This slide was made for my University presentation .
In this slide is full of the basic of Tree.I hope, you will get most basic information from this slide.
2. Course: CSE131 (Discrete Mathematics)
Course Teacher: Ms. Shadaab Kawnain Bashir (SKB)
Section: P Group: A Depertment: CSE(43 Batch)
Group Members:
01. Md. Ashaf Uddaula (161-15-7473)
02. Alamin Hossain (161-15-7483)
03. Md. Khasrur Rahman (161-15-7214)
04. Ijaz Ahmed Utsa (161-15-7180)
3. Going to Tell About…….
Definition of Tree
Basic Terminology of Tree
Classification of Tree
M-ary Tree
Full M-ary Tree
Binary Tree
Strictly Binary Tree (SBT)
Complete Binary Tree (CBT)
Almost Binary Tree (ALT)
Ordered Rooted Tree
Decision Tree
Traversing Binary Tree
4. What is Tree?
• An undirected graph is a tree if
and only if there is a unique simple
path between any two of its
vertices.
• Every Tree is a Graph ,but every
Graph is not a tree.
5. Basic Terminology of Tree
Node
Edge
Root
Leaf Node
Depth
Height
Parent
Children
Siblings
Ancestors
Descendants
Sub-Tree
6. Basic Terminology of Tree
Node: A node is a fundamental part of a
tree. Each letter represents one node.
Edge: The arrows from one node to
another are called edges.
7. Basic Terminology of Tree
Root: The root of the tree is the
only node in the tree that has no
incoming edges.
Here, a is the root.
Leaf Node: A leaf node is a node
that has no children.
The bottom nodes (with no outgoing
edges) are the leaves .
Here, c , i , j , k , l , m are leaves Node.
8. Basic Terminology of Tree
Depth: Depth tells the number of
steps (nodes) to get from a node back
to the root.
Height: The height of a tree is equal to
the maximum level of any node in the
tree.
This tree has height 5, so the
maximum depth is 4 (height - 1).
9. Basic Terminology of Tree
Parent:
a is the parent of b , c , d
b is the parent of e
d is the parent of f , g , h
e is the parent of i , j
f is the parent of k
h is the parent of l , m
Siblings:
b , c , d are siblings of each other
f , g , h are siblings of each other
i , j are siblings of each other
l , m are siblings of each other
Children:
b , c , d are children of a
f , g , h are children of d
e is the children of b
i , j are the children of e
k is the children of f
l , m are the children of h
13. m-ary tree : A rooted tree is
called an m-ary tree if every
internal vertex has no more than
m children.
full m-ary tree :A tree is called a
full m-ary tree if every internal
vertex has exactly m children.
binary tree :An m-ary tree with
m 2 is called a binary tree
14. Strictly Binary Tree (SBT)
• The tree is said to be strictly binary tree , if every non-leaf node made
in a binary tree has non empty left & right sub-tree.
• A strictly binary tree with n leaves node always contains 2n-1 nodes.
15. Complete Binary Tree (CBT)
• . A complete binary tree is a binary tree in which every level,
except possibly the last, is completely filled, and all nodes are as
far left as possible.
16. Almost Binary Tree (ALT)
• An almost complete binary tree is a tree where for a right child,
there is always a left child, but for a left child there may not be a
right child.
17. Decision Tree
• A decision tree is a decision support tool that uses atree-like graph
or model of decisions and their possible consequences, including
chance event outcomes, resource costs, and utility. It is one way to
display an algorithm.