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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)

Going to Tell About…….Definition of TreeBasic Terminology of TreeClassification of TreeM-ary TreeFull M-ary TreeBinary TreeStrictly Binary Tree (SBT)Complete Binary Tree (CBT)Almost Binary Tree (ALT)Ordered Rooted Tree

Decision Tree Traversing Binary Tree

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.

Basic Terminology of Tree Node

Edge

Root

Leaf Node

Depth

Height

Parent

Children

Siblings

Ancestors

Descendants

Sub-Tree

Basic Terminology of TreeNode: 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.

Basic Terminology of TreeRoot: 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.

Basic Terminology of TreeDepth: 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).

Basic Terminology of TreeParent: 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

Basic Terminology of Tree

Basic Terminology of Tree

• Sub-Tree: A sub-tree of a given node includes one of its children and all of that child's descendants.

Classification of Tree

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

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.

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.

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.

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.

Traversing Binary Tree

Traversal in Binary Tree

Pre-order Traversal

In-order Traversal

Post-order Traversal