked list is similar to singly linked list. The only difference is
that in circular linked list, the last node points to the first node in the
list.
• In the above figure we see that, each node points to its next node in the
sequence but the last node points to the first node in the list. The previous
node stores the address of the next node and the last node stores the
address of the starting node.
• Circular linked list is used in personal computers, where multiple applications
are running. The operating system provides a fixed time slot for all running
applications and the running applications are kept in a circular linked list until
all the applications are completed. This is a real life example of circular linked
list.

Circular Doubly Linked List
• A circular doubly linked list or a circular two-way linked list is a more
complex type of linked list which contains a pointer to the next as well
as the previous node in the sequence.
• The next field of the last node stores the address of the first node of
the list.
• Similarly, the previous field of the first field stores the address of the
last node.
• The previous link of the first node points to the last node and the next
link of the last node points to the first node.
• In doubly circular linked list, each node contains two fields called links
used to represent references to the previous and the next node in the
sequence of nodes.

Binary Tree Traversal
• Traversal is the process of visiting every node once.
• Visiting a node means doing some processing at that
node, but when describing a traversal strategy, we
need not concern ourselves with what that processing
is.
• Three recursive techniques for binary tree traversal
• In each technique, the left subtree is traversed
recursively, the right subtree is traversed
recursively, and the root is visited
• What distinguishes the techniques from one another is
the order of those 3 tasks

Preorder, Inorder, Postorder
• In Preorder, the root
is visited before (pre)
the subtrees traversals
• In Inorder, the root is
visited in-between left
and right subtree traversal
• In Preorder, the root
is visited after (pre)
the subtrees traversals
Preorder Traversal:
1. Visit the root
2. Traverse left subtree in preorder
3. Traverse right subtree in preorder
Inorder Traversal:
1. Traverse left subtree in inorder
2. Visit the root
3. Traverse right subtree in inorder
Postorder Traversal:
1. Traverse left subtree in postorder
2. Traverse right subtree in postorder
3. Visit the root

Example of Traversal
• Assume: visiting a node
is printing its label
• Preorder:
1 3 5 4 6 7 8 9 10 11 12
• Inorder:
4 5 6 3 1 8 7 9 11 10 12
• Postorder:
4 6 5 3 8 11 12 10 9 7 1
1
3
11
9
8
4 6
5
7
12
10

• Preorder: 1,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1,
1
3
11
9
8
4 6
5
7
12
10
Visit the left
subtree in
preorder

• Preorder: 1, 3,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3,
1
3
11
9
8
4 6
5
7
12
10
Visit the left
subtree in
preorder

• Preorder: 1, 3, 5
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5
1
3
11
9
8
4 6
5
7
12
10
Visit the left
subtree in
preorder

• Preorder: 1, 3, 5, 4,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5, 4,
1
3
11
9
8
4 6
5
7
12
10
There is no left or
right subtree so
preorder traversal
is over at this
node

• Preorder: 1, 3, 5, 4,
1
3
11
9
8
4 6
5
7
12
10
Visit the right
subtree in
preorder

• Preorder: 1, 3, 5, 4, 6,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5, 4, 6,
1
3
11
9
8
4 6
5
7
12
10
There is no left or
right subtree so
preorder traversal
is over at this
node

• Preorder: 1, 3, 5, 4, 6,
1
3
11
9
8
4 6
5
7
12
10
Visit the right
subtree in
preorder

• Preorder: 1, 3, 5, 4, 6, 7,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5, 4, 6, 7,
1
3
11
9
8
4 6
5
7
12
10
Visit the left
subtree in
preorder

• Preorder: 1, 3, 5, 4, 6, 7, 8,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5, 4, 6, 7, 8,
1
3
11
9
8
4 6
5
7
12
10
There is no left or
right subtree so
preorder traversal
is over at this
node

• Preorder: 1, 3, 5, 4, 6, 7, 8,
1
3
11
9
8
4 6
5
7
12
10
Visit the right
subtree in
preoder

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9,
1
3
11
9
8
4 6
5
7
12
10
There is no
left subtree

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9,
1
3
11
9
8
4 6
5
7
12
10
Visit the right
subtree in
preorder

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9, 10,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9, 10,
1
3
11
9
8
4 6
5
7
12
10
Visit the left
subtree in
preorder

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9, 10, 11,
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9, 10, 11,
1
3
11
9
8
4 6
5
7
12
10
There is no left or
right subtree so
preorder traversal
is over at this
node

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9, 10, 11,
1
3
11
9
8
4 6
5
7
12
10
Visit the right
subtree

• Preorder: 1, 3, 5, 4, 6, 7, 8, 9, 10, 11, 12.
1
3
11
9
8
4 6
5
7
12
10
Visit the root
node

Insertion Operation in BST
The insertion operation is performed as follows...
Step 1 - Create a newNode with given value and set its left and right to
NULL.
Step 2 - Check whether tree is Empty.
Step 3 - If the tree is Empty, then set root to newNode.
Step 4 - If the tree is Not Empty, then check whether the value of newNode
is smaller or larger than the node (here it is root node).
Step 5 - If newNode is smaller than or equal to the node then move to its
left child. If newNode is larger than the node then move to its right
child.
Step 6- Repeat the above steps until we reach to the leaf node (i.e.,
reaches to NULL).
Step 7 - After reaching the leaf node, insert the newNode as left child if the
newNode is smaller or equal to that leaf node or else insert it as
right child.

Insertion Operation in BST
•
• Construct a Binary Search Tree by
inserting the following sequence of
numbers...
10,12,5,4,20,8,7,15 and 13
Above elements are inserted into a
Binary Search Tree as follows...

Deletion Operation in BST
• In a binary search tree, the deletion operation is
performed with O(log n) time complexity. Deleting a
node from Binary search tree includes following
three cases...
➢ Case 1: Deleting a Leaf node (A node with no
children)
➢ Case 2: Deleting a node with one child
➢ Case 3: Deleting a node with two children

Case 1: Deleting a leaf node
• We use the following steps to delete a leaf node from BST...
Step 1 - Find the node to be deleted using search operation
Step 2 - Delete the node using free function (If it is a leaf) and
terminate the function.

Case 2: Deleting a node with one child
• We use the following steps to delete a node with one child from BST...
Step 2 - If it has only one child then create a link between its parent node
and child node.
Step 3 - Delete the node using free function and terminate the function.

Case 3: Deleting a node with two children
• We use the following steps to delete a node with two children from BST...
Step 2 - If it has two children, then find the largest node in its left subtree
(OR) the smallest node in its right subtree.
Step 3 - Swap both deleting node and node which is found in the above
step.
Step 4 - Then check whether deleting node came to case 1 or case 2 or
else goto step 2
Step 5 - If it comes to case 1, then delete using case 1 logic.
Step 6- If it comes to case 2, then delete using case 2 logic.
Step 7 - Repeat the same process until the node is deleted from the tree.

Case 3: Deleting a node with two children

ASSIGNMENT
Q 1. Explain all the cases of deletion operation
in binary search tree.
Q 2. Create a binary search tree from the
following list of elements :
32, 14, 23, 40, 17, 48, 35, 45

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