The document discusses trees and binary trees as data structures. It defines what a tree is, including parts like the root, parent, child, leaf nodes. It then defines binary trees as trees where each node has no more than two children. Binary search trees are introduced as binary trees where all left descendants of a node are less than or equal to the node and all right descendants are greater. The document concludes by discussing how to build a binary search tree class with Node objects.

1. DATA STRUCTURE
Chapter 8: Tree & binary tree
Prepared & Presented by
Mr. Mahmoud R. Alfarra
2011-2012
College of Science & Technology
Dep. Of Computer Science & IT
BCs of Information Technology
http://mfarra.cst.ps

2. Out Line
 What we mean by a tree?
 Parts of tree
 Binary tree
 Binary search tree
 Building a Binary Search Tree
2

3. What we mean by a tree?
3
 Trees are a very common data structure in
computer science.
 A tree is a nonlinear data structure that is used
to store data in a hierarchical manner.

4. What we mean by a tree?
4
 A tree is a set of nodes connected by edges.
 Each box is a node and the lines connecting
the boxes are the edges.
 The nodes, obviously,
represent the entities
(people) that make up an
organization.
 The edges represent the
relationship between the
entities.

5. Parts of tree
5

6. Parts of tree
6
 The top node of a tree is called the root node.
 If a node is connected to other nodes below it,
the top node is called the parent, and the
nodes below it are called the parent’s
children.
 A node without any child node is called a leaf.
 The series of edges you follow to get from one
node to another is called a path.
 Visiting all the nodes in a tree in some
particular order is known as a tree
transversal.

7. Parts of tree
7
 A tree can be broken down into levels.
 A node at any level is considered the root of a
subtree, which consists of that root node’s
children, its children’s children, and so on.
 We can define the depth of a tree as the
number of layers in the tree.
 Finally, each node in a tree has a value. This
value is sometimes referred to as the key
value.

8. Binary tree
8
 A binary tree is defined as a tree where each
node can have no more than two children.
 By limiting the number of children to 2, we can
write efficient programs for inserting data,
deleting data, and searching for data in a
binary tree.
 The child nodes of a parent node are referred
to as the left node and the right node.
5
10
45
2 25 30

9. Binary search tree
9
 The binary search tree is a binary tree where
data with lesser values are stored in left
nodes and values with greater values are
stored in right nodes.
 This property provides for very efficient
searches.

10. Binary search tree
10
Binary
search trees
Not a binary
search tree
5
10
30
2 25 45
5
10
45
2 25 30
5
10
30
2
25
45

11. Building a Binary Search Tree
11
 A binary search tree is made up of nodes, so
we need a Node class that is similar to the
Node class we used in the linked list
implementation.

12. Building a Binary Search Tree
12
 Next we’re ready to build a BinarySearchTree
(BST) class.
 The class consists of just one data member- a
Node object that represents the root node of
the BST.

13. Building a Binary
Search Tree

14. Thank You …
14
Remember that: question is the key of knowledge

15. Ahl Eljanna 

‫ف‬ِ ‫نا‬‫ن‬‫ن‬‫ن‬َ‫ن‬ َ ‫ف‬ِ‫ن‬‫ن‬‫ن‬‫ن‬‫ن‬ََِ
َّ‫ف‬َ
َ‫نا‬‫ن‬‫ن‬‫ن‬َ
‫ب‬َ
‫فر‬َ
‫نام‬‫ن‬‫ن‬‫ن‬َ
َ‫ف‬‫ا‬
َ‫ن‬‫ن‬‫ن‬‫ن‬َ
‫م‬ِ‫ل‬َ
‫و‬
)::(
‫ف‬
‫ن‬ََِ
َّ‫ف‬ِ
َ َِ‫ف‬‫ن‬ِ
‫َآ‬ِّ‫ن‬‫ن‬‫ن‬‫ن‬ِ‫ب‬َ‫ف‬
‫ناف‬‫ن‬‫ن‬‫ن‬َ
‫م‬ُ
‫ك‬
‫ف‬ِ
َ
‫َب‬‫ن‬
ِ
‫ذ‬َ
‫ك‬ُ‫ت‬
)::(
‫ف‬ ‫نا‬َ‫ا‬
‫ن‬‫ف‬َ‫أ‬‫ىف‬َ‫ت‬‫ا‬َ
‫و‬َ‫ذ‬
)::(
‫ف‬
َ‫ف‬
‫ف‬ُ
‫ك‬‫ن‬ََِ
َّ‫ف‬ِ
َ َِ‫ف‬‫ن‬ِ
‫َآ‬ِّ‫ن‬ِ‫ب‬
‫ف‬ِ
َ
‫َب‬‫ن‬
ِ
‫نذ‬َ
‫ك‬ُ‫ت‬‫ناف‬َ
‫م‬
)::(
‫ف‬ِ
َِ‫ن‬‫ن‬‫ا‬َ
ِ‫ف‬ِ ‫نا‬‫ن‬َ‫ا‬
‫ن‬‫ي‬َ
‫نافي‬‫ن‬َ
‫م‬ِ
‫ه‬‫ي‬ِ‫ف‬
)::(
‫ف‬
َ‫ف‬
‫ن‬‫ن‬َ
‫م‬ُ
‫ك‬‫ن‬ََِ
َّ‫ف‬ِ
َ َِ‫ف‬‫ن‬ِ
‫َآ‬ِّ‫ن‬‫ن‬ِ‫ب‬
‫ف‬ِ
َ
‫َب‬‫ن‬
ِ
‫نذ‬‫ن‬َ
‫ك‬ُ‫ت‬‫اف‬
)::(
‫ن‬‫ن‬َ ‫ا‬
‫و‬َ‫ف‬ ‫ن‬‫ن‬َ
‫ه‬ِِّ‫ا‬َ‫ف‬‫ف‬‫ن‬ِ
‫نا‬‫ن‬ُ
ِّ‫ف‬‫ا‬
َ‫ن‬‫ن‬ِ
‫نافر‬‫ن‬َ
‫م‬ِ
‫ه‬‫ي‬ِ‫ف‬
‫ف‬ِ ‫ا‬
)::(
‫ف‬
‫ن‬ََِ
َّ‫ف‬ِ
َ َِ‫ف‬‫ن‬ِ
‫َآ‬ِّ‫ن‬‫ن‬ِ‫ب‬َ‫ف‬
‫ناف‬‫ن‬َ
‫م‬ُ
‫ك‬
‫ف‬ِ
َ
‫َب‬‫ن‬
ِ
‫نذ‬‫ن‬‫ن‬َ
‫ك‬ُ‫ت‬
)::(
‫ن‬‫ن‬‫ن‬ُ
‫ن‬‫ف‬‫نىف‬‫ن‬‫ن‬ََ
‫في‬َ
‫نع‬‫ن‬‫ن‬ِ‫ئ‬ِ
‫ك‬ ُ
‫ر‬
‫ن‬‫ن‬‫ن‬‫ا‬ ِ‫ف‬‫ا‬
َ‫ن‬‫ن‬‫ن‬ِ
‫نافر‬‫ن‬‫ن‬َ
‫ه‬ُ
‫ن‬ ِ‫ائ‬َ‫ط‬ََ‫ف‬‫ش‬ُ
‫ف‬‫ق‬َ‫ا‬
‫ن‬‫ب‬َ
‫ن‬
‫ف‬ ‫ا‬َ
‫فد‬ِ‫ا‬
‫ع‬َ
‫ن‬ ‫ن‬َ‫ا‬
‫ْل‬‫فا‬ َ
‫َن‬َ َ
‫و‬
)::(
15