Advanced Data Structures
Introduction to Data Structures
Data Structures:
A data structure is an arrangement of data in a computer's memory or even disk storage.
Data structures can be classified into two types

Linear Data Structures
 Non Linear Data Structures
Linear Data Structures:
Linear data structures are those data structures in which data elements are accessed (read and
written) in sequential fashion ( one by one)
Eg: Stacks , Queues, Lists, Arrays
Non Linear Data Structures:
Non Linear Data Structures are those in which data elements are not accessed in sequential
fashion.
Eg: trees, graphs
Algorithm:
Step by Step process of representing solution to a problem in words is called an Algorithm.
Characteristics of an Algorithm:
1

Input : An algorithm should have zero or more inputs

Output: An algorithm should have one or more outputs

Finiteness: Every step in an algorithm should end in finite amount of time

Unambiguous: Each step in an algorithm should clearly stated

Effectiveness: Each step in an algorithm should be effective
Advanced Data Structures
Characteristics of Data Structures
Data
Structure
Advantages
Disadvantages
Array
Quick inserts
Fast access if index known
Slow search
Slow deletes
Fixed size
Ordered
Array
Faster search than unsorted array
Slow inserts
Slow deletes
Fixed size
Stack
Last-in, first-out acces
Slow access to other items
Queue
First-in, first-out access
Slow access to other items
Linked List
Quick inserts
Quick deletes
Slow search
Binary Tree
Quick search
Quick inserts
Quick deletes
(If the tree remains balanced)
Deletion algorithm is complex
Red-Black
Tree
Quick search
Quick inserts
Quick deletes
(Tree always remains balanced)
Complex to implement
2-3-4 Tree
Quick search
Complex to implement
Quick inserts
Quick deletes
(Tree always remains balanced)
(Similar trees good for disk storage)
Hash Table
Very fast access if key is known
Quick inserts
Slow deletes
Access slow if key is not known
Inefficient memory usage
Heap
Quick inserts
Quick deletes
Access to largest item
Slow access to other items
Graph
Best models real-world situations
Some algorithms are slow and very
complex
2
Advanced Data Structures
Stack :
Stack is a Linear Data Structure which follows Last in First Out mechanism.
It means: the first element inserted is the last one to be removed
Stack uses a variable called top which points topmost element in the stack. top is incremented
while pushing (inserting) an element in to the stack and decremented while poping (deleting) an
element from the stack
A
top
Push(A)
B
A
Push(B)
C
B
A
top
top
Push(C)
D
C
B
A
Push(D)
top
C
B
A
Pop()
Valid Operations on Stack:

Inserting an element in to the stack (Push)

Deleting an element in to the stack (Pop)

Displaying the elements in the queue (Display)
Note:
While pushing an element into the stack, stack is full condition should be checked
While deleting an element from the stack, stack is empty condition should be checked
Applications of Stack:
3

Stacks are used in recursion programs

Stacks are used in function calls

Stacks are used in interrupt implementation
top
Advanced Data Structures
Queue:
Queue is a Linear Data Structure which follows First in First out mechanism.
It means: the first element inserted is the first one to be removed
Queue uses two variables rear and front. Rear is incremented while inserting an element into the
queue and front is incremented while deleting element from the queue
B
A
rear
front
A
Insert(A)
Insert(B)
rear
front
C
B
A
Insert(C)
rear
front
D
C
B
A
Insert(D)
rear
D
C
B
front
Delete()
Valid Operations on Queue:

Inserting an element in to the queue

Deleting an element in to the queue

Displaying the elements in the queue
Note:
While inserting an element into the queue, queue is full condition should be checked
While deleting an element from the queue, queue is empty condition should be checked
Applications of Queues:
Real life examples
Waiting in line
Waiting on hold for tech support
Applications related to Computer Science
Threads
Job scheduling (e.g. Round-Robin algorithm for CPU allocation)
4
rear
front
Advanced Data Structures
Linked List:
To overcome the disadvantage of fixed size arrays linked list were introduced.
A linked list consists of nodes of data which are connected with each other. Every node consist
of two parts data and the link to other nodes. The nodes are created dynamically.
NODE
bat
Data

link
bat

cat

Types of Linked Lists:

Single linked list

Double linked list

Circular linked list
Valid operations on linked list:
5

Inserting an element at first position

Deleting an element at first position

Inserting an element at end

Deleting an element at end

Inserting an element after given element

Inserting an element before given element

Deleting given element
sat

vat
NULL
Advanced Data Structures
Trees :
A tree is a Non-Linear Data Structure which consists of set of nodes called vertices and set of
edges which links vertices
Terminology:

Root Node: The starting node of a tree is called Root node of that tree

Terminal Nodes: The node which has no children is said to be terminal node or leaf .

Non-Terminal Node: The nodes which have children is said to be Non-Terminal Nodes

Degree: The degree of a node is number of sub trees of that node

Depth: The length of largest path from root to terminals is said to be depth or height of
the tree

Siblings: The children of same parent are said to be siblings

Ancestors: The ancestors of a node are all the nodes along the path from the root to the
node
A
C
B
D
E
F
G
H
6
I
Property
Number of nodes
Height
Root Node
Leaves
Interior nodes
Number of levels
Ancestors of H
Descendants of B
Siblings of E
Value
:
:
:
:
:
:
:
:
:
9
4
A
ED, H, I, F, C
D, E, G
5
I
D,E, F
D, F
Advanced Data Structures
Binary Trees:
Binary trees are special class of trees in which max degree for each node is 2
Recursive definition:
A binary tree is a finite set of nodes that is either empty or consists of a root and two disjoint
binary trees called the left subtree and the right subtree.
Any tree can be transformed into binary tree. By left child-right sibling representation.
A
B
C
E
K
F
G
D
Binary Tree Traversal Techniques:
There are three binary tree traversing techniques
 Inorder
 Preorder
 Postorder
Inorder: In inorder traversing first left subtree is visited followed by root and right subtree
Preorder: In preorder traversing first root is visited followed by left subtree and right subtree.
Postorder: In post order traversing first left tree is visited followed by right subtree and root.
7
Advanced Data Structures
Binary Search Tree:
A Binary Search Tree (BST) is a binary tree which follows the following conditons

Every element has a unique key.

The keys in a nonempty left subtree are smaller than the key in the root of subtree.

The keys in a nonempty right subtree are grater than the key in the root of subtree.

The left and right subtrees are also binary search trees.
63
89
41
34
56
Valid Operations on Binary Search Tree:
8

Inserting an element

Deleting an element

Searching for an element

Traversing
72
95
Advanced Data Structures
Avl Tree:
If in a binary search tree, the elements are inserted in sorted order then the height will be n,
where n is number of elements. To overcome this disadvantage balanced trees were introduced.

Balanced binary search trees

An AVL Tree is a binary search tree such that for every internal node v of T, the
heights of the children of v can differ by at most 1.
4
44
2
3
17
78
1
2
32
1
88
50
1
48
Operations of Avl tree:
9

Inserting an element

Deleting an element

Searching for an element

Traversing

Height balancing
62
1
Advanced Data Structures
Graphs
A graph is a Non-Linear Data Structure which consists of set of nodes called vertices V and set
of edges E which links vertices
Note: A tree is a graph with out loops
0
0
1
1
2
2
3
Graph
3
5
4
6
Tree
Graph Traversal:
Problem: Search for a certain node or traverse all nodes in the graph
Depth First Search
Once a possible path is found, continue the search until the end of the path
Breadth First Search
Start several paths at a time, and advance in each one step at a time
10
Advanced Data Structures
Introduction to Object Oriented Programming
Object Oriented Programming:
You've heard it a lot in the past several years. Everybody is saying it.
What is all the fuss about objects and object-oriented technology? Is it real? Or is it hype? Well,
the truth is--it's a little bit of both. Object-oriented technology does, in fact, provide many
benefits to software developers and their products. However, historically a lot of hype has
surrounded this technology, causing confusion in both managers and programmers alike. Many
companies fell victim to this hardship (or took advantage of it) and claimed that their software
products were object-oriented when, in fact, they weren't. These false claims confused
consumers, causing widespread misinformation and mistrust of object-oriented technology.
Object:
As the name object-oriented implies, objects are key to understanding object-oriented
technology. You can look around you now and see many examples of real-world objects: your
dog, your desk, your television set, your bicycle.
Definition: An object is a software bundle of variables and related methods
Class:
In the real world, you often have many objects of the same kind. For example, your bicycle is
just one of many bicycles in the world. Using object-oriented terminology, we say that your
11
Advanced Data Structures
bicycle object is an instance of the class of objects known as bicycles. Bicycles have some state
(current gear, current cadence, two wheels) and behavior (change gears, brake) in common.
However, each bicycle's state is independent of and can be different from other bicycles.
Definition: A class is a blueprint or prototype that defines the variables and methods common to
all objects of a certain kind.
Inheritance:
Acquiring the properties of one class in another class is called inheritance
The Benefits of Inheritance

Subclasses provide specialized behaviors from the basis of common elements provided
by the super class. Through the use of inheritance, programmers can reuse the code in the
superclass many times.

Programmers can implement superclasses called abstract classes that define "generic"
behaviors. The abstract superclass defines and may partially implement the behavior but
much of the class is undefined and unimplemented. Other programmers fill in the details
with specialized subclasses.
Data Abstraction:
The essential element of object oriented programming in abstraction. The complexity of
programming in object oriented programming is maintained through abstraction.
For example, the program consist of data and code which work over data. While executing a
program we don’t thing in which location that data is being stored how the input device is
transferring the input to the memory etc. this abstraction allows us to execute the program
without thinking deeply about the complexity of execution of program.
Encapsulation:
Encapsulation is the mechanism that binds together code and the data and keeps them safe from
outside world. In the sense it is a protective wrapper that prevents the code and data from being
12
Advanced Data Structures
accessed by other code defied outside the wrapper. Access is controlled through a well defined
interface.
Polymorphism:
Existing in more that one form is called polymorphism.
Polymorphism means the ability to take more that one form. For example an operation may
exhibit different behavior in different behavior in different instances.
For example consider operation of addition. For two numbers the operation will generate a sum.
If the operands are string the operation would produces a third string by concatenation.
C++ supports polymorphism through method overloading and operator overloading
Method overloading:
if the same method name used for different procedures that the method is said to be overloaded.
Dynamic Binding:
Binding refer to the linking of a procedure call to the code to be executed in response to the call.
Dynamic binding means that the code associated with a given procedure call is not know until
the time of the call at runtime. It is associated with a polymorphism reference depends on the
dynamic type of that reference.
Message communication:
An object oriented program consists of objects that communicate with each other. The process
of programming in an object oriented language therefore involves the following basic steps:
1. creating classes that define objects and their behaviors.
2. creating objects from class definitions.
3. establishing communication among objects.
13
Advanced Data Structures
Abstract Data Types:
An Abstract Data Type (ADT) is more a way of looking at a data structure: focusing on what it
does and ignoring how it does its job. A stack or a queue is an example of an ADT. It is
important to understand that both stacks and queues can be implemented using an array. It is also
possible to implement stacks and queues using a linked list. This demonstrates the "abstract"
nature of stacks and queues: how they can be considered separately from their implementation.
To best describe the term Abstract Data Type, it is best to break the term down into "data type"
and then "abstract".
Data type:
When we consider a primitive type we are actually referring to two things: a data item with
certain characteristics and the permissible operations on that data. An int in Java, for example,
can contain any whole-number value from -2,147,483,648 to +2,147,483,647. It can also be used
with the operators +, -, *, and /. The data type's permissible operations are an inseparable part of
its identity; understanding the type means understanding what operations can be performed on it.
In C++, any class represents a data type, in the sense that a class is made up of data (fields) and
permissible operations on that data (methods). By extension, when a data storage structure like a
stack or queue is represented by a class, it too can be referred to as a data type. A stack is
different in many ways from an int, but they are both defined as a certain arrangement of data
and a set of operations on that data.
abstract
Now lets look at the "abstract" portion of the phrase. The word abstract in our context stands for
"considered apart from the detailed specifications or implementation".
In C++, an Abstract Data Type is a class considered without regard to its implementation. It can
be thought of as a "description" of the data in the class and a list of operations that can be carried
out on that data and instructions on how to use these operations. What is excluded though, is the
14
Advanced Data Structures
details of how the methods carry out their tasks. An end user (or class user), you should be told
what methods to call, how to call them, and the results that should be expected, but not HOW
they work.
We can further extend the meaning of the ADT when applying it to data structures such as a
stack and queue. In Java, as with any class, it means the data and the operations that can be
performed on it. In this context, although, even the fundamentals of how the data is stored should
be invisible to the user. Users not only should not know how the methods work, they should also
not know what structures are being used to store the data.
Consider for example the stack class. The end user knows that push() and pop() (amoung other
similar methods) exist and how they work. The user doesn't and shouldn't have to know how
push() and pop() work, or whether data is stored in an array, a linked list, or some other data
structure like a tree.
15
Advanced Data Structures
Stack ADT Algorithms
Push(item)
{
If (stack is full) print “ stack over flow”
else
Increment top ;
Stack [top]= item;
}
Pop()
{
If( stack is empty) print” stack under flow”
else
Decrement top
}
Display()
{
If ( stack is empty) print” no element to display”
else
for i= top to 0 step -1
Print satck[i];
}
16
Advanced Data Structures
Stack ADT
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class stack
{
int stk[5];
int top;
public:
stack()
{
top=-1;
}
void push(int x)
{
if(top > 4)
{
cout <<"stack over flow";
return;
}
stk[++top]=x;
cout <<"inserted" <<x;
}
void pop()
{
if(top <0)
{
cout <<"stack under flow";
return;
}
cout <<"deleted" <<stk[top--];
}
void display()
{
if(top<0)
{
cout <<" stack empty";
return;
}
17
Advanced Data Structures
for(int i=top;i>=0;i--)
cout <<stk[i] <<" ";
}
};
void main()
{
int ch;
stack st;
clrscr();
while(1)
{
cout <<"\n1.push 2.pop 3.display 4.exit\nEnter ur choice";
cin >> ch;
switch(ch)
{
case 1: cout <<"enter the element";
cin >> ch;
st.push(ch);
break;
case 2: st.pop(); break;
case 3: st.display();break;
case 4: exit(0);
}
}
}
OUTPUTS
1.push 2.pop 3.display
Enter ur choice2
stack under flow
1.push 2.pop 3.display
Enter ur choice1
enter the element2
inserted2
1.push 2.pop 3.display
Enter ur choice1
enter the element3
inserted3
1.push 2.pop 3.display
Enter ur choice2
deleted3
1.push 2.pop 3.display
Enter ur choice1
enter the element5
18
4.exit
4.exit
4.exit
4.exit
4.exit
Advanced Data Structures
Queue ADT Algorithms
Insert ( item)
{
If rear = max -1
then print “ queue is full”
else
{
Increment rear
Queue [rear]=item;
}
}
Delete()
{
If front = rear print “queue is empty”
else
Increment front
}
Display()
{
If front=rear print “queue is empty “
else
For i =front to rear
Print queue[i];
}
19
Advanced Data Structures
Queue ADT
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class queue
{
int queue[5];
int rear,front;
public:
queue()
{
rear=-1;
front=-1;
}
void insert(int x)
{
if(rear > 4)
{
cout <<"queue over flow";
front=rear=-1;
return;
}
queue[++rear]=x;
cout <<"inserted" <<x;
}
void delet()
{
if(front==rear)
{
cout <<"queue under flow";
return;
}
cout <<"deleted" <<queue[++front];
}
void display()
{
if(rear==front)
{
cout <<" queue empty";
20
Advanced Data Structures
return;
}
for(int i=front+1;i<=rear;i++)
cout <<queue[i]<<" ";
}
};
void main()
{
int ch;
queue qu;
clrscr();
while(1){
cout <<"\n1.insert 2.delet 3.display 4.exit\nEnter ur choice";
cin >> ch;
switch(ch)
{
case 1: cout <<"enter the element";
cin >> ch;
qu.insert(ch);
break;
case 2: qu.delet(); break;
case 3: qu.display();break;
case 4: exit(0);
}
}
}
OUTPUT
1.insert 2.delet 3.display 4.exit
Enter ur choice1
enter the element21
inserted21
1.insert 2.delet 3.display 4.exit
Enter ur choice1
enter the element22
inserted22
1.insert 2.delet 3.display 4.exit
Enter ur choice1
enter the element16
inserted16
1.insert 2.delet 3.display 4.exit
Enter ur choice3
21 22 16 1.insert 2.delet 3.display 4.exit
21
Advanced Data Structures
Algorithm for Stack Using Linked List
Push(item)
{
If (stack is full) print “ stack over flow”
else
goto end of list and let it be temp
temp->next=item
item->next=NULL;
}
Pop()
{
If(head is null) print” stack under flow”
else
goto last but one node and let it be temp
temp->next=NULL
}
Display()
{
If ( head=NULL) print” no element to display”
else
{
Temp=head;
While(temp!=NULL)
{
Print(“temp->data)
Temp=temp->next;
}
}
22
Advanced Data Structures
Stack Using Linked List
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class node
{
public:
class node *next;
int data;
};
class stack : public node
{
node *head;
int tos;
public:
stack()
{
os=-1;
}
void push(int x)
{
if (tos < 0 )
{
head =new node;
head->next=NULL;
head->data=x;
tos ++;
}
else
{
node *temp,*temp1;
temp=head;
if(tos >= 4)
{
cout <<"stack over flow";
return;
}
tos++;
while(temp->next != NULL)
temp=temp->next;
temp1=new node;
23
Advanced Data Structures
temp->next=temp1;
temp1->next=NULL;
temp1->data=x;
}
}
void display()
{
node *temp;
temp=head;
if (tos < 0)
{
cout <<" stack under flow";
return;
}
while(temp != NULL)
{
cout <<temp->data<< " ";
temp=temp->next;
}
}
void pop()
{
node *temp;
temp=head;
if( tos < 0 )
{
cout <<"stack under flow";
return;
}
tos--;
while(temp->next->next!=NULL)
{
temp=temp->next;
}
temp->next=NULL;
}
};
void main()
{
stack s1;
int ch;
clrscr();
while(1)
{
24
Advanced Data Structures
cout <<"\n1.PUSH\n2.POP\n3.DISPLAY\n4.EXIT\n enter ru choice:";
cin >> ch;
switch(ch)
{
case 1:
cout <<"\n enter a element";
cin >> ch;
s1.push(ch);
break;
case 2: s1.pop();break;
case 3: s1.display();
break;
case 4: exit(0);
}
}
}
OUTPUT
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:1
enter a element23
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:1
enter a element67
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:3
23 67
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:2
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:3
23
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:2
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:2
stack under flow
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:4
25
Advanced Data Structures
Algorithm Queue using Linked List
Insert ( item)
{
If rear = max -1 then print “ queue is full”
else
{
Increment rear
Create a new node called item
goto last node in the list and let it be temp
temp-next=item;
item-next=NULL;
}
}
Delete()
{
If front = rear print “queue is empty”
else
{
Increment front
head=head-next;
}
}
Display()
{
If front=rear print “queue is empty “
else Temp=head;
While(temp!=NULL)
{
Print(“temp-data)
Temp=temp-next;
}
}
26
Advanced Data Structures
Queue using Linked List
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class node
{
public:
class node *next;
int data;
};
class queue : public node
{
node *head;
int front,rare;
public:
queue()
{
front=-1;
rare=-1;
}
void push(int x)
{
if (rare < 0 )
{
head =new node;
head->next=NULL;
head->data=x;
rare ++;
}
else
{
node *temp,*temp1;
temp=head;
if(rare >= 4)
{
cout <<"queue over flow";
return;
}
rare++;
while(temp->next != NULL)
temp=temp->next;
27
Advanced Data Structures
temp1=new node;
temp->next=temp1;
temp1->next=NULL;
temp1->data=x;
}
}
void display()
{
node *temp;
temp=head;
if (rare < 0)
{
cout <<" queue under flow";
return;
}
while(temp != NULL)
{
cout <<temp->data<< " ";
temp=temp->next;
}
}
void pop()
{
node *temp;
temp=head;
if( rare < 0)
{
cout <<"queue under flow";
return;
}
if(front == rare)
{
front = rare =-1;
head=NULL;
return;
}
front++;
head=head->next;
}
};
void main()
{
queue s1;
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Advanced Data Structures
int ch;
clrscr();
while(1)
{
cout <<"\n1.PUSH\n2.POP\n3.DISPLAY\n4.EXIT\n enter ru choice:";
cin >> ch;
switch(ch)
{
case 1:
cout <<"\n enter a element";
cin >> ch;
s1.push(ch);
break;
case 2: s1.pop();break;
case 3: s1.display();
break;
case 4: exit(0);
}
}
}
OUTPUT
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:1
enter a element23
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:1
enter a element54
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:3
23 54
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:2
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:2
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:2
queue under flow
1.PUSH 2.POP 3.DISPLAY 4.EXIT
enter ru choice:4
29
Advanced Data Structures
Algorithms fo DeQueue Using Double Linked List
Algorithm Insertfirst(item)
{
if dequeue is empty
{
Item-next=item-prev=NULL;
tail=head=item;
}
else if(dequeue is full) print” insertion is not possible”
else
{
item-next=head;
item-prev=NULL;
head=item;
}
}
Algorithm Insertlast (item)
{
if dequeue is empty
{
Item-next=item-prev=NULL;
tail=head=item;
}
else if(dequeue is full) print” insertion is not possible”
else
{
tail-next=head;
item-prev=tail;
tail=item;
}
}
Deletefirst()
{
If (dequeue is empty) print” no node to delete”;
else
{
Head=head-next;
Head-prev=NULL;
}
}
30
Advanced Data Structures
Deletelast()
{
if (dequeue is empty) print” no node to delete”;
else
{
tail=tail-prev;
tail-next=NULL;
}
}
Displayfirst()
{
if( dequeue is empty) print “ no node to display”
else
{
temp=head;
while(temp-next!=null) then do
{
print(temp-data);
temp=temp-next;
}
}
}
Displaylast()
{
if( dequeue is empty) print “ no node to display”
else
{
temp=tail
while(temp-prevt!=null) then do
{
print(temp-data);
temp=temp-prev;
}
}
}
31
Advanced Data Structures
Implementation of DeQueue Using Double Linked List
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class node
{
public:
int data;
class node *next;
class node *prev;
};
class dqueue: public node
{
node *head,*tail;
int top1,top2;
public:
dqueue()
{
top1=0;
top2=0;
head=NULL;
tail=NULL;
}
void push(int x)
{
node *temp;
int ch;
if(top1+top2 >=5)
{
cout <<"dqueue overflow";
return ;
}
if( top1+top2 == 0)
{
head = new node;
head->data=x;
head->next=NULL;
head->prev=NULL;
tail=head;
top1++;
32
Advanced Data Structures
}
else
{
cout <<" Add element 1.FIRST 2.LAST\n enter ur choice:";
cin >> ch;
if(ch==1)
{
top1++;
temp=new node;
temp->data=x;
temp->next=head;
temp->prev=NULL;
head->prev=temp;
head=temp;
}
else
{
top2++;
temp=new node;
temp->data=x;
temp->next=NULL;
temp->prev=tail;
tail->next=temp;
tail=temp;
}
}
}
void pop()
{
int ch;
cout <<"Delete 1.First Node 2.Last Node\n Enter ur choice:";
cin >>ch;
if(top1 + top2 <=0)
{
cout <<"\nDqueue under flow";
return;
}
if(ch==1)
{
head=head->next;
head->prev=NULL;
top1--;
}
33
Advanced Data Structures
else
{
top2--;
tail=tail->prev;
tail->next=NULL;
}
}
void display()
{
int ch;
node *temp;
cout <<"display from 1.Staring 2.Ending\n Enter ur choice";
cin >>ch;
if(top1+top2 <=0)
{
cout <<"under flow";
return ;
}
if (ch==1)
{
temp=head;
while(temp!=NULL)
{
cout << temp->data <<" ";
temp=temp->next;
}
}
else
{
temp=tail;
while( temp!=NULL)
{
cout <<temp->data << " ";
temp=temp->prev;
}
}
}
};
void main()
{
dqueue d1;
int ch;
clrscr();
34
Advanced Data Structures
while (1)
{
cout <<"1.INSERT 2.DELETE 3.DISPLAU 4.EXIT\n Enter ur choice:";
cin >>ch;
switch(ch)
{
case 1: cout <<"enter element";
cin >> ch;
d1.push(ch); break;
case 2: d1.pop(); break;
case 3: d1.display(); break;
case 4: exit(1);
}
}
}
OUTPUT
1.INSERT 2.DELETE 3.DISPLAU 4.EXIT
Enter ur choice:1
enter element4
1.INSERT 2.DELETE 3.DISPLAU 4.EXIT
Enter ur choice:1
enter element5
Add element 1.FIRST 2.LAST
enter ur choice:1
1.INSERT 2.DELETE 3.DISPLAU 4.EXIT
Enter ur choice:1
enter element6
Add element 1.FIRST 2.LAST
enter ur choice:2
1.INSERT 2.DELETE 3.DISPLAU 4.EXIT
Enter ur choice:3
display from 1.Staring 2.Ending
Enter ur choice1
5 4 6 1.INSERT 2.DELETE 3.DISPLAU 4.EXIT
Enter ur choice:2
Delete 1.First Node 2.Last Node
Enter ur choice:1
1.INSERT 2.DELETE 3.DISPLAU 4.EXIT
Enter ur choice:3
display from 1.Staring 2.Ending
Enter ur choice1
4 6 1.INSERT 2.DELETE 3.DISPLAU 4.EXIT
Enter ur choice:4
35
Advanced Data Structures
Algorithm for Circular Queue
Algorithm Insertfirst(item)
{
if cqueue is empty
then
head=item;
else if(cqueue is full) print” insertion is not possible”
else
{
Rear=(rear +1) mod max
}
cqueue[rear]=x;
}
Algorithm Deletet()
{
If (dequeue is empty) print” no node to delete”;
else
{
Front=(front+1) mod max
}
}
Algorithm display()
{
If (front >rear) display elements for front to max and 0 to rear
Else display elements from front to rear
}
36
Advanced Data Structures
Implementation of Circular Queue Using Array
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class cqueue
{
int q[5],front,rare;
public:
cqueue()
{
front=-1;
rare=-1;
}
void push(int x)
{
if(front ==-1 && rare == -1)
{
q[++rare]=x;
front=rare;
return;
}
else if(front == (rare+1)%5 )
{
cout <<" Circular Queue over flow";
return;
}
rare= (rare+1)%5;
q[rare]=x;
}
void pop()
{
if(front==-1 && rare==
-1)
{
cout <<"under flow";
return;
}
else if( front== rare )
{
front=rare=-1;
return;
37
Advanced Data Structures
}
front= (front+1)%5;
}
void display()
{
int i;
if( front <= rare)
{
for(i=front; i<=rare;i++)
cout << q[i]<<" ";
}
else
{
for(i=front;i<=4;i++)
{
cout <<q[i] << " ";
}
for(i=0;i<=rare;i++)
{
cout << q[i]<< " ";
}
}
}
};
void main(){
int ch;
cqueue q1;
clrscr();
while( 1)
{
cout<<"\n1.INSERT 2.DELETE 3.DISPLAY
cin >> ch;
switch(ch)
{
case 1: cout<<"enter element";
cin >> ch;
q1.push(ch);
break;
case 2: q1.pop(); break;
case 3: q1.display(); break;
case 4: exit(0);
}
}
}
38
4.EXIT\nEnter ur choice";
Advanced Data Structures
OUTPUT
1.INSERT 2.DELETE 3.DISPLAY 4.EXIT
Enter ur choice1
enter element4
1.INSERT 2.DELETE 3.DISPLAY 4.EXIT
Enter ur choice1
enter element5
1.INSERT 2.DELETE 3.DISPLAY 4.EXIT
Enter ur choice1
enter element3
1.INSERT 2.DELETE 3.DISPLAY 4.EXIT
Enter ur choice3
453
1.INSERT 2.DELETE 3.DISPLAY 4.EXIT
Enter ur choice2
1.INSERT 2.DELETE 3.DISPLAY 4.EXIT
Enter ur choice3
53
1.INSERT 2.DELETE 3.DISPLAY 4.EXIT
Enter ur choice4
39
Advanced Data Structures
Program to Algorithm
Implementfor
Functions
Dictionary
of a Dictionary
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
# define max 10
typedef struct list
{
int data;
struct list *next;
}node_type;
node_type *ptr[max],*root[max],*temp[max];
class Dictionary
{
public:
int index;
Dictionary();
void insert(int);
void search(int);
void delete_ele(int);
};
Dictionary::Dictionary()
{
index=-1;
for(int i=0;i<max;i++)
{
root[i]=NULL;
ptr[i]=NULL;
temp[i]=NULL;
}
}
void Dictionary::insert(int key)
{
index=int(key%max);
ptr[index]=(node_type*)malloc(sizeof(node_type));
ptr[index]->data=key;
if(root[index]==NULL)
{
40
Advanced Data Structures
root[index]=ptr[index];
root[index]->next=NULL;
temp[index]=ptr[index];
}
else
{
temp[index]=root[index];
while(temp[index]->next!=NULL)
temp[index]=temp[index]->next;
temp[index]->next=ptr[index];
}
}
void Dictionary::search(int key)
{
int flag=0;
index=int(key%max);
temp[index]=root[index];
while(temp[index]!=NULL)
{
if(temp[index]->data==key)
{
cout<<"\nSearch key is found!!";
flag=1;
break;
}
else temp[index]=temp[index]->next;
}
if (flag==0)
cout<<"\nsearch key not found.......";
}
void Dictionary::delete_ele(int key)
{
index=int(key%max);
temp[index]=root[index];
while(temp[index]->data!=key && temp[index]!=NULL)
{
ptr[index]=temp[index];
temp[index]=temp[index]->next;
}
ptr[index]->next=temp[index]->next;
cout<<"\n"<<temp[index]->data<<" has been deleted.";
temp[index]->data=-1;
41
Advanced Data Structures
temp[index]=NULL;
free(temp[index]);
}
void main()
{
int val,ch,n,num;
char c;
Dictionary d;
clrscr();
do
{
cout<<"\nMENU:\n1.Create";
cout<<"\n2.Search for a value\n3.Delete an value";
cout<<"\nEnter your choice:";
cin>>ch;
switch(ch)
{
case 1: cout<<"\nEnter the number of elements to be inserted:";
cin>>n;
cout<<"\nEnter the elements to be inserted:";
for(int i=0;i<n;i++)
{
cin>>num;
d.insert(num);
}
break;
case 2: cout<<"\nEnter the element to be searched:";
cin>>n;
d.search(n);
case 3: cout<<"\nEnter the element to be deleted:";
cin>>n;
d.delete_ele(n);
break;
default: cout<<"\nInvalid choice....";
}
cout<<"\nEnter y to continue......";
cin>>c;
}while(c=='y');
getch();
}
42
Advanced Data Structures
OUTPUT
MENU:
1.Create
2.Search for a value
3.Delete an value
Enter your choice:1
Enter the number of elements to be inserted:8
Enter the elements to be inserted:10 4 5 8 7 12 6 1
Enter y to continue......y
MENU:
1.Create
2.Search for a value
3.Delete an value
Enter your choice:2
Enter the element to be searched:12
Search key is found!!
Enter the element to be deleted:1
1 has been deleted.
Enter y to continue......y
43
Advanced Data Structures
AVL TREE
Algorithm insertion(int x)
{
If(tree is empty) then root is empty
Otherwise
{
temp=search(item); // temp is the node where search for the
item halts
if( item > temp) then temp-right=item;
otherwise temp-left =item





Reconstruction procedure: rotating tree
left rotation and right rotation
Suppose that the rotation occurs at node x
Left rotation: certain nodes from the right subtree of x
move to its left subtree; the root of the right subtree of
x becomes the new root of the reconstructed subtree
Right rotation at x: certain nodes from the left subtree of
x move to its right subtree; the root of the left subtree
of x becomes the new root of the reconstructed subtree
}
Algorithm Search(int x)
Algorithm delete()
{
 Case 1: the node to be deleted
 Case 2: the node to be deleted
is, its right subtree is empty
 Case 3: the node to be deleted
is, its left subtree is empty
 Case 4: the node to be deleted
right child
}
is a leaf
has no right child, that
has no left child, that
has a left child and a
Algorithm Search(x, root)
{
if(tree is empty ) then print” tree is empty”
otherwise
If(x grater than root) search(root-right);
Otherwise if(x less than root ) search(root-left)
Otherwise return true
}
}
44
Advanced Data Structures
AVL TREE
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
#include<math.h>
void insert(int,int );
void delte(int);
void display(int);
int search(int);
int search1(int,int);
int avltree[40],t=1,s,x,i;
void main()
{
int ch,y;
for(i=1;i<40;i++)
avltree[i]=-1;
while(1)
{
cout <<"1.INSERT\n2.DELETE\n3.DISPLAY\n4.SEARCH\n5.EXIT\nEnter
your choice:";
cin >> ch;
switch(ch)
{
case 1:
cout <<"enter the element to insert";
cin >> ch;
insert(1,ch);
break;
case 2:
cout <<"enter the element to delete";
cin >>x;
y=search(1);
if(y!=-1) delte(y);
else cout<<"no such element in avlavltree";
break;
case 3:
display(1);
cout<<"\n";
for(int i=0;i<=32;i++)
cout <<i;
45
Advanced Data Structures
cout <<"\n";
break;
case 4:
cout <<"enter the element to search:";
cin >> x;
y=search(1);
if(y == -1) cout <<"no such element in avltree";
else cout <<x << "is in" <<y <<"position";
break;
case 5:
exit(0);
}
}
}
void insert(int s,int ch )
{
int x,y;
if(t==1)
{
avltree[t++]=ch;
return;
}
x=search1(s,ch);
if(avltree[x]>ch)
{ avltree[2*x]=ch;
y=log(2*x)/log(2);
if(height(1,y))
{
if( x%2==0 )
update1();
else
update2();
}
}
else {
avltree[2*x+1]=ch;
y=log(2*x)/log(2);
if(height(1,y))
{
if(x%2==1)
update1();
else
update2();
}
46
Advanced Data Structures
}
t++;
}
void delte(int x)
{
if( avltree[2*x]==-1 && avltree[2*x+1]==-1)
avltree[x]=-1;
else if(avltree[2*x]==-1)
{ avltree[x]=avltree[2*x+1];
avltree[2*x+1]=-1;
}
else if(avltree[2*x+1]==-1)
{ avltree[x]=avltree[2*x];
avltree[2*x]=-1;
}
else
{
avltree[x]=avltree[2*x];
delte(2*x);
}
t--;
}
int search(int s)
{
if(t==1)
{
cout <<"no element in avltree";
return -1;
}
if(avltree[s]==-1)
return avltree[s];
if(avltree[s]>x)
search(2*s);
else if(avltree[s]<x)
search(2*s+1);
else
return s;
}
void display(int s)
{
if(t==1)
{
cout <<"no element in avltree:";
47
Advanced Data Structures
return;
}
for(int i=1;i<40;i++)
if(avltree[i]==-1)
cout <<" ";
else cout <<avltree[i];
return ;
}
int search1(int s,int ch)
{
if(t==1)
{
cout <<"no element in avltree";
return -1;
}
if(avltree[s]==-1)
return s/2;
if(avltree[s] > ch)
search1(2*s,ch);
else search1(2*s+1,ch);
}
int height(int s,int y)
{
if(avltree[s]==-1)
return;
}
48
Advanced Data Structures
OUTPUT
1.insert 2.display 3.delete 4.search 5.exit
Enter u r choice to perform on AVL tree1
Enter an element to insert into tree4
do u want to continuey
1.insert 2.display 3.delete 4.search 5.exit
Enter u r choice to perform on AVL tree1
Enter an element to insert into tree5
do u want to continuey
1.insert 2.display 3.delete 4.search 5.exit
Enter u r choice to perform on AVL tree3
Enter an item to deletion5
itemfound
do u want to continuey
1.insert 2.display 3.delete 4.search 5.exit
Enter u r choice to perform on AVL tree2
4
do u want to continue4
49
Advanced Data Structures
Breath First Search Algorithm
Algorithm BFS(s):
Input: A vertex s in a graph
Output: A labeling of the edges as “discovery” edges and “cross
edges”
initialize container L0 to contain vertex s
i  0
while Li is not empty do
create container Li+1 to initially be empty
for each vertex v in Li do
if edge e incident on v do
let w be the other endpoint of e
if vertex w is unexplored then
label e as a discovery edge
insert w into Li+1
else label e as a cross edge
i  i + 1
50
Advanced Data Structures
Breath First Search Implementation
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
int cost[10][10],i,j,k,n,qu[10],front,rare,v,visit[10],visited[10];
void main()
{
clrscr();
int m;
cout <<"enterno of vertices";
cin >> n;
cout <<"ente no of edges";
cin >> m;
cout <<"\nEDGES \n";
for(k=1;k<=m;k++)
{
cin >>i>>j;
cost[i][j]=1;
}
cout <<"enter initial vertex";
cin >>v;
cout <<"Visitied vertices\n";
cout << v;
xvisited[v]=1;
k=1;
while(k<n)
{
for(j=1;j<=n;j++)
if(cost[v][j]!=0 && visited[j]!=1 && visit[j]!=1)
{
visit[j]=1;
qu[rare++]=j;
}
v=qu[front++];
cout<<v << " ";
k++;
visit[v]=0; visited[v]=1;
}
}
51
Advanced Data Structures
OUTPUT
enterno of vertices9
ente no of edges9
EDGES
12
23
15
14
47
78
89
26
57
enter initial vertex1
Visited vertices
12 4 5 3 6 7 8 9
52
Advanced Data Structures
Depth First Search Algorithm
Algorithm DFS(v); Input: A vertex v in a graph
Output: A labeling of the edges as “discovery” edges and
“backedges”
for each edge e incident on v do
if edge e is unexplored then let w be the other
endpoint of e
if vertex w is unexplored then label e as a discovery
edge recursively call DFS(w)
else label e as a backedge
53
Advanced Data Structures
Depth First Search
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
int cost[10][10],i,j,k,n,stk[10],top,v,visit[10],visited[10];
void main()
{
int m;
clrscr();
cout <<"enterno of vertices";
cin >> n;
cout <<"ente no of edges";
cin >> m;
cout <<"\nEDGES \n";
for(k=1;k<=m;k++)
{
cin >>i>>j;
cost[i][j]=1;
}
cout <<"enter initial vertex";
cin >>v;
cout <<"ORDER OF VISITED VERTICES";
cout << v <<" ";
visited[v]=1;
k=1;
while(k<n)
{
for(j=n;j>=1;j--)
if(cost[v][j]!=0 && visited[j]!=1 && visit[j]!=1)
{
visit[j]=1;
stk[top]=j;
top++;
}
v=stk[--top];
cout<<v << " ";
k++;
visit[v]=0; visited[v]=1;
}
}
54
Advanced Data Structures
OUTPUT
enterno of vertices9
ente no of edges9
EDGES
12
23
26
15
14
47
57
78
89
enter initial vertex1
ORDER OF VISITED VERTICES1 2 3 6 4 7 8 9 5
55
Advanced Data Structures
Prim’s Algorithm
Algorithm Prim(E,Cost,n,t)
{
Let (k, l) be an edge of minimum cost in E;
Mincost= cost[k,l];
t[1,1]=k;
t[1,2]=l;
for i=1 to n
do
{
If (cost[i, l]<cost[k,l]) then near[i]=l;
Else
Near[i]=k;
Near[k]=near[j]=0;
}
For i=2 to n -1
do
{
Let j be an index such that nearpj]!= 0 and cost[j,near[j]]
is minimum
T[I,1]=j ; t[I,2]=near[j]
mincost=mincost + cost[j,near[j]];
near[j]=0;
for k=1 to n do
if(near[k] !=0 ) and cost[k,near[k]])
then near[j]=k
}
}
56
>cost[k,j])
Advanced Data Structures
Prim’s Algorithm
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
int cost[10][10],i,j,k,n,stk[10],top,v,visit[10],visited[10],u;
void main()
{
int m,c;
clrscr();
cout <<"enterno of vertices";
cin >> n;
cout <<"ente no of edges";
cin >> m;
cout <<"\nEDGES Cost\n";
for(k=1;k<=m;k++)
{
cin >>i>>j>>c;
cost[i][j]=c;
}
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
if(cost[i][j]==0)
cost[i][j]=31999;
cout <<"ORDER OF VISITED VERTICES";
k=1;
while(k<n)
{
m=31999;
if(k==1)
{
for(i=1;i<=n;i++)
for(j=1;j<=m;j++)
if(cost[i][j]<m)
{
m=cost[i][j];
u=i;
}
}
else
{
for(j=n;j>=1;j--)
57
Advanced Data Structures
if(cost[v][j]<m && visited[j]!=1 && visit[j]!=1)
{
visit[j]=1;
stk[top]=j;
top++;
m=cost[v][j];
u=j;
}
}
cost[v][u]=31999;
v=u;
cout<<v << " ";
k++;
visit[v]=0; visited[v]=1;
}
}
OUTPUT
enterno of vertices7
ente no of edges9
EDGES Cost
1 6 10
6 5 25
5 4 22
4 3 12
3 2 16
2 7 14
5 7 24
4 7 18
1 2 28
ORDER OF VISITED VERTICES1 6 5 4 3 2
58
Advanced Data Structures
Kruskal’s Algorithm
Algorithm Krushkal(E, cost,n,t)
{
for i=1 to n do parent[i]=-1;
i=0;
mincost=0;
while( I < n-1)
{
Delete a minimum coast edge (u,v) form the heap and
reheapfy using adjust
J=find(u);
K=find(v);
If(j!=k) then
{
i=i+1;
t[I,1]=u; t[I,2]=v;
mincost=mincost+ cost[u,v];
union(j,k)
}
If( i !=
n-1) the write (“ no spanning tree”);
else
Return mincost
}
}
59
Advanced Data Structures
Kruskal’s Algorithm
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
int cost[10][10],i,j,k,n,m,c,visit,visited[10],l,v,count,count1,vst,p;
main()
{
int dup1,dup2;
cout<<"enter no of vertices";
cin >> n;
cout <<"enter no of edges";
cin >>m;
cout <<"EDGE Cost";
for(k=1;k<=m;k++)
{
cin >>i >>j >>c;
cost[i][j]=c;
cost[j][i]=c;
}
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
if(cost[i][j]==0)
cost[i][j]=31999;
visit=1;
while(visit<n)
{
v=31999;
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
if(cost[i][j]!=31999 && cost[i][j]<v && cost[i][j]!=-1 )
{
count =0;
for(p=1;p<=n;p++)
{
if(visited[p]==i || visited[p]==j)
count++;
}
if(count >= 2)
{
for(p=1;p<=n;p++)
if(cost[i][p]!=31999 && p!=j)
dup1=p;
60
Advanced Data Structures
for(p=1;p<=n;p++)
if(cost[j][p]!=31999 && p!=i)
dup2=p;
if(cost[dup1][dup2]==-1)
continue;
}
l=i;
k=j;
v=cost[i][j];
}
cout <<"edge from " <<l <<"-->"<<k;
cost[l][k]=-1;
cost[k][l]=-1;
visit++;
count=0;
count1 =0;
for(i=1;i<=n;i++)
{
if(visited[i]==l)
count++;
if(visited[i]==k)
count1++;
}
if(count==0)
visited[++vst]=l;
if(count1==0)
visited[++vst]=k;
}
}
61
Advanced Data Structures
Single Source Shortest Path
#include<iostream.h>
#include<conio.h>
#include<stdio.h>
int shortest(int ,int);
int cost[10][10],dist[20],i,j,n,k,m,S[20],v,totcost,path[20],p;
void main()
{
int c;
clrscr();
cout <<"enter no of vertices";
cin >> n;
cout <<"enter no of edges";
cin >>m;
cout <<"\nenter\nEDGE Cost\n";
for(k=1;k<=m;k++)
{
cin >> i >> j >>c;
cost[i][j]=c;
}
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
if(cost[i][j]==0)
cost[i][j]=31999;
cout <<"enter initial vertex";
cin >>v;
cout << v<<"\n";
shortest(v,n);
}
shortest(int v,int n)
{
int min;
for(i=1;i<=n;i++)
{
S[i]=0;
dist[i]=cost[v][i];
}
path[++p]=v;
62
Advanced Data Structures
S[v]=1;
dist[v]=0;
for(i=2;i<=n-1;i++)
{
k=-1;
min=31999;
for(j=1;j<=n;j++)
{
if(dist[j]<min && S[j]!=1)
{
min=dist[j];
k=j;
}
}
if(cost[v][k]<=dist[k])
p=1;
path[++p]=k;
for(j=1;j<=p;j++)
cout<<path[j];
cout <<"\n";
//cout <<k;
S[k]=1;
for(j=1;j<=n;j++)
if(cost[k][j]!=31999 && dist[j]>=dist[k]+cost[k][j] && S[j]!=1)
dist[j]=dist[k]+cost[k][j];
}
}
OUTPUT
enter no of vertices6
enter no of edges11
enter
EDGE Cost
1 2 50
1 3 45
1 4 10
2 3 10
2 4 15
3 5 30
63
Advanced Data Structures
4 1 10
4 5 15
5 2 20
5 3 35
653
enter initial vertex1
1
14
145
1452
13
64
Advanced Data Structures
Non recursive Pre order Traversing Algorithm
Algorithm preorder( root)
{
1. current = root;
//start the traversal at the root node
2. while(current is not NULL or stack is nonempty)
if(current is not NULL)
{
visit current;
push current onto stack;
current = current->llink;
}
else
{
pop stack into current;
current = current->rlink;
//prepare to visit
//the right subtree
}
65
Advanced Data Structures
Non recursive Pre order Traversing
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class node
{
public:
class node *left;
class node *right;
int data;
};
class tree: public node
{
public:
int stk[50],top;
node *root;
tree()
{
root=NULL;
top=0;
}
void insert(int ch)
{
node *temp,*temp1;
if(root== NULL)
{
root=new node;
root->data=ch;
root->left=NULL;
root->right=NULL;
return;
}
temp1=new node;
temp1->data=ch;
temp1->right=temp1->left=NULL;
temp=search(root,ch);
if(temp->data>ch)
temp->left=temp1;
else
temp->right=temp1;
66
Advanced Data Structures
}
node *search(node *temp,int ch)
{
if(root== NULL)
{
cout <<"no node present";
return NULL;
}
if(temp->left==NULL && temp->right== NULL)
return temp;
if(temp->data>ch)
{ if(temp->left==NULL) return temp;
search(temp->left,ch);}
else
{ if(temp->right==NULL) return temp;
search(temp->right,ch);
}
}
void display(node *temp)
{
if(temp==NULL)
return ;
display(temp->left);
cout<<temp->data <<" ";
display(temp->right);
}
void preorder( node *root)
{
node *p,*q;
p=root;
q=NULL;
top=0;
while(p!=NULL)
{
cout <<p->data << " ";
if(p->right!=NULL)
{
stk[top]=p->right->data;
top++;
}
p=p->left;
if(p==NULL && top>0)
67
Advanced Data Structures
{
p=pop(root);
}
}
}
node * pop(node *p)
{
int ch;
ch=stk[top-1];
if(p->data==ch)
{
top--;
return p;
}
if(p->data>ch)
pop(p->left);
else
pop(p->right);
}
};
void main()
{
tree t1;
int ch,n,i;
while(1)
{
cout <<"\n1.INSERT\n2.DISPLAY 3.PREORDER TRAVERSE\n4.EXIT\nEnter
your choice:";
cin >> ch;
switch(ch)
{
case 1: cout <<"enter no of elements to insert:";
cout<<"\n enter the elements";
cin >> n;
for(i=1;i<=n;i++)
{ cin >> ch;
t1.insert(ch);
}
break;
case 2: t1.display(t1.root);break;
case 3: t1.preorder(t1.root); break;
case 4: exit(1);
}
}
}
68
Advanced Data Structures
OUTPUT
1.INSERT
2.DISPLAY 3.PREORDER TRAVERSE
4.EXIT
Enter your choice:1
enter no of elements to insert
enter the elements7
5 24 36 11 44 2 21
1.INSERT
2.DISPLAY 3.PREORDER TRAVERSE
4.EXIT
Enter your choice:2
2 5 11 21 24 36 44
1.INSERT
2.DISPLAY 3.PREORDER TRAVERSE
4.EXIT
Enter your choice:3
5 2 24 11 21 36 44
1.INSERT
2.DISPLAY 3.PREORDER TRAVERSE
4.EXIT
Enter your choice:4
69
Advanced Data Structures
Non recursive In order Traversing
Algorithm inorder(
root)
{
1. current = root;
//start traversing the binary tree at
// the root node
2. while(current is not NULL or stack is nonempty)
if(current is not NULL)
{
push current onto stack;
current = current->llink;
}
else
{
pop stack into current;
visit current;
//visit the node
current = current->rlink;
//move to the
//right child
}
}
70
Advanced Data Structures
Non recursive In order Traversing
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class node
{
public:
class node *left;
class node *right;
int data;
};
class tree: public node
{
public:
int stk[50],top;
node *root;
tree()
{
root=NULL;
top=0;
}
void insert(int ch)
{
node *temp,*temp1;
if(root== NULL)
{
root=new node;
root->data=ch;
root->left=NULL;
root->right=NULL;
return;
}
temp1=new node;
temp1->data=ch;
temp1->right=temp1->left=NULL;
temp=search(root,ch);
if(temp->data>ch)
temp->left=temp1;
else
temp->right=temp1;
71
Advanced Data Structures
}
node *search(node *temp,int ch)
{
if(root== NULL)
{
cout <<"no node present";
return NULL;
}
if(temp->left==NULL && temp->right== NULL)
return temp;
if(temp->data>ch)
{ if(temp->left==NULL) return temp;
search(temp->left,ch);}
else
{ if(temp->right==NULL) return temp;
search(temp->right,ch);
}
}
void display(node *temp)
{
if(temp==NULL)
return ;
display(temp->left);
cout<<temp->data;
display(temp->right);
}
void inorder( node *root)
{
node *p;
p=root;
top=0;
do
{
while(p!=NULL)
{
stk[top]=p->data;
top++;
p=p->left;
}
if(top>0)
{
p=pop(root);
72
Advanced Data Structures
cout << p->data;
p=p->right;
}
}while(top!=0 || p!=NULL);
}
node * pop(node *p)
{
int ch;
ch=stk[top-1];
if(p->data==ch)
{
top--;
return p;
}
if(p->data>ch)
pop(p->left);
else
pop(p->right);
}
};
void main()
{
tree t1;
int ch,n,i;
while(1)
{
cout <<"\n1.INSERT\n2.DISPLAY 3.INORDER TRAVERSE\n4.EXIT\nEnter
your choice:";
cin >> ch;
switch(ch)
{
case 1: cout <<"enter no of elements to insert:";
cin >> n;
for(i=1;i<=n;i++)
{ cin >> ch;
t1.insert(ch);
}
break;
case 2: t1.display(t1.root);break;
case 3: t1.inorder(t1.root); break;
case 4: exit(1);
}
}
73
Advanced Data Structures
}
OUTPUT
1.INSERT
2.DISPLAY 3.INORDER TRAVERSE
4.EXIT
Enter your choice:1
enter no of elements to inser
5 24 36 11 44 2 21
1.INSERT
2.DISPLAY 3.INORDER TRAVERSE
4.EXIT
Enter your choice:3
251121243644
1.INSERT
2.DISPLAY 3.INORDER TRAVERSE
4.EXIT
Enter your choice:3
251121243644
1.INSERT
2.DISPLAY 3.INORDER TRAVERSE
4.EXIT
Enter your choice:4
74
Advanced Data Structures
Non recursive Post order Traversing Algorithm
Algorithm
postorder( node
root)
{
1.
current = root;
//start traversal at root node
2. v = 0;
3. if(current is NULL)
the binary tree is empty
4. if(current is not NULL)
a. push current into stack;
b. push 1 onto stack;
c. current = current->llink;
d. while(stack is not empty)
if(current is not NULL and v is 0)
{
push current and 1 onto stack;
current = current->llink;
}
else
{
pop stack into current and v;
if(v == 1)
{
push current and 2 onto stack;
current = current->rlink;
v = 0;
}
else
visit current;
}}
75
Advanced Data Structures
Non recursive Post order Traversing
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class node
{
public:
class node *left;
class node *right;
int data;
};
class tree: public node
{
public:
int stk[50],top;
node *root;
tree()
{
root=NULL;
top=0;
}
void insert(int ch)
{
node *temp,*temp1;
if(root== NULL)
{
root=new node;
root->data=ch;
root->left=NULL;
root->right=NULL;
return;
}
temp1=new node;
temp1->data=ch;
temp1->right=temp1->left=NULL;
temp=search(root,ch);
if(temp->data>ch)
temp->left=temp1;
else
temp->right=temp1;
76
Advanced Data Structures
}
node *search(node *temp,int ch)
{
if(root== NULL)
{
cout <<"no node present";
return NULL;
}
if(temp->left==NULL && temp->right== NULL)
return temp;
if(temp->data>ch)
{ if(temp->left==NULL) return temp;
search(temp->left,ch);}
else
{ if(temp->right==NULL) return temp;
search(temp->right,ch);
}
}
void display(node *temp)
{
if(temp==NULL)
return ;
display(temp->left);
cout<<temp->data << " ";
display(temp->right);
}
void postorder( node *root)
{
node *p;
p=root;
top=0;
while(1)
{
while(p!=NULL)
{
stk[top]=p->data;
top++;
if(p->right!=NULL)
stk[top++]=-p->right->data;
p=p->left;
}
77
Advanced Data Structures
}
while(stk[top-1] > 0 || top==0)
{
if(top==0) return;
cout << stk[top-1] <<" ";
p=pop(root);
}
if(stk[top-1]<0)
{
stk[top-1]=-stk[top-1];
p=pop(root);
}
}
node * pop(node *p)
{
int ch;
ch=stk[top-1];
if(p->data==ch)
{
top--;
return p;
}
if(p->data>ch)
pop(p->left);
else
pop(p->right);
}
};
void main()
{
tree t1;
int ch,n,i;
clrscr();
while(1)
{
cout <<"\n1.INSERT\n2.DISPLAY 3.POSTORDER
TRAVERSE\n4.EXIT\nEnter your choice:";
cin >> ch;
switch(ch)
{
case 1: cout <<"enter no of elements to insert:";
cout<<"\n enter the elements";
cin >> n;
for(i=1;i<=n;i++)
{ cin >> ch;
t1.insert(ch);
78
Advanced Data Structures
}
break;
case 2: t1.display(t1.root);break;
case 3: t1.postorder(t1.root); break;
case 4: exit(1);
}
}
}
OUTPUT
1.INSERT
2.DISPLAY 3.POSTORDER TRAVERSE
4.EXIT
Enter your choice:1
enter no of elements to insert:
enter the elements7
5 24 36 11 44 2 21
1.INSERT
2.DISPLAY 3.POSTORDER TRAVERSE
4.EXIT
Enter your choice:2
2 5 11 21 24 36 44
1.INSERT
2.DISPLAY 3.POSTORDER TRAVERSE
4.EXIT
Enter your choice:3
2 21 11 44 36 24 5
1.INSERT
2.DISPLAY 3.POSTORDER TRAVERSE
4.EXIT
Enter your choice:4
79
Advanced Data Structures
Quick Sort Algorithm
Algorithm quicksort(a[],p,q)
{
V=a[p];
i=p;
j=q;
if(i<j)
{
repeat
{
repeat
I=i+1;
Until( a[i]> v);
Repeat
J=j-1;
Until(a[j]<v);
If(i<j) then interchange ( a[i],a[j])
}until (i<=j);
interchange(a[j], a[p])
}
quicksort(a[],p,j);
quicksort(a[],j+1,q);
}
80
Advanced Data Structures
Quick Sort
#include<iostream.h>
#include<conio.h>
int a[10],l,u,i,j;
void quick(int *,int,int);
void main()
{
clrscr();
cout <<"enter 10 elements";
for(i=0;i<10;i++)
cin >> a[i];
l=0;
u=9;
quick(a,l,u);
cout <<"sorted elements";
for(i=0;i<10;i++)
cout << a[i] << " ";
getch();
}
void quick(int a[],int l,int u)
{
int p,temp;
if(l<u)
{
p=a[l];
i=l;
j=u;
while(i<j)
{
while(a[i] <= p && i<j )
i++;
while(a[j]>p && i<=j )
j--;
if(i<=j)
{
temp=a[i];
a[i]=a[j];
a[j]=temp;}
}
temp=a[j];
a[j]=a[l];
81
Advanced Data Structures
a[l]=temp;
cout <<"\n";
for(i=0;i<10;i++)
cout <<a[i]<<" ";
quick(a,l,j-1);
quick(a,j+1,u);
}
}
OUTPUT
enter 10 elements5 2 3 16 25 1 20 7 8 61 14
1 2 3 5 25 16 20 7 8 61
1 2 3 5 25 16 20 7 8 61
1 2 3 5 25 16 20 7 8 61
1 2 3 5 25 16 20 7 8 61
1 2 3 5 25 16 20 7 8 61
1 2 3 5 8 16 20 7 25 61
1 2 3 5 7 8 20 16 25 61
1 2 3 5 7 8 16 20 25 61
1 2 3 5 7 8 16 20 25 61 sorted elements1 2 3 5 7 8 16 20 25 61
82
Advanced Data Structures
Merge Sort Algorithm
Algorithm Mergesort(low,high)
{
If(low<high)
{
Mid=(low+high)/2;
Mergesort(low,mid);
Mergesort(mid+1,high)
Merge(low,mid,high);
}
}
Algorithm Merge(low,mid,high)
{
h=low; i=low; j=mid+1;
While(h<=mid and j<=high) do
{
If(a[h]<a[j]) then
{
b[i]=a[h];
h=h+1;
}
else
{
b[i]=a[j];
J=j+1;
}
if(h>mid)
{
For k= j to high do
b[i]=a[k]; i=i+1;
}
Else
{
For k=h to mid do
b[i]=a[k]; i=i+1;
}
For k= low to high do a[k]=b[k];
}
}
83
Advanced Data Structures
Merge Sort
#include<iostream.h>
#include<conio.h>
void mergesort(int *,int,int);
void merge(int *,int,int,int);
int a[20],i,n,b[20];
void main()
{
clrscr();
cout <<"\N enter no of elements";
cin >> n;
cout <<"enter the elements";
for(i=0;i<n;i++)
cin >> a[i];
mergesort(a,0,n-1);
cout <<" numbers after sort";
for(i=0;i<n;i++)
cout << a[i] << " ";
getch();
}
void mergesort(int a[],int i,int j)
{
int mid;
if(i<j)
{
mid=(i+j)/2;
mergesort(a,i,mid);
mergesort(a,mid+1,j);
merge(a,i,mid,j);
}
}
void merge(int a[],int low,int mid ,int high)
{
int h,i,j,k;
h=low;
i=low;
j=mid+1;
84
Advanced Data Structures
while(h<=mid && j<=high)
{
if(a[h]<=a[j])
b[i]=a[h++];
else
b[i]=a[j++];
i++;
}
if( h > mid)
for(k=j;k<=high;k++)
b[i++]=a[k];
else
for(k=h;k<=mid;k++)
b[i++]=a[k];
cout <<"\n";
for(k=low;k<=high;k++)
{
a[k]=b[k];
cout << a[k] <<" ";
}
}
OUTPUT
N enter no of elements8 12 5 61 60 50 1 70 81
enter the elements
5 12
60 61
5 12 60 61
1 50
70 81
1 50 70 81
1 5 12 50 60 61 70 81 numbers after sort1 5 12 50 60 61 70 81
85
Advanced Data Structures
Heap Sort Algorithm
Definition: A heap is a list in which each element contains a key, such that the key in the
element at position k in the list is at least as large as the key in the element at position 2k + 1
(if it exists), and 2k + 2 (if it exists)
Algorithm Heapify(a[],n)
{
For i=n/2 to 1 step -1
Adjustify (a,i,n);
}
Algorithm Adjustify(a[],i,n)
{
Repeat
{
J=leftchild(i)
Compare left and right child of a[i] and store the index of grater number in j
Compare a[j] and a[i]
If (a[j]>a[i]) then
Copy a[j] to a[i] and move to next level
}until(j<n)
}
86
Advanced Data Structures
Heap Sort
#include<stdio.h>
#include<conio.h>
int a[20],n;
main()
{
int i,j,temp;
clrscr();
printf("ente n");
scanf("%d",&n);
printf("enter the elements");
for(i=1;i<=n;i++)
scanf("%d",&a[i]);
heapify(a,n);
for(j=1;j<=n;j++)
printf("%d",a[j]);
for(i=n;i>=2;i--)
{
temp=a[i];
a[i]=a[1];
a[1]=temp;
adjust(a,1,i-1);
printf("\n");
for(j=1;j<=n;j++)
printf("%d ",a[j]);
}
printf("\nelements after sort");
for(i=1;i<=n;i++)
printf("%d ",a[i]);
}
heapify(int a[],int n)
{
int i;
for( i=n/2;i>=1;i--)
adjust(a,i,n);
}
87
Advanced Data Structures
adjust(int a[],int i,int n)
{
int j,iteam;
j=2*i;
iteam=a[i];
while(j<=n)
{
if(j<n && a[j]<a[j+1])
j=j+1;
if(iteam>=a[j])
break;
a[j/2]=a[j]; j=2*j;
}
a[j/2]=iteam;
}
88
Advanced Data Structures
All Paris Shortest Path
#include<iostream.h>
#include<conio.h>
int min(int a,int b);
int cost[10][10],a[10][10],i,j,k,c;
void main()
{
int n,m;
cout <<"enter no of vertices";
cin >> n;
cout <<"enter no od edges";
cin >> m;
cout<<"enter the\nEDGE Cost\n";
for(k=1;k<=m;k++)
{
cin>>i>>j>>c;
a[i][j]=cost[i][j]=c;
}
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
{
if(a[i][j]== 0 && i !=j)
a[i][j]=31999;
}
for(k=1;k<=n;k++)
for(i=1;i<=n;i++)
for(j=1;j<=n;j++)
a[i][j]=min(a[i][j],a[i][k]+a[k][j]);
cout <<"Resultant adj matrix\n";
for(i=1;i<=n;i++)
{
for( j=1;j<=n;j++)
{
if(a[i][j] !=31999)
cout << a[i][j] <<" ";
}
cout <<"\n";
}
89
Advanced Data Structures
getch();
}
int min(int a,int b)
{
if(a<b)
return a;
else
return b;
}
OUTPUT
enter no of vertices3
enter no od edges5
enter the
EDGE Cost
124
216
1 3 11
313
232
Resultant adj matrix
046
502
370
90
Advanced Data Structures
Algorithms for Binary Search Tree
Algorithm Insert(item)
{
If(tree is empty) then root is empty
Otherwise
{
temp=search(item); // temp is the node where search for the
item halts
if( item > temp) then temp-right=item;
otherwise temp-left =item
}
}
Algorithm Search(x, root)
{
if(tree is empty ) then print” tree is empty”
otherwise
If(x grater than root) search(root-right);
Otherwise if(x less than root ) search(root-left)
Otherwise return true
}
}
Algorithm Delete(x)
{
Search for x in the tree
If (not found) print” not found”
Otherwise{
If ( x has no child) delete x;
If(x has left child) move the left child to x position
If(x has right child) move the right child to x position
If(x has both left and right children) replace ‘x’ with
greatest of left subtree of ‘x ‘ or smallest of right
subtree of ‘x’ and delete selected node in the subtree
}
}
91
Advanced Data Structures
Binary Search Tree
#include<iostream.h>
#include<conio.h>
#include<stdlib.h>
class node
{
public:
class node *left;
class node *right;
int data;
};
class tree: public node
{
public:
int stk[50],top;
node *root;
tree()
{
root=NULL;
top=0;
}
void insert(int ch)
{
node *temp,*temp1;
if(root== NULL)
{
root=new node;
root->data=ch;
root->left=NULL;
root->right=NULL;
return;
}
temp1=new node;
temp1->data=ch;
temp1->right=temp1->left=NULL;
temp=search(root,ch);
if(temp->data>ch)
temp->left=temp1;
else
temp->right=temp1;
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Advanced Data Structures
}
node *search(node *temp,int ch)
{
if(root== NULL)
{
cout <<"no node present";
return NULL;
}
if(temp->left==NULL && temp->right== NULL)
return temp;
if(temp->data>ch)
{ if(temp->left==NULL) return temp;
search(temp->left,ch);}
else
{ if(temp->right==NULL) return temp;
search(temp->right,ch);
}
}
void display(node *temp)
{
if(temp==NULL)
return ;
display(temp->left);
cout<<temp->data << " ";
display(temp->right);
}
node * pop(node *p)
{
int ch;
ch=stk[top-1];
if(p->data==ch)
{
top--;
return p;
}
if(p->data>ch)
pop(p->left);
else
pop(p->right);
}
};
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Advanced Data Structures
void main()
{
tree t1;
int ch,n,i;
clrscr();
while(1)
{
cout <<"\n1.INSERT\n2.POP\n3.DISPLAY\n4.EXIT\nEnter your choice:";
cin >> ch;
switch(ch)
{
case 1: cout <<"enter no of elements to insert:";
cout<<"\n enter the elements";
cin >> n;
for(i=1;i<=n;i++)
{ cin >> ch;
t1.insert(ch);
}
break;
case 2: t1.pop(); break;
case 3: t1.display(t1.root);break;
case 4: exit(1);
}
}
}
1.INSERT
2.POP 3.DISPLAY 4.EXIT
Enter your choice:1
enter no of elements to insert:
enter the elements7
5 24 36 11 44 2 21
1.INSERT
2.POP 3.DISPLAY 4.EXIT
Enter your choice:3
2 5 11 21 24 36 44
1.INSERT 2.POP 3.DISPLAY 4.EXIT
Enter your choice2
2 11 21 24 36 44
1.INSERT 2.POP 3.DISPLAY 4.EXIT
4.EXITEnter your choice:4
94
Advanced Data Structures
Optimal Binary Search Tree
#include<iostream.h>
#include<conio.h>
#include<stdio.h>
#define MAX 10
int find(int i,int j);
void print(int,int);
int p[MAX],q[MAX],w[10][10],c[10][10],r[10][10],i,j,k,n,m;
char idnt[7][10];
void main()
{
clrscr();
cout << "enter the no, of identifiers";
cin >>n;
cout <<"enter identifiers";
for(i=1;i<=n;i++)
gets(idnt[i]);
cout <<"enter success propability for identifiers";
for(i=1;i<=n;i++)
cin >>p[i];
cout << "enter failure propability for identifiers";
for(i=0;i<=n;i++)
cin >> q[i];
for(i=0;i<=n;i++)
{
w[i][i]=q[i];
c[i][i]=r[i][i]=0;
w[i][i+1]=q[i]+q[i+1]+p[i+1];
r[i][i+1]=i+1;
c[i][i+1]=q[i]+q[i+1]+p[i+1];
}
w[n][n]=q[n];
r[n][n]=c[n][n]=0;
for(m=2;m<=n;m++)
{
for(i=0;i<=n-m;i++)
{
j=i+m;
w[i][j]=w[i][j-1]+p[j]+q[j];
k=find(i,j);
r[i][j]=k;
95
Advanced Data Structures
c[i][j]=w[i][j]+c[i][k-1]+c[k][j];
}
}
cout <<"\n";
print(0,n);
}
int find(int i,int j)
{
int min=2000,m,l;
for(m=i+1;m<=j;m++)
if(c[i][m-1]+c[m][j]<min)
{
min=c[i][m-1]+c[m][j];
l=m;
}
return l;
}
void print(int i,int j)
{
if(i<j)
puts(idnt[r[i][j]]);
else
return;
print(i,r[i][j]-1);
print(r[i][j],j);
}
OUTPUT
enter the no, of identifiers4
enter identifiersdo
if
int
while
enter success propability for identifiers3 3 1 1
enter failure propability for identifiers2 3 1 1 1
tree in preorder form
if
do
int
while
96
Advanced Data Structures
Viva Voice Questions
1. What is the difference between an ARRAY and a LIST?
2. What is faster : access the element in an ARRAY or in a LIST?
3. Define a constructor - what it is and how it might be called (2 methods).
4. Describe PRIVATE, PROTECTED and PUBLIC - the differences and give examples.
5. What is a COPY CONSTRUCTOR and when is it called (this is a frequent question !)?
6. Explain term POLIMORPHISM and give an example using eg. SHAPE object: If I have
a base class SHAPE, how would I define DRAW methods for two objects CIRCLE and
SQUARE.
7. What is the word you will use when defining a function in base class to allow this
function to be a polimorphic function?
8. You have two pairs: new() and delete() and another pair : alloc() and free(). Explain
differences between eg. new() and malloc()
9. Difference between “C structure” and “C++ structure”.
10. Diffrence between a “assignment operator” and a “copy constructor”
11. What is the difference between “overloading” and “overridding”?
12. Explain the need for “Virtual Destructor”.
13. Can we have “Virtual Constructors”?
14. What are the different types of polymorphism?
15. What are Virtual Functions? How to implement virtual functions in “C”
16. What are the different types of Storage classes?
17. What is Namespace?
97
Advanced Data Structures
18. Difference between “vector” and “array”?
19. How to write a program such that it will delete itself after exectution?
20. Can we generate a C++ source code from the binary file?
21. What are inline functions?
22. What is “strstream” ?
23. Explain “passing by value”, “passing by pointer” and “passing by reference”
24. Have you heard of “mutable” keyword?
25. Is there something that I can do in C and not in C++?
26. What is the difference between “calloc” and “malloc”?
27. What will happen if I allocate memory using “new” and free it using “free” or allocate
sing “calloc” and free it using “delete”?
28. When shall I use Multiple Inheritance?
29. How to write Multithreaded applications using C++?
30. Write any small program that will compile in “C” but not in “C++”
31. What is Memory Alignment?
32. what is the difference between a tree and a graph?
33. How to insert an element in a binary search tree?
34. How to delete an element from a binary search tree?
35. How to search an element in a binary search tree?
36. what is the disadvantage in binary search tree?
37. what is ment by height balanced tree?
38. Give examples for height blanced tree?
39. What is a 2-3 tree?
98
Advanced Data Structures
40. what is a dictonary?
41.What is a binary search tree?
42. what is an AVL tree?
43. how height balancing is performed in AVL tree?
44. what is a Red Black tree?
45. what is difference between linked list and an array?
46. how dynamic memory allocation is performed in c++?
47. what are tree traversing techniques?
48. what are graph traversing techniques?
49. what is the technique in quick sort.?
50 what is the technique in merge sort?
51. what is data structure.
52. how to implement two stacks in an array?
53. what is ment by generic programming?
54. write the syntax for function templet?
55. write the syntax for class templet?
56. what is ment by stream?
57. what is the base class for all the streams?
58. how to create a file in c++?
59. how do you read a file in c++?
60. how do you write a file in c++?
99