1. Lecture 1 (UNIT -4) TREE
SUNIL KUMAR
CIT-UPES

2. 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

3. 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.

4. REVIEW

5. 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
It is a logical & mathematical representation of data.
The organization of data element and the interrelationships among them.
A data structure is a way to store and organize data in order to facilitate access and modifications

6. 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.

8. Non-Linear Data Structure
Type of Data Structure
Data Structure
Linear Data Structure
Array
Linked List
Stack
Queue
Non-Linear Data Structure
Tree
Graph
Stack & Queue can be implemented with the help of Array and linked List

9. Nature View of Tree
leaves
branches
root

10. Computer Vision
root
branches
leaves

11. 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.
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.

12. 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

13. 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 non-empty (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

14. 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 E C F G
D E B F G C A A B C D E F G
D B E A F C G A B C D E F G A B C D E F G
Source: David Matuszek