data structure module fourth module linked list

Module 4
Presented by
Bhavana G
Assistant Professor
Dept. of Computer Science(MCA)
Center for post Graduate studies, VTU
Muddenahalli.
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Bhavana G, Assistant Professor, Dept. of CS(MCA), CPGSB,VTU, Muddenahalli

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Introduction of Trees in Data
Structure
Course Code: OBCA201

Course outcomes
• CO 1 : Identify different types of data structures, operations and algorithms.
• CO2: Illustrate searching and sorting operations on files.
• CO3:Demonstrate the working of stack, Queue, Lists, Trees and Graphs in
problem solving & implement all data structures in a high-level language for
problem solving.
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Textbooks & Reference Books
1. Adam Drozdek, “Data Structures and Algorithms in C++”, 2013, Fourth Edition,
Cengage Learning .
2. Bhushan Trivedi, “Programming with ANSI C++”, Oxford Press, Second Edition, 2012.
3. Balagurusamy E, Object Oriented Programming with C++, Tata McGraw Hill
Education Pvt.Ltd, Fourth Edition 2010.
4. R.S. Salaria, “ Data Structures & Algorithms” , Khanna Book Publishing Co.
(P)Ltd..,2002
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AGENDA:
• What is Tree Data Structure?
• Why Tree Data Structure?
• Tree Terminologies.
• Tree Node.
• Types of Trees.
• Tree Traversal
• Application of Trees(BST)
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WHAT IS TREE DATA STRUCTURE?
• A Tree is a Non-Linear data Structure that consists of
nodes and is connected by edges.
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WHY TREE DATA STRUCTURE?
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• A linear Data structure that stores data elements in sequential form.
• In operation performed in linear data structure, the time complexity
increases with increased data size.
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10 20 30 40 50 60 70

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10
20 30
40 50 60 70
The Tree Data structure is non-linear and allows easier and
quicker access to the data elements.

The Tree data structure can be useful in many
cases:
• Hierarchical Data: File systems, organizational models, etc.
• Databases: Used for quick data retrieval.
• Routing Tables: Used for routing data in network algorithms.
• Sorting/Searching: Used for sorting data and searching for data.
• Priority Queues: Priority queue data structures are commonly implemented using
trees, such as binary heaps.
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Tree Terminologies
• Tree Node :A node is a structure or an entity that contains a key or
value and pointers to its child node.
•
•
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Tree Terminologies
• Root: In a tree data structure, the root is the first node of
the tree. The root node is the initial node of the tree in data
structures.
• In the tree data structure, there must be only one root node.
•
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• Edge :In a tree in data structures, the connecting link of any
two nodes is called the edge of the tree data structure.
• In the tree data structure, N number of nodes connecting
with N -1 number of edges.
Tree Terminologies

• Parent :In the tree in data structures, the node that is the
predecessor of any node is known as a parent node, or a node
with a branch from itself to any other successive node is called
the parent node.
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Tree Terminologies

Tree Terminologies
Child:
• The node, a descendant of any node, is
known as child nodes in data structures.
• In a tree, any number of parent nodes can
have any number of child nodes.
• In a tree, every node except the root node
is a child node.
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Tree Terminologies
Siblings:
• In trees in the data structure, nodes
that belong to the same parent are
called siblings.
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Tree Terminologies
Leaf :
• Trees in the data structure, the
node with no child, is known as a
leaf node.
• In trees, leaf nodes are also called
external nodes or terminal nodes.
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Tree Terminologies
Internal nodes
• Trees in the data structure have at least one child
node known as internal nodes.
• In trees, nodes other than leaf nodes are internal
nodes.
• Sometimes root nodes are also called internal nodes
if the tree has more than one node.
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Tree Terminologies
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Degree:
• In the tree data structure, the total number of
children of a node is called the degree of the
node.
•The highest degree of the node among all the
nodes in a tree is called the Degree of Tree.

Tree Terminologies
Level:
• In tree data structures, the root node
is said to be at level 0, and the root
node's children are at level 1, and the
children of that node at level 1 will be
level 2, and so on.
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Tree Terminologies
• Height:
• In a tree data structure, the number of
edges from the leaf node to the particular
node in the longest path is known as the
height of that node.
• In the tree, the height of the root node is
called "Height of Tree".
• The tree height of all leaf nodes is 0.
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Depth:
• In a tree, many edges from the root
node to the particular node are called
the depth of the tree.
• In the tree, the total number of edges
from the root node to the leaf node in
the longest path is known as "Depth of
Tree".
• In the tree data structures, the depth of
the root node is 0.
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Tree Terminologies

Path:
• In the tree in data structures, the
sequence of nodes and edges from one
node to another node is called the path
between those two nodes.
• The length of a path is the total number
of nodes in a path.zx
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Tree Terminologies

Subtree
• In the tree in data structures, each
child from a node shapes a sub-tree
recursively and every child in the tree
will form a sub-tree on its parent
node.
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Tree Terminologies

Here are the different kinds of tree in data structures:
General Tree:
• The general tree is the type of tree where there are no
constraints on the hierarchical structure.
Properties
• The general tree follows all properties of the tree data
structure.
• A node can have any number of nodes.
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Types of Tree in Data Structures

Types of Tree in Data Structures
Binary Tree
• A binary tree has the following properties:
Properties
• Follows all properties of the tree data structure.
• Binary trees can have at most two child nodes.
• These two children are called the left child and the
right child.
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Binary Search Tree
• A binary search tree is a type of tree that is a
more constricted extension of a binary tree data
structure.
Properties
• The binary search tree has a unique property
known as the binary search property. This states
that the value of a left child node of the tree
should be less than or equal to the parent node
value of the tree. And the value of the right child
node should be greater than or equal to the
parent value.
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AVL Tree
• An AVL tree is a type of tree that is a self-balancing
binary search tree.
Properties
• Self-balancing.
• Each node stores a value called a balanced factor, which
is the difference in the height of the left sub-tree and
right sub-tree.
• All the nodes in the AVL tree must have a balance factor
of -1, 0, and 1.
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Tree Traversal
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Traversal of the tree in data structures is a process of visiting
each node and prints their value. There are three ways to
traverse tree data structure.
Pre-order Traversal
In-Order Traversal
Post-order Traversal

In the in-order traversal, the left subtree is visited first, then
the root, and later the right subtree.
Algorithm:
Inorder(tree)
• Traverse the left subtree, i.e., call Inorder(left->subtree)
• Visit the root.
• Traverse the right subtree, i.e., call Inorder(right-
>subtree)
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In-Order Traversal

In pre-order traversal, it visits the root node
first, then the left subtree, and lastly right
subtree.
Algorithm:
Preorder(tree)
• Visit the root.
• Traverse the left subtree, i.e., call Preorder(left->subtree)
• Traverse the right subtree, i.e., call Preorder(right-
>subtree)
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Pre-Order Traversal

Post-Order Traversal
It visits the left subtree first in post-order traversal, then the
right subtree, and finally the root node.
Algorithm:
Postorder(tree)
• Traverse the left subtree, i.e., call Postorder(left->subtree)
• Traverse the right subtree, i.e., call Postorder(right->subtree)
• Visit the root.
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• Binary Search Tree (BST) is used to check whether elements
present or not.
• Heap is a type of tree that is used to heap sort.
• Tries are the modified version of the tree used in modem routing to
information of the router.
• The widespread database uses B-tree.
• Compilers use syntax trees to check every syntax of a program.
• With this, you’ve come to the end of this tutorial about the tree in
data structures.
Application of Tree in Data Structures

Latharani T R, Assistant Professor, Dept. of CS&E, JIT, Davangere 34

data structure module fourth module linked list

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