Cupdf.com introduction to-data-structures-and-algorithm

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Introduction to Data Structures & Algorithms

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Session Objectives
 To understand the concepts of
– Data structures
– Types of Data Structures
– Applications
– Algorithms
– ADTs

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Session Topics
 Algorithms
 ADTs
 Properties of an Algorithm
 Data structures
 Types of Data structures
 Problem Solving Phase
 Stacks and Queues

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Good Computer Program
 A computer program is a series of instructions to carry out
a particular task written in a language that a computer can
understand.
 The process of preparing and feeding the instructions into
the computer for execution is referred as programming.
 There are a number of features for a good program
Run efficiently and correctly
Have a user friendly interface
Be easy to read and understand
Be easy to debug
Be easy to modify
Be easy to maintain

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Good Computer Program
 Programs consists of two things: Algorithms and data
structures
 A Good Program is a combination of both algorithm and a
data structure
 An algorithm is a step by step recipe for solving an
instance of a problem
 A data structure represents the logical relationship that
exists between individual elements of data to carry out
certain tasks
 A data structure defines a way of organizing all data items
that consider not only the elements stored but also stores
the relationship between the elements

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Algorithms
 An algorithm is a step by step recipe for solving an
instance of a problem.
 Every single procedure that a computer performs is an
algorithm.
 An algorithm is a precise procedure for solving a problem
in finite number of steps.
 An algorithm states the actions to be executed and the
order in which these actions are to be executed.
 An algorithm is a well ordered collection of clear and
simple instructions of definite and effectively computable
operations that when executed produces a result and stops
executing at some point in a finite amount of time rather
than just going on and on infinitely.

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Algorithm Properties
An algorithm possesses the following properties:
– It must be correct.
– It must be composed of a series of concrete steps.
– There can be no ambiguity as to which step will be
performed next.
– It must be composed of a finite number of steps.
– It must terminate.
– It takes zero or more inputs
– It should be efficient and flexible
– It should use less memory space as much as possible
– It results in one or more outputs

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Various steps in developing Algorithms
 Devising the Algorithm:
It’s a method for solving a problem. Each step of an
algorithm must be precisely defined and no vague
statements should be used. Pseudo code is used to describe
the algorithm , in less formal language than a programming
language.
 Validating the Algorithm:
The proof of correctness of the algorithm. A human
must be able to perform each step using paper and pencil
by giving the required input , use the algorithm and get the
required output in a finite amount of time.

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Various steps in developing Algorithms
 Expressing the algorithm:
To implement the algorithm in a programming language.
The algorithm used should terminate after a finite number
of steps.

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Efficiency of an algorithm
 Writing efficient programs is what every programmer
hopes to be able to do. But what kinds of programs are
efficient? The question leads to the concept of
generalization of programs.
 Algorithms are programs in a general form. An algorithm
is an idea upon which a program is built. An algorithm
should meet three things:
It should be independent of the programming language in which
the idea is realized
Every programmer having enough knowledge and experience
should understand it
It should be applicable to inputs of all sizes

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Efficiency of an algorithm
 Efficiency of an algorithm denotes the rate at which an
algorithm solves a problem of size n.
 It is measured by the amount of resources it uses, the time
and the space.
 The time refers to the number of steps the algorithm
executes while the space refers to the number of unit
memory storage it requires.
 An algorithm’s complexity is measured by calculating the
time taken and space required for performing the
algorithm.
 The input size, denoted by n, is one parameter , used to
characterize the instance of the problem.
 The input size n is the number of registers needed to hold
the input (data segment size).

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Time Complexity of an Algorithm
 Time Complexity of an algorithm is the amount of time(or
the number of steps) needed by a program to complete its
task (to execute a particular algorithm)
 The way in which the number of steps required by an
algorithm varies with the size of the problem it is solving.
The time taken for an algorithm is comprised of two times
Compilation Time
Run Time
 Compilation time is the time taken to compile an
algorithm. While compiling it checks for the syntax and
semantic errors in the program and links it with the
standard libraries , your program has asked to.

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 Run Time: It is the time to execute the compiled program.
The run time of an algorithm depend upon the number of
instructions present in the algorithm. Usually we consider,
one unit for executing one instruction.
 The run time is in the control of the programmer , as the
compiler is going to compile only the same number of
statements , irrespective of the types of the compiler used.
 Note that run time is calculated only for executable
statements and not for declaration statements
 Time complexity is normally expressed as an order of
magnitude, eg O(n2) means that if the size of the problem n
doubles then the algorithm will take four times as many
steps to complete.

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 Time complexity of a given algorithm can be defined for
computation of function f() as a total number of statements
that are executed for computing the value of f(n).
 Time complexity is a function dependent from the value of
n. In practice it is often more convenient to consider it as a
function from |n|
 Time complexity of an algorithm is generally classified as
three types.
(i) Worst case
(ii) Average Case
(iii) Best Case

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Time Complexity
 Worst Case: It is the longest time that an algorithm will
use over all instances of size n for a given problem to
produce a desired result.
 Average Case: It is the average time( or average space)
that the algorithm will use over all instances of size n for a
given problem to produce a desired result. It depends on
the probability distribution of instances of the problem.
 Best Case: It is the shortest time ( or least space ) that the
algorithm will use over all instances of size n for a given
problem to produce a desired result.

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Space Complexity
 Space Complexity of a program is the amount of memory
consumed by the algorithm ( apart from input and output,
if required by specification) until it completes its
execution.
 The way in which the amount of storage space required by
an algorithm varies with the size of the problem to be
solved.
 The space occupied by the program is generally by the
following:
A fixed amount of memory occupied by the space for the program
code and space occupied by the variables used in the program.
A variable amount of memory occupied by the component variable
whose size is dependent on the problem being solved. This space
increases or decreases depending upon whether the program uses
iterative or recursive procedures.

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Space Complexity
 The memory taken by the instructions is not in the control
of the programmer as its totally dependent upon the
compiler to assign this memory.
 But the memory space taken by the variables is in the
control of a programmer. More the number of variables
used, more will be the space taken by them in the memory.
 Space complexity is normally expressed as an order of
magnitude, eg O(n2)means that if the size of the problem n
doubles then four times as much working storage will be
needed.
 There are three different spaces considered for determining
the amount of memory used by the algorithm.

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Space Complexity
 Instruction Space is the space in memory occupied by the
compiled version of the program. We consider this space
as a constant space for any value of n. We normally ignore
this value , but remember that is there. The instruction
space is independent of the size of the problem
 Data Space is the space in memory , which used to hold
the variables , data structures, allocated memory and other
data elements. The data space is related to the size of the
problem.
 Environment Space is the space in memory used on the run
time stack for each function call. This is related to the run
time stack and holds the returning address of the previous
function. The memory each function utilises on the stack is
a constant as each item on the stack has a return value and
pointer on it.

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Iterative Factorial Example
fact ( long n)
{
for (i=1; i<=n; i++)
x=i*x;
return x;
}
 Space occupied is
 Data Space: i, n and x
 Environment Space: Almost nothing because the
function is called only once.
 The algorithm has a complexity of O(1) because it does
not depend on n. No matter how big the problem
becomes ,the space complexity remains the same since
the same variables are used , and the function is called
only once.

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Recursive Factorial Example
long fact (long x)
{
if (x<=1)
return(1);
else
return (x * fact(x-1));
}
 Space occupied is
 Data space : x
 Environment Space: fact() is called recursively , and so the
amount of space this program used is based on the size of
the problem

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Recursive Factorial Example
 The space complexity is
O(n)= (x + function call) * n
= x + function call + memory needed for fact(x-1)
x+function call + x+ function call + ……+
x+ function call n(n-1)+…….+1
 Note that in measuring space complexity, memory space is
always allocated for variables whether they are used in the
program or not.
 Space Complexity is not as big of an issue as time
complexity because space can be reused, whereas time
cannot.

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Problem Solving Phase
 A problem/Project needs programs to create ,append,
update the database, print data, permit online enquiry and
so on.
 A Programmer should identify all requirements to solve
the problem. Each problem should have the following
specifications
Type of Programming language
Narration of the program describing the tasks to be performed
Frequency of Processing (hourly, daily, weekly etc)
Output and input of the program
Limitations and restrictions for the program
Detailed Specifications

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Method 1: Algorithm Analysis
Code each algorithm and run them to see how long they take.
Problem: How will you know if there is a better program or
whether there is no better program?
What will happen when the number of inputs is twice as
many? Three? A hundred?

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Method 2: Algorithm Analysis
Develop a model of the way computers work and compare
how the algorithms behave in the model.
Goal: To be able to predict performance at a coarse level.
That is, to be able to distinguish between good and bad
algorithms.
Another benefit: when assumptions change, we can predict
the effects of those changes.

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Why algorithm analysis?
As computers get faster and problem sizes get bigger,
analysis will become more important.
Why? The difference between good and bad algorithms will
get bigger.

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How to Measure Algorithm Performance
 What metric should be used to judge algorithms?
– Length of the program (lines of code)
– Ease of programming (bugs, maintenance)
– Memory required
Running time
 Running time is the dominant standard.
– Quantifiable and easy to compare
– Often the critical bottleneck

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The Need for Data Structures
Data structures organize data
 more efficient programs.
More powerful computers  more complex applications.
More complex applications demand more calculations.
Complex computing tasks are unlike our everyday experience.
 More typically, a data structure is meant to be an organization for a
collection of data items.
 Any organization for a collection of records can be searched, processed
in any order, or modified.
 The choice of data structure and algorithm can make the difference
between a program running in a few seconds or many days. A data
structure requires a certain amount of:
 space for each data item it stores
 time to perform a single basic operation
 programming effort.

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Selecting a Data Structure
Select a data structure as follows:
1. Analyze the problem to determine the resource constraints a
solution must meet.
2. Determine the basic operations that must be supported.
Quantify the resource constraints for each operation.
3. Select the data structure that best meets these requirements.

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Data Structures
DS includes
• Logical or mathematical description of the structure
and Implementation of the structure on a computer
• Quantitative analysis of the structure, which includes
determining the amount of memory needed to store
the structure and the time required to process the
structure.

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Classification of Data Structures
“Data Structures ”deals with the study of how the data is
organized in the memory, how efficiently the data can be
retrieved and manipulated, and the possible ways in which
different data items are logically related.
Types:
Primitive Data Structure: Ex. int,float,char
Non-primitive Data Structures:
Ex.Arrays,Structures,stacks
Linear Data Structures: Ex.Stacks,queues,linked list
Non-Linear Data Structures: Ex.Trees,Graphs.

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1. Primary Data structures are the basic data structures that
directly operate upon the machine instructions. They
have different representations on different computers.
2. All the basic constants (integers, floating point numbers,
character constants, string constants)and pointers are
considered as primary data structures
3. Secondary Data Structures are more complicated data
structures derived from primary data structures
4. They emphasize on grouping same or different data items
with relationship between each data item
5. Secondary data structures can be broadly classified as
static data structures and dynamic data structures

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 If a data structure is created using static memory allocation
(ie. a data structure formed when the number of data items
are known in advance), it is known as static data structure
or fixed size data structure
 If a data structure is created , using dynamic memory
allocation(ie. a data structure formed when the number of
data items are not known in advance) it is known as
dynamic data structure or variable size data structure
 Dynamic data structures can be broadly classified as linear
data structures and non linear data structures
 Linear data structures have a linear relationship between its
adjacent elements. Linked lists are examples of linear data
structures.

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 A linked list is a linear dynamic data structure that can
grow and shrink during its execution time
 A circular linked list is similar to a linked list except that
the first and last nodes are interconnected
 Non linear data structures don’t have a linear relationship
between its adjacent elements
 In a linear data structure , each node has a link which
points to another node, whereas in a non linear data
structure, each node may point to several other nodes
 A tree is a nonlinear dynamic data structure that may point
to one or more nodes at a time
 A graph is similar to tree except that it has no hierarchical
relationship between its adjacent elements

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Abstract data type (ADTs)
 A data type that is defined entirely by a set of operations is
referred to as Abstract data type or simply ADT
 Abstract data types are a way of separating the
specification and representation of data types
 An ADT is a black box, where users can only see the
syntax and semantics of its operations
 An ADT is a combination of interface and implementation
The interface defines the logical properties of the ADT and
especially the signatures of its operations
 The implementation defines the representation of data
structure and the algorithms that implement the operations
 An abstract data type encapsulates data and functions into
a named data type

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Abstract data type (ADTs)
 It is similar to a structure in C, but can include functions in
it
 The basic difference between ADTs and primitive data
types is that the latter allow us to look at the
representation, whereas former hide the representation
from us
 An ADT consists of a collection of values and operations
with the values derive their meaning solely through the
operations that can be performed upon them
 Benefits of using ADTs:
Code is easier to understand
Implementations of ADTs can be changed without requiring changes
to the program that uses the ADTs

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Data Structures: Data Collections
 Linear structures
– Array: Fixed-size
– Linked-list: Variable-size
– Stack: Add to top and remove from top
– Queue: Add to back and remove from front
– Priority queue: Add anywhere, remove the highest
priority
 Tree: A branching structure with no loops
 Hash tables: Unordered lists which use a ‘hash
function’ to insert and search
 Graph: A more general branching structure, with
less stringent connection conditions than for a tree

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ADTs Collection
 ADT is a data structure and a set of operations which can
be performed on it.
– A class in object-oriented design is an ADT
 The pre-conditions define a state of the program which the
client guarantees will be true before calling any method,
 post-conditions define the state of the program that the
object's method will guarantee to create for you when it
returns.
 create Create a new collection
 add Add an item to a collection
 delete Delete an item from a collection find Find an item
matching some criterion in the collection
 destroy Destroy the collection

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Data Structures and ADTs
 A container in which data is being stored
– Example: structure, file, or array
 An ADT is a data structure which does not exist within the
host language, but rather must be created out of existing
tools
 It is both a collection of data and a set of rules that govern
how the data will be manipulated
 Examples: list, stack, queue, tree, table, and graph
 An ADT sits on top of the data structure, and the rules that
govern the use of the data define the interface between the
data structure and the ADT

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Lists
 Lists are ordered data sets
– The type of ordering is entirely dependent upon the application
 Lists come in two basic forms: sequential and linked
 The primary difference is how the items are laid out in memory
– Can be described as the difference between physical order and
logical order:
• Sequential implementation – the physical arrangement of the
data elements defines the logical order of entries on the list.
Typically an array-based structure, possibly of fixed maximum
size
• Linked implementation – The physical order of data elements
is unrelated to the logical order of the entries on the list.
Typically a linked set of nodes, each allocated dynamically as
needed

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Lists
 This key difference is reflected in the types of applications
for which 2- list types are suited:
– Sequential–best when the order of the data does not
matter, when ordering can be done after it has all been
loaded into the array, or when direct indexing of
elements is useful
– Linked– the lack of relationship between physical and
logical order means that a new value can be placed
anywhere in memory, lending this list type to
applications where flexibility is desired

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Sequential List Implementation
 Inefficiency: If the list is to be maintained in alphabetical order,
inserting a new value may mean having to shift existing ones out of the
way
 Likewise, if an element were to be deleted, we might have to shift
remaining values ‘forward’ toward the front of the array
Features of Sequential Lists
 directly indexable
 easy to traverse – can move backwards and forwards easily
 fast access
 easy to implement
 contiguous locations
 physical and logical order the same
 not particularly flexible

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Data Structures
 Dynamic data structures - grow and shrink during
execution
 Linked lists - insertions and removals made anywhere
 Stacks - insertions and removals made only at top of stack
 Queues - insertions made at the back and removals made
from the front
 Binary trees - high-speed searching and sorting of data and
efficient elimination of duplicate data items

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Stacks
A Stack is defined as a special type of data structure where
items are inserted from one end called top of stack and
items are deleted from the same end.
Stack is organized as a Last In First Out(LIFO) data
structure.
Operations performed on Stacks are:
 Insert an item into the stack (Store)
 Delete an item from the stack (Retrieve)
 Display the contents of the stack

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Stacks
 A stack is an ordered collection of items, generally
implemented with only two principle operations, called
Push and Pop.
 stack – new nodes can be added and removed only at the
top
 Push adds an item to a stack
 Pop extracts the most recently
pushed item from the stack
– similar to a pile of dishes
– last-in, first-out (LIFO)
– Bottom of stack indicated by a link member to null
– stores the popped value
– constrained version of a linked list

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40
30
20
10
30
20
10
20
10 10
top
Stack full
top
40
deleted
top
30
deleted
20
deleted
top
Empty
Stack
Since, items are inserted from one end, in stack deletions should be done
from the same end..
When stack is empty it is not possible to delete any item and this situation is
called Stack Underflow.
top
Deletion Operations

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00
Implementation
0
1
2
:
Top
int top

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Insert/ Push Operation
Inserting an element into the stack is called push operation.
Function to insert an item: (Push )
void push(int item, int *top, int s[])
{
if(*top == STACKSIZE - 1) /*Is stack empty?*/
{
printf(“Stack Overflown”);
return;
}
/* Increment top and then insert an item*/
s[++(*top)] = item;
}

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Delete/Pop Operation
Deleting an element from the stack is called pop operation.
Function to delete an item: (Pop )
int pop(int *top, int s[])
{
int item_deleted /*Holds the top most item */
if(*top == -1)
{
return 0; /*Indicates empty stack*/
}
/*Obtain the top most element and change the position
of top item */
item_deleted=s[(*top)--];
/*Send to the calling function*/
return item_deleted;
}

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Display Procedure
If the stack already has some elements, all those items are displayed one
after the other.
void display(int top, int s[]){
int i;
if(top == -1) /* Is stack empty?*/
{
printf(“Stack is emptyn”);
return;
}
/*Display contents of a stack*/
printf(“Contents of the stackn”);
for(i = 0;i <= top; i++)
{
printf(“%dn”,s[i]);
}
}

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Applications of Stack
 Conversion of expressions.
Infix to postfix, postfix to prefix, prefix to infix, vice-
versa.
 Evaluation of expressions.
Arithmetic expression in the form of either postfix or
prefix.
can be easily evaluated.
 Recursion.
Ex. Tower of Hanoi etc.
 Other applications.
Ex:Checking if a string is a palindrome or not.
Topological Sort.
 System Software and Compiler Design

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Towers of Hanoi
 Three pegs labeled A, B,C
 In A, there are finite number of disks with decreasing size
 Objective- move the disks from A to C using B as an
auxiliary.
 The rules of the game are as follows
• Only one disk may be moved at a time.
• At no time can a larger disk be placed on a smaller
disk
A
B C

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Procedure
 For n disks
1. Move the top n-1 disks from peg A to peg B
2. Move the top disk from peg A to C
3. Move the top n-1 disks from peg B to peg C
 Tower(N-1, BEG, END, AUX)
 Tower(1,BEG, AUX, END)
 Tower(N-1,AUX,BEG,END)

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Procedure
Tower(4,A,B,C) A C
Tower(3, A,C,B)
Tower(3, B,A,C)
A B
Tower (2, A,B,C)
Tower(2, C,A,B)
B C
Tower(2, A,B,C)
Tower(2, B,C,A)
C B
Tower(1,C,B,A)
Tower(1,A,C,B)

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Algorithm
 Tower(N,BEG,AUX,END)
 If N=1, then BEG END
 return
 Tower(N-1, BEG,END,AUX) // Move N-1 disks from
BEG to AUX
 BEG END
 Tower(N-1, AUX, BEG,END)
 return

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Queues
A queue is defined as a special type of data structure
where the elements are inserted from one end and
elements are deleted from the other end.
The end from where the elements are inserted is called
REAR end.
The end from where the elements are deleted is called
FRONT end.
Queue is organized as First In First Out (FIFO)Data
Structure.

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Queues
In a queue, the elements are always inserted at the rear end and deleted from
the front end.
10 20 30
Insert
delete
Front end
Rear end
0 1 2 3 4
Pictorial representation of a Queue

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Operations Performed on Queues
 Insert an item into a queue
 Delete an item from queue
 Display the contents of queue
Different types of Queues
 Queue(Ordinary queue)
 Circular Queue
 Double ended Queue
 Priority Queue

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Insertion of Elements
 The ordinary queue operates on first come first serve basis.
Items will be inserted from one end and deleted at the
other end in the same order in which they are inserted.
40
30
20
10
0 1 2 3 4
f r
50
40
30
20
10
4
3
2
1
0
r
f
To insert an item 50
Whenever queue is full, it is not possible to insert any element
into queue and this condition is called OVERFLOW.
Insert at the rear end

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Function to insert an item at the rear end of the queue
void insert_rear(int item,int q[],int *r)
{
if(q_full(*r)) /* Is queue full */
{
printf(“Queue overflown”);
return;
}
/* Queue is not full */
q[++(*r)] = item;
}
int q_full(int r)
{
return (r == QUEUE_SIZE -1)? 1 : 0;
}

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Delete from the front end
 Whenever the value of f is greater than r ,then the queue is
said to be empty and is not possible to delete an element
from queue. This condition is called Underflow.
40
30
20
10
0 1 2 3 4
f r
40
30
20
0 1 2 3 4
f r
50
0 1 2 3 4
f , r
40
0 1 2 3 4
f , r

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Function to delete an item from the front end
void delete_front(int q[], int *f, int *r) {
if( q_empty(f , r) ) /* Is queue empty*/
{
printf(“Queue underflown”);
return;
}
printf(“The element deleted is %dn”,q[(*f)++]);
if( f > r )
{
f = 0;
r = -1;
}
}
int q_empty(int f,int r)
{
return (f>r) ? 1 : 0;
}

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Function to display the contents of queue
The contents of queue can be displayed only if queue is not empty. If
queue is empty an appropriate message is displayed.
void display(int q[], int f, int r)
{
int i;
if( q_empty (f , r )) /* Is queue empty*/
{
printf(“Queue is emptyn”);
return;
}
printf(“Contents of queue is n”);
for(i = f;i <=r;i++)
printf(“%dn”,q[i]);
}

63
Double Ended Queue
A Deque is a special type of data structure in which insertions
and deletions will be done either at the front end or at the
rear end of the queue. Here, insertion and deletion are done
from both the ends.
Operations performed on Deques are:
 Insert an item from front end
 Insert an item from rear end
 Delete an item from front end
 Delete an item from rear end
 Display the contents of queue

64
Insert at the front end
0 1 2 3 4
r
f
if(f==0 && r == -1)
q[++r] = item;
40
30
0 1 2 3 4
f r
40
30
20
10
0 1 2 3 4
f r
if( f != 0)
q[--f] = item;
Not possible to insert
an item at the front end

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Function to insert an item at front end
void insert_front(int item,int q[],int *f,int *r)
{
if(*f == 0 && *r == -1)
{
q[++(*r)] = item;
return;
}
if(*f != 0)
{
q[--(*f)] = item;
return;
}
printf(“Front insertion not possible”);
}

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Function to delete an item from the rear end
void delete_rear(int q[], int *f,int *r)
{
if(q_empty(f, r))
{
printf(“Queue underflown”);
return;
}
printf(“The element deleted is %d”,q[(*r)--]);
if(f > r)
{
f = 0;
r = -1;
}
}

67
Circular Queue
 In circular queue, the elements of a given queue can be
stored efficiently in an array so as to “wrap around” so
that end of the queue is followed by the front of the queue.
10
0 1 2 3 4
f r
30
20
10
0 1 2 3 4
r
f
After inserting 20 & 30
Initial queue

68
Circular Queue
50
40
30
20
10
0 1 2 3 4
f r
After inserting 40 and 50
50
40
30
0 1 2 3 4
f r
After deleting 10 and 20
50
40
30
60
0 1 2 3 4
f
r
After inserting 60

69
Operations Performed on Circular Queues
 Insert rear
 Delete front
 Display the contents of Queue
Function to insert an item at the rear end
void insert_rear(int item,int q[],int *r,int *count)
{
if(q_full(*count))
{
printf(“Overflow of Queuen”);
return;
}
r = (*r + 1) % QUEUE_SIZE; /* Increment rear pointer */
q[*r]=item; /* Insert the item */
*count +=1; /* Update the counter */
}
int(q_full(int count))
{
/* Return true if Q is full,else false */
return (count == QUEUE_SIZE - 1) ? 1 : 0;
}

70
Function to delete an item from the front end
void delete_front(int q[], int *f, int *count)
{
if(q_empty(*count))
{
printf(“Underflow of queuen”);
return;
}
/* Access the item */
printf(“The deleted element is %dn”,q[*f]);
/* Point to next first item */
f = (*f + 1) % QUEUE_SIZE;
/* Update counter */
*count -= 1;
}
int(q_empty(int count))
{
/* Return true if Q is empty ,else false */
return(count == 0) ? 1 : 0;
}

71
Priority Queue
The priority queue is a special type of data structure in which items
can be inserted or deleted based on the priority.
If the elements in the queue are of same priority, then the element,
which is inserted first into the queue, is processed.
Types of Priority queues:
Ascending priority queue –
Elements can be inserted in any order.
While deleting, smallest item is deleted first.
Descending priority queue –
Elements can be inserted in any order.
While deleting, largest item is deleted first.
Operations performed on Priority Queue
 Insert an element.
 Delete an element.
 Display the contents of Queue.

72
Function to insert an item at the correct place in priority queue.
void insert_item(int item,int q[], int *r)
{
int j;
if(q_full(*r))
{
printf(“Queue is fulln”);
return;
}
j = *r; /* Compare from this initial point */
/* Find the appropriate position */
while(j >= 0 && item < q[j])
{
q[j+1] = q[j]; /*Move the item at q[j] to its next position */
j--;
}
/* Insert an item at the appropriate position */
q[j+1]=item;
/* Update the rear item */
*r = *r + 1;
}

73
Summary
 “Data Structures ”deals with the study of how the data is organized in
the memory, how efficiently the data can be retrieved and manipulated,
and the possible ways in which different data items are logically
related.
 A Stack is defined as a special type of data structure where items are
inserted from one end called top of stack and items are deleted from
the same end.
 A queue is defined as a special type of data structure where the
elements are inserted from one end and elements are deleted from the
other end.
 A Deque is a special type of data structure in which insertions and
deletions will be done either at the front end or at the rear end of the
queue.
 In circular queue, the elements of a given queue can be stored
efficiently in an array so as to “wrap around” so that end of the queue
is followed by the front of the queue.
 The priority queue is a special type of data structure in which items
can be inserted or deleted based on the priority.

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