Lecture 1 (UNIT -4)
TREE
SUNIL KUMAR
CIT-UPES
| Jan 2016|
© 2012 UPES
Objectives of Unit -2
After completion of this unit, You will be able to: Understand the fundamentals of Tree Data Structure.
 Understand concepts of Binary tree and its operations
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Objectives of Today’s Lecture
After completion of today’s Lecture, You will be able to : Understand the basic terminologies of tree data structure
 Understand the fundamentals of binary tree.
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© 2012 UPES
REVIEW
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Data Structure
 What is Data Structure ?
 Data Structure = Data + Structure
 Data – Atomic (single and non decomposable entity)
– or Composite (broken into subfields that have meaning)
 Structure –A set of rules that holds the data together
1. It is a logical & mathematical representation of data.
2. The organization of data element and the interrelationships among
them.
3. A data structure is a way to store and organize data in order to
facilitate access and modifications
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Data Structure
 Data Structure also describe that
► How efficiently data store, access, manage.
►
Data structures effect algorithm’s performance
 No single data structure works well for all purposes, and so it is
important to know the strengths and limitations of several of them.
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Type of Data Structure
Data
Structure
Linear Data
Structure
Array
Linked
List
Non-Linear Data
Structure
Stack
Queue
Tree
Graph
Stack & Queue can be implemented with the help of Array and
linked List
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Nature View of Tree
leaves
branches
root
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Computer Vision
root
branches
leaves
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Tree Terminologies
Root: node without parent (A)
Siblings: nodes share the same parent
Internal node: node with at least one
child (A, B, C, F)
External node (leaf ): node without
children (E, I, J, K, G, H, D)
Ancestors of a node: parent,
grandparent, grand-grandparent, etc.
Descendant of a node: child,
grandchild, grand-grandchild, etc.
Depth of a node: number of ancestors
Height of a tree: maximum depth of
any node (3)
Degree of a node: the number of its
children
Degree of a tree: the maximum
number of its node.
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Subtree: tree consisting of a
node and its descendants
A path from node n1 to nk is
defined as a sequence of nodes
n1, n2, …, nk such that ni is the
parent of ni+1 for 1<= i <= k.
© 2012 UPES
Tree Properties
Property
Value
Number of nodes
Height
Root Node
Leaves
Interior nodes
Ancestors of H
Descendants of B
Siblings of E
Right subtree of A
Degree of this tree
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Tree and its properties
 A tree nonlinear data structure with finite nonempty set of elements.
 It is an abstract model of a hierarchical structure consists of nodes with a
parent-child relation.
 Tree defined recursively
 A tree is a collection of nodes. The collection can be empty; otherwise, a tree
consists of a distinguished node r, called the root, and zero or more nonempty (sub) trees T1, T2, …, Tk each of whose roots are connected by a
directed edge from r.
 A tree is a collection of N nodes, one of which is the root and N-1 edges.
 Applications:
► Organization charts
► File systems
► Programming environments
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Tree traversals using “flags”
• The order in which the nodes are visited during a tree
traversal can be easily determined by imagining there
is a “flag” attached to each node, as follows:
preorder
inorder
postorder
• To traverse the tree, collect the flags:
A
B
D
C
E
F
ABDECFG
Source: David Matuszek
A
A
B
G
D
B
C
E
F
DBEAFCG
G
D
C
E
F
DEBFGCA
G