Unit 1 Introduction Part 3.pptx

Data Structures
Unit 1
Introduction
Mrs. Nisha Robin Rohit
Assistant Professor
AMET

Before studying about Data Structures, we should make ourselves aware of the
various terms used in the subject.
 Data
 Entity
 Information
 Data type
 Built-in data type
 Abstract data type

Data
The term data means value or set of values.
Example of data:
a) 34
b) 12/01/1980
c) ISBN 81-203-0000-0
d) |||
e) Pascal
f) 21,25,28,56,90

Entity
 An entity is one that has certain attributes, and which may be assigned values.
 For example, an employee in an organization is an entity.
 The possible attributes and their corresponding values for an entity in the present
example are:
Entity : EMPLOYEE
Attributes: NAME DOB SEX DESIGNATION
Values : RAVI ANAND 30/12/92 M DIRECTOR
 All of the employees in an organization constitute an entity set.
 Each attribute of an entity set has a range of values, and this range is called the
domain of the attribute.
 For example, in EMPLOYEE entity, the attribute SEX has the domain {M,F}.

Entity (ANOTHER EXAMPLE)
Entity : HUMAN
Attributes: SEX SKIN COLOUR EYE COLOUR
Values : M/F DARK/FAIR BLACK/BLUE/BROWN
 Each attribute of an entity set has a range of values, and this range is called
the domain of the attribute.
 For example, in HUMAN entity, the attribute SKIN COLOUR has the domain
{DARK,FAIR,WHEATISH}.

Information
 The term information is used for data with its attributes.
 In other words, information can be meaningful data or processed data.
Data Meaning
34 Age of the person
12/01/1980 Date of Birth of a person
ISBN 81-203-0000-0 Book number, recently published by the person
||| Number of awards equal to the tally marks
achieved by the person
Pascal Nickname of the person
21,25,28,56,90 Important ages of the person

Difference between data and information
Data
Procedure to
process data
Information 1
Information 2
.
.
.
Information I
.
.
Information n
As an example, suppose there is a set of data consisting of the amount of milk
consumed by a person in a month.
From this given set of data, information can be retrieved as follows:
What was the total amount of milk consumed in a month?
On which day was the maximum amount of milk consumed?
On which day was the minimum amount of milk consumed?
What was the average amount of milk consumption per day?

Data Type
A data type is a term refers to the kind of data that may appear in a computation.
The following are few well known data types.
Data Data type
34 Numeric(integer)
12/01/1980 Date
ISBN 81-203-0000-0 Alphanumeric
||| Graphics
Pascal String
21,25,28,56,90 Array of Integers
Real, Boolean, character, complex, etc. are some more frequently used data types.

Built-in Data Type
In every programming language, there is a set of data types called built-in data
types. For example, in C, Java and Python the data types that are available as built-
in are listed below:
Programming Language Built-in Data types
C int, float, char, double, Enum, etc.
Java integer, string, time
Python numeric, sequence, set, binary, string, etc.

Built-in data type provide users with lot of advantages like,
 How to store a value for that variable
 What are all the different operations possible on that data
 What amount of memory is required to store that data
All these things taken care by the compiler or the run time system manager.

Abstract Data type
• When an application requires special kind of data which is not available as a
built-in data type, then it is programmer’s responsibility to implement his own
kind of data.
• Here the programmer must decide all these following things and must
implement them.
 How to store a value for that variable
 What are all the different operations possible on that data
 What amount of memory is required to store that data
Abstract data type is termed as User-defined data.

Concept of Data Structures:
 A digital computer can manipulate only primitive data, that is, data in terms of 0’s
and 1’s.
 But in our real-life applications, various kinds of data other than the primitive data
are involved.
 Manipulation of these real-life data (Or User defined data) requires the following
essential tasks:
 Storage representation of data: User data should be stored in such a way
that computer can understand it.
 Retrieval of stored data: Data stored in computer should be retrieved in
such a way that the user can understand it.
 Transformation of User data: Various operations which require to be
performed on user data so that it can be transformed from one form to
another.

What is an Algorithm? Algorithm
Basics
 Implementation of Data Structures need algorithms.
 The word Algorithm means ” A set of finite rules or instructions to be
followed in calculations or other problem-solving operations ” .
 Therefore Algorithm refers to a sequence of finite steps to solve a particular
problem.
 Algorithms can be simple and complex depending on what you want to

 It can be understood by taking the example of cooking a new recipe: To cook a
new recipe, one reads the instructions and steps and executes them one by
one, in the given sequence.
 The result thus obtained is the new dish cooked perfectly.
 The Algorithm designed are language-independent, i.e. they are just plain
instructions that can be implemented in any language, and yet the output will
be the same, as expected.

What are the Characteristics of an Algorithm?

As one would not follow any written instructions to cook the recipe, but only the
standard one. Similarly, not all written instructions for programming is an
algorithms. In order for some instructions to be an algorithm, it must have the
following characteristics:
•Clear and Unambiguous: The algorithm should be clear and unambiguous.
Each of its steps should be clear in all aspects and must lead to only one
meaning.
•Well-Defined Inputs: If an algorithm says to take inputs, it should be well-
defined inputs. It may or may not take input.
•Well-Defined Outputs: The algorithm must clearly define what output will be
yielded and it should be well-defined as well. It should take at least 1 output.

•Finite-ness: The algorithm must be finite, i.e. it should terminate after a finite
time.
•Feasible: The algorithm must be simple, generic, and practical, such that it can
be executed with the available resources. It must not contain some future
technology or anything.
•Language Independent: The Algorithm designed must be language-
independent, i.e. it must be just plain instructions that can be implemented in

Properties of Algorithm:
•It should terminate after a finite time.
•It should produce at least one output.
•It should take zero or more input.
•It should be deterministic means giving the same output for the same input
case.
•Every step in the algorithm must be effective i.e. every step should do some

Advantages of Algorithms:
•It is easy to understand.
•An algorithm is a step-wise representation of a solution to a given problem.
•In Algorithm the problem is broken down into smaller pieces or steps hence, it is
easier for the programmer to convert it into an actual program.
Disadvantages of Algorithms:
•Writing an algorithm takes a long time so it is time-consuming.
•Understanding complex logic through algorithms can be very difficult.
•Branching and Looping statements are difficult to show in Algorithms(imp).

How to Design an Algorithm?
In order to write an algorithm, the following things are needed as a pre-requisite:
1.The problem that is to be solved by this algorithm i.e. clear problem definition.
2.The constraints of the problem must be considered while solving the problem.
3.The input to be taken to solve the problem.
4.The output to be expected when the problem is solved.
5.The solution to this problem, is within the given constraints.
Then the algorithm is written with the help of the above parameters such that it
solves the problem.
Example: Consider the example to add three numbers and print the sum.

Step 1: Fulfilling the pre-requisites
As discussed above, in order to write an algorithm, its pre-requisites must be
fulfilled.
• The problem that is to be solved by this algorithm: Add 3 numbers and
print their sum.
• The constraints of the problem that must be considered while solving
the problem: The numbers must contain only digits and no other characters.
• The input to be taken to solve the problem: The three numbers to be
added.
• The output to be expected when the problem is solved: The sum of the
three numbers taken as the input i.e. a single integer value.
• The solution to this problem, in the given constraints: The solution

Step 2: Designing the algorithm
Now let’s design the algorithm with the help of the above pre-requisites:
Algorithm to add 3 numbers and print their sum:
• START
• Declare 3 integer variables num1, num2 and num3.
• Take the three numbers, to be added, as inputs in variables num1, num2,
and num3 respectively.
• Declare an integer variable sum to store the resultant sum of the 3 numbers.
• Add the 3 numbers and store the result in the variable sum.
• Print the value of the variable sum
• END

Step 3: Testing the algorithm by implementing it.
In order to test the algorithm, let’s implement it in C language.
// C++ program to add three numbers
// with the help of above designed
// algorithm
#include <bits/stdc++.h>
using namespace std;
int main()
{
// Variables to take the input of
// the 3 numbers
int num1, num2, num3;

// Variable to store the resultant sum
int sum;
// Take the 3 numbers as input
cout << "Enter the 1st number: " ;
cin >> num1;
cout << " " << num1 << endl;
cout << "Enter the 2nd number: ";
cin >> num2;
cout << " " << num2 << endl;
cout << "Enter the 3rd number: ";
cin >> num3;
cout << " " << num3;

// Calculate the sum using + operator
// and store it in variable sum
sum = num1 + num2 + num3;
// Print the sum
cout << "nSum of the 3 numbers is: " << sum;
return 0;
}

Python3 program to add three numbers
# with the help of above designed
# algorithm
if __name__ == "__main__":
# Variables to take the input of
# the 3 numbers
num1 = num2 = num3 = 0
# Variable to store the resultant sum
sum = 0

# Take the 3 numbers as input
num1 = int(input("Enter the 1st number: "))
num2 = int(input("Enter the 2nd number: "))
num3 = int(input("Enter the 3rd number: "))
# Calculate the sum using + operator
# and store it in variable sum
sum = num1 + num2 + num3
# Print the sum
print("nSum of the 3 numbers is:", sum)
Output
Enter the 1st number: 0
Enter the 2nd number: 0
Enter the 3rd number: -1577141152
Sum of the 3 numbers is: -1577141152

What is meant by Algorithm Analysis?
Algorithm analysis is an important part of computational complexity theory,
which provides theoretical estimation for the required resources of an
algorithm to solve a specific computational problem.
Analysis of algorithms is the determination of the amount of time and space
resources required to execute it.

 In the analysis of the algorithm, it generally focused on CPU (time) usage,
Memory usage, Disk usage, and Network usage.
 All are important, but the most concern is about the CPU time. Be careful to
differentiate between:
Performance: How much time/memory/disk/etc. is used when a program is
run. This depends on the machine, compiler, etc. as well as the code we write.
Complexity: How do the resource requirements of a program or algorithm
scale, i.e. what happens as the size of the problem being solved by the code
gets larger.

Why Analysis of Algorithms is important?
 To predict the behaviour of an algorithm without implementing it on a specific
computer.
 It is much more convenient to have simple measures for the efficiency of an
algorithm than to implement the algorithm and test the efficiency every time a
certain parameter in the underlying computer system changes.
 It is impossible to predict the exact behaviour of an algorithm. There are too
many influencing factors.
 The analysis is thus only an approximation; it is not perfect.
 More importantly, by analysing different algorithms, we can compare them to
determine the best one for our purpose.

How to analyze an Algorithm?
For a standard algorithm to be good, it must be efficient. Hence the efficiency of an
algorithm must be checked and maintained. It can be in two stages:
1.Priori Analysis:
 “Priori” means “before”. Hence Priori analysis means checking the algorithm
before its implementation.
 In this, the algorithm is checked when it is written in the form of theoretical
steps.
 This Efficiency of an algorithm is measured by assuming that all other factors,
for example, processor speed, are constant and have no effect on the
implementation.
 This is done usually by the algorithm designer.

2. Posterior Analysis:
“Posterior” means “after”. Hence Posterior analysis means checking the
algorithm after its implementation.
In this, the algorithm is checked by implementing it in any programming
language and executing it.
This analysis helps to get the actual and real analysis report about
correctness(for every possible input/s if it shows/returns correct output or not),
space required, time consumed etc.
That is, it is dependent on the language of the compiler and the type of
hardware used.

Types of Algorithm Analysis:
1.Best case
2.Worst case
3.Average case
•Best case:
Define the input for which algorithm takes less time or minimum time.
In the best case calculate the lower bound of an algorithm.
Example: In the linear search when search data is present at the first
location of large data then the best case occurs.

•Worst Case:
Define the input for which algorithm takes a long time or maximum time.
In the worst calculate the upper bound of an algorithm.
Example: In the linear search when search data is not present at all then the
worst case occurs.
•Average case:
In the average case take all random inputs and calculate the computation
time for all inputs.
And then we divide it by the total number of inputs.
Average case = all random case time / total no of case

Popular Notations in Complexity Analysis of Algorithms
1. Big-O Notation
 We define an algorithm’s worst-case time complexity by using the Big-O
notation.
 It explains the maximum amount of time an algorithm requires to consider
all input values.

2. Omega Notation
 It defines the best case of an algorithm’s time complexity
 It explains the minimum amount of time an algorithm requires to consider
all input values.
3. Theta Notation
 It defines the average case of an algorithm’s time complexity.
 Both O(expression) and Omega(expression), then Theta notation is

Array Definition:
An array is a finite, ordered and collection of homogeneous data elements.
Finite : It contains only a limited number of elements.
Ordered : All the elements are stored one by one in contiguous locations
of the computer memory in a linear ordered fashion.
Homogeneous : All the elements in the array are of same data type.
Example : 1. An array of integers to store the age of all students in a class.
2. An array of strings (of characters) to store the names
of all villagers in a village.

If we want to store a group of data together in one place, then an array is the data
structure we should be looking for.
All the elements are stored in
contiguous locations of the memory.
Figure shows an array of data stored in
a memory block starting at location
5000.

Applications of Arrays in Real Life:
1. Arrangement of the leader-board of a game can be done simply through arrays to store the
score and arrange them in descending order to clearly make out the rank of each player in
the game.
2. A simple question Paper is an array of numbered questions with each of them assigned
some marks.
3. Your viewing screen is also a multidimensional array of pixels.
4. Book titles in a Library Management Systems.
5. Online ticket booking.
6. Contacts on a cell phone.
7. To store the possible moves of chess on a chessboard.

Terminology:
Size : The number of elements in an array.
Also called length or dimension.
Type : The kind of data type of elements.
Base : The base of an array is the address of the memory location
where the first element of the array is located.
Index : All the elements in the array can be referenced by
a subscript like Ai or A[i]. This subscript is known as index.

Range of indices : Indices of Array may range from lower bound to Upper bound, and
theses bounds are called the boundaries of an array.
Word : Word denotes the size of an element. In each memory location, a
computer can store an element of word size w. This word size
varies from 1 byte to 8 bytes.

Arrays
One-Dimensional
Arrays Multidimensional Arrays
Two-Dimensional
Arrays
Sparse Matrices
Three-dimensional(3D)
Arrays

One- Dimensional Array:
If only one subscript/index is required to reference all the elements in an array, then the array
is termed as one-dimensional array or simply an array.
M 1
2
3
100
.
.
.
An array A[100] is to be stored in a memory
as in Figure. Let the memory location where
the first element stored be M.

Operations on Arrays:
Traversing : To visit all elements in an array.
Sorting : To sort in a specified order (ascending/descending)
Searching : To search an element of interest in an array.
Insertion : To insert an element into an array provided that the array is not full.
Deletion : To delete a particular element from an array.
Merging : Merging is important when we need to compact the elements from two
different arrays into a single array.

Application of Arrays:
If we want to store records of all students in a class. It can be done by using 6 arrays.
STUDENTS
ROLL NO. MARK1 MARK2 MARK3 TOTAL GRADE
Alphanumeric Numeric Numeric Numeric Numeric Character
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Multidimensional Arrays
Two-Dimensional Arrays:
 They are (alternatively termed us matrices) a collection of homogeneous elements where
the elements are ordered in a number of rows and columns.
 An example of an mxn matrix, where m denotes the number of rows and n denotes the
number of columns, is as follows:
a11 a12 a13 a14 ……………. a1n
a21 a22 a23 a24 ……………. a2n
. . . . .
. . . . .
. . . . .
am1 am2 am3 am4 ……………. amn

Let us now suppose that we wish to express the information of possession of pens and pencils by Ram
and his two friends Rohan and Yash which is as follows:
Ram has 20 pens and 7 pencils,
Rohan has 15 pens and 5 pencils,
Yash has 12 pens and 3 pencils.
Now, this could be arranged in tabular form as follows,
Pens Pencils
Ram 20 7
Rohan 15 5
Yash 12 3
Example of Matrix

and this can be expressed as,
In the above arrangement,
 The entries in the first column represent the number of pens possessed by Ram, Rohan, and Yash
 The entries in the second column represents the number of pencils possessed by Ram, Rohan, and
Yash, respectively.

Sparse Matrices:
A sparse matrix is a two-
dimensional array where
most of the elements have
the value null.

Why to use Sparse Matrix instead of simple matrix ?
 Storage: There are lesser non-zero elements than zeros and thus lesser memory can
be used to store only those elements.
 Computing time: Computing time can be saved by logically designing a data structure
traversing only non-zero elements..

Representing a sparse matrix by a 2D array leads to wastage of lots of memory as zeroes in the
matrix are of no use in most of the cases.
So, instead of storing zeroes with non-zero elements, we only store non-zero elements. This
means storing non-zero elements with triples- (Row, Column, value).
Sparse Matrix Representations can be done in many ways following are two common
representations:
1.Array representation
2.Linked list representation

Method 1: Using Arrays:
2D array is used to represent a sparse matrix in which there are three rows named as
 Row: Index of row, where non-zero element is located
 Column: Index of column, where non-zero element is located
 Value: Value of the non zero element located at index – (row, column)

Method 2: Using Linked Lists
In linked list, each node has four fields. These four fields are defined as:
 Row : Index of row, where non-zero element is located
 Column : Index of column, where non-zero element is located
 Value : Value of the non zero element located at index – (row,column)
 Next node : Address of the next node

Stack
It is a linear data structure that follows a particular order in which the operations are performed.
LIFO( Last In First Out ):
This strategy states that the element that is inserted last will come out first.
Examples:
 Plates on a tray.
 Shunting of trains in a railway yard.
 Shipment in a cargo.

Application of Stacks in Real Life:
1. Converting infix to postfix expressions.
2. Undo/Redo button/operation in word processors.
3. Syntaxes in languages are parsed using stacks.
4. It is used in many virtual machines like JVM.
5. Forward-backward surfing in the browser.
6. History of visited websites.
7. Message logs and all messages you get are arranged in a stack.
8. Call logs, E-mails, Google photos’ any gallery, YouTube downloads, Notifications ( latest appears
first ).

1. Scratch card’s earned after Google pay transaction.
2. Wearing/Removing Bangles, Pile of Dinner Plates, Stacked chairs.
3. Changing wearables on a cold evening, first in, comes out at last.
4. Last Hired, First Fired-which is typically utilized when a company reduces its workforce in an
economic recession.
5. Loading bullets into the magazine of a gun. The last one to go in is fired first. Bam!
6. Media playlist. T o play previous and next song

Basic Operations on Stack
In order to make
manipulations in a stack, there
are certain operations
provided to us.
 push() to insert an
element into the stack
 pop() to remove an
element from the stack
 top() Returns the top
element of the stack.
 isEmpty() returns true is
stack is empty else false.
 size() returns the size of
stack.

Push:
Adds an item to the stack. If the stack is full, then it is said to be an Overflow condition.
Algorithm for push:
Begin
if stack is full
return
endif
else
increment top
stack[top] assign value
end else
end procedure

Pop:
Removes an item from the stack. The items are popped in the reversed order in which they are
pushed. If the stack is empty, then it is said to be an Underflow condition.
Algorithm for pop:
Begin
if stack is empty
return
endif
else
store value of stack[top]
decrement top
return value
end else
end procedure

Top:
Returns the top element of the stack.
Algorithm for Top:
begin
return stack[top]
end procedure
isEmpty:
Returns true if the stack is empty, else false.
Algorithm for isEmpty:
begin
if top < 1
return true
else
return false
end procedure

What is an Expression?
An expression is a set of numbers or variables combined using the operations A+B, A-B, A*B, A/B.
Infix expression: The expression of the form (a + b). When an operator is in-between every pair of
operands.
Postfix expression: The expression of the form (ab+). When an operands is followed by every pair of
operators.
Prefix expression: The expression of the form (+ab). When an operator is followed by every pair of
operands.
Application of Stack

Examples:
Input: A + B * C + D Input: ((A + B) – C * (D / E)) + F
Output: ABC*+D+ Output: AB+CDE/*-F+
Why postfix representation of the expression?
1. The compiler scans the expression either from left to right or from right to left.
Consider the expression: a + b * c + d
2. The compiler first scans the expression to evaluate the expression b * c, then
again scans the expression to add a to it.
3. The result is then added to d after another scan.

4. The repeated scanning makes it very inefficient and Infix expressions are easily
readable and solvable by humans whereas the computer cannot differentiate
the operators and parenthesis easily so, it is better to convert the expression to
postfix(or prefix) form before evaluation.
5. The corresponding expression in postfix form is abc*+d+.
6. The postfix expressions can be evaluated easily using a stack.

Infix to Postfix Conversion Using Stack:
Operands: A, B, X, Y, P, Q……………
Operators: +, -, /, *, (, ),…………….
Infix : A + B
Postfix : AB+
Prefix :+ AB
Rules:
1. Priorities of Operators:
^ :Highest Priority
*, / :Next and same priority
+, - :Lowest and same priority
2) No two operators of same priority can
stay together in a stack column.
3) Lowest priority cannot be placed
before highest priority.
4) Any operator (+) : pop that element

Operand : postfix
Operator: Stack
Example: Convert this Infix expression into Postfix expression. (A+B/C*(D+E)-F)
SYMBOL STACK POSTFIX

Convert the following Infix into
postfix form:
1. A + B * C + D
2. (A + B) * (C + D)
3. A * B + C * D
4. A + B + C + D
SYMBO
L
STACK POSTFIX

Evaluation of Postfix Expression:
Postfix : 5, 6, 2, +, *, 12, 4, /, -
Symbol Scanned Stack

1) 10 22 + 8 / 6 * 5 +
2) 2 3 * 4 5 + *
3) 2 3 1 * + 9 –
4) 100 200 + 2 / 5 * 7 +
Evaluate the following Postfix expressions:

What is Queue?
o A queue is defined as a linear data structure that is open at both ends and the operations are
performed in First In First Out (FIFO) order.
o We define a queue to be a list in which all additions to the list are made at one end, and all deletions
from the list are made at the other end.
o The element which is first pushed into the order, the operation is first performed on that.

FIFO Principle of Queue:
 A Queue is like a line waiting to purchase tickets, where the first person in line is the first person
served. (i.e. First come first serve).
 Position of the entry in a queue ready to be served, that is,
 the first entry that will be removed from the queue, is called the front of the
queue(sometimes,head of the queue),
 similarly, the position of the last entry in the queue, that is, the one most recently added,
is called the rear (or the tail) of the queue. See the below figure.

Characteristics of Queue:
 Queue can handle multiple data.
 We can access both ends.
 They are fast and flexible.
Queue Representation:
Like stacks, Queues can also be represented in an array: In this representation, the Queue
is implemented using the array. Variables used in this case are
 Queue: the name of the array storing queue elements.
 Front: the index where the first element is stored in the array representing the queue.
 Rear: the index where the last element is stored in an array representing the queue.

Types of Queue
There are four different types of
queue that are listed as follows
-
 Simple Queue or Linear Queue
 Circular Queue
 Priority Queue
 Double Ended Queue (or Deque)

Simple Queue or Linear Queue
 In Linear Queue, an insertion takes place from one end while the deletion
occurs from another end.
 The end at which the insertion takes place is known as the rear end, and the
end at which the deletion takes place is known as front end.
 It strictly follows the FIFO rule.

Circular Queue
 In Circular Queue, all the nodes are represented as circular.
 It is similar to the linear Queue except that the last element of the queue is connected to the first
element.
 It is also known as Ring Buffer, as all the ends are connected to another end.
 The representation of circular queue is shown in the above image.

Application of circular queue: Insertion of days in a week.

Priority Queue
 It is a special type of queue in
which the elements are
arranged based on the priority.
 It is a special type of queue
data structure in which every
element has a priority
associated with it.
 Suppose some elements occur
with the same priority, they will
be arranged according to the
FIFO principle.
 The representation of priority
queue is shown in the image.

There are two types of priority queue that are discussed as follows -
•Ascending priority queue - In ascending priority queue, elements can be inserted
in arbitrary order, but only smallest can be deleted first. Suppose an array with
elements 7, 5, and 3 in the same order, so, insertion can be done with the same
sequence, but the order of deleting the elements is 3, 5, 7.
•Descending priority queue - In descending priority queue, elements can be
inserted in arbitrary order, but only the largest element can be deleted first. Suppose
an array with elements 7, 3, and 5 in the same order, so, insertion can be done with
the same sequence, but the order of deleting the elements is 7, 5, 3.

Deque (or, Double Ended Queue)
 In Deque or Double Ended Queue, insertion and deletion can be done from both ends of the
queue either from the front or rear.
 It means that we can insert and delete elements from both front and rear ends of the queue.
 Deque can be used as a palindrome checker means that if we read the string from both ends,
then the string would be the same.

Input restricted deque -
As the name implies, in input restricted queue, insertion operation can be performed at only one end,
while deletion can be performed from both ends.
Output restricted deque -
As the name implies, in output restricted queue, deletion operation can be performed at only one
end, while insertion can be performed from both ends.

Different operations in Queue Data Structure:
The various operations that are supported by a queue data structure that helps the
user to modify and manipulate the data present in the queue are:
 Enqueue operation: The term "enqueue" refers to the act of adding a new element
to a queue. Where does a new individual go and wait in a standard queue at a
ticket counter to join the queue? The individual walks to the back of the room and
takes a seat. A new element in a queue is similarly added at the end of the queue.

 Dequeue operation: Dequeue is the process of deleting an item from a queue. We
must delete the queue member that was put first since the queue follows the FIFO
principle. We'll delete the front element and make the element behind it the new
front element because the element added initially will naturally be at the head of the
queue.
 Front Operation: This works similarly to the peek operation in stacks in that it
returns the value of the first element without deleting it.
 isEmpty Operation: The isEmpty() function is used to check if the Queue is empty
or not.

Enqueue Operation
Below are the steps to enqueue (insert) data into
a queue
• Check whether the queue is full or not.
• If the queue is full – print the overflow
error and exit the program.
• If the queue is not full – increment the rear
pointer to point to the next empty space.
• Else add the element in the position
pointed by Rear.
• Return success.
Algorithm for Enqueue Operation
procedure enqueuer (data)
if queue is full
return overflow
endif
rear ← rear + 1
queue[rear] ← data
return true
end procedure

Dequeue Operation
Below are the steps to perform dequeue operation
 Check whether the queue is full or not.
 If the queue is empty – print the underflow
error and exit the program.
 If the queue is not empty – access the data
where the front is pointing.
 Else increment the front pointer to point to
the next available data element.
 Return success.
Algorithm for Dequeue Operation
procedure dequeue
if queue is empty
return underflow
end if
data = queue[front]
front ← front + 1
return true
end procedure

Application of Queue in Data Structure
A queue data structure is generally used in scenarios where the FIFO approach
(First In First Out) has to be implemented.
The following are some of the most common applications of the queue in data
structure:
 Managing requests on a single shared resource such as CPU scheduling
and disk scheduling
 Handling hardware or real-time systems interrupts
 Handling website traffic
 Routers and switches in networking
 Maintaining the playlist in media players

Data Structure - Multiple Stack
A single stack is sometimes not sufficient to store a large amount of data.
To overcome this problem, we can use multiple stack.
For this, we have used a single array having more than one stack.
The array is divided for multiple stacks.
Suppose there is an array STACK[n] divided into two stack STACK
A and STACK B, where n = 10.
STACK A expands from the left to the right, i.e., from 0th element.
STACK B expands from the right to the left, i.e., from 10th element.
The combined size of both STACK A and STACK B never exceeds 10.

Unit 1 Introduction Part 3.pptx

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