The document discusses implementing binary tree data structures. It defines what a binary tree is - a hierarchical data structure where each node has at most two child nodes. It describes how to implement common binary tree operations like inserting and deleting nodes, searching the tree, and traversing the tree. The key concepts covered are binary tree representation using nodes and pointers, binary search trees, and the different cases to handle when deleting nodes from a binary tree.

1. Implementing Binary Tree
Objectives
In this lesson, you will learn to:
Define binary tree structure
Identify applications of binary tree
Implement the following operations on binary trees
Inserting nodes in a binary tree
Searching in a binary tree
Traversing a binary tree
Deleting nodes from a binary tree
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2. Implementing Binary Tree
Introducing Binary Tree
A tree is a data structure used to represent data
containing an hierarchical relation between its
elements.
The sample tree is as follows:
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3. Implementing Binary Tree
Binary Tree (Contd..)
Each item is called a node or leaf.
The first node in the tree is called the root.
Each piece under a node is called a subtree.
A node under which there is a subtree is called the
parent node.
A node that has no subtrees is called a terminal node.
The height of the tree is the number of layers in the
tree.
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4. Implementing Binary Tree
Application of Trees
Trees are used in applications in which the relation
between data elements has to be represented as a
hierarchy.
A tree represent a non-linear data structure.
Trees are used to represent the records in a file in
which elementary items are stored under group items.
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5. Implementing Binary Tree
Just a Minute:
2. Can a linked list be used to represent the UNIX file
system?
3. Refer the following figure to answer the following:
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6. Implementing Binary Tree
Just a Minute(Contd..):
a. The number of nodes in the tree is
_______________.
b. The root contains the INFO _____________.
c. The number of subtrees which the root has is
_______.
d. The number of terminal nodes is
________________.
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7. Implementing Binary Tree
Just a Minute (Contd..):
a. The height of the tree is _________________.
b. A terminal node is the ___________ node in the
tree.
c. The address part of the terminal node stores the
value __________ , just like the last node in a
linked list.
d. The number of subtrees which the node with
INFO c has is
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8. Implementing Binary Tree
Categories of Binary Tree
There are various types of binary tree,out of which two
are as follows:
Balanced binary tree: It is a binary tree in which
the heights of the two subtrees of every node
never differ by more than one. The figure of
balanced binary tree is as follows:
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9. Implementing Binary Tree
Categories of Binary Tree (Contd..)
Unbalanced binary tree: In an unbalanced binary
tree, each node can have a maximum of two
subtrees (the left subtree and the right subtree). It
may also have zero nodes (unlike a tree). The
figure of unbalanced binary tree is as follows:
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10. Implementing Binary Tree
Categories of Binary Tree (Contd..)
Binary sorted tree
It is the most common form of binary tree.
It has the data in organized manner.
Through this, the data can be searched, inserted,
or deleted much faster.
The structure of sorted binary tree is as follows:
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11. Implementing Binary Tree
Representing Binary Trees
The representation of a binary tree is similar to a
linked list.
Through this, more efficient searches, insertions and
deletions in a binary tree can be performed as
compared to other data structures like linked lists and
arrays.
The figure for sample sorted binary tree is as follows:
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12. Implementing Binary Tree
Just a Minute:
7. The tree represented in above figure, the left pointer
of the node whose INFO is e points to the node
whose INFO is __________ while the right pointer
points to the node whose INFO is_____________.
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13. Implementing Binary Tree
Just a Minute (Contd..):
2. In above figure, which of the pointers have NULL value?
The left and right pointers of the node with INFO A.
The left and right pointers of the node with INFO D.
The left and right pointers of the node with INFO K.
(a), (b) and (c).
3. Using the example of the linked list containing only item
numbers, give a declaration for a binary tree which can
store these item numbers. Also give the declaration for a
pointer to the root node of this tree. Item numbers are 4
characters long.
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14. Implementing Binary Tree
Manipulating Tree Structures
Insertion in a Binary Tree- It involve the following
processes:
Allocation of memory for the new node.
The left and right pointers of the new node are also
initialized to NULL.
The comparison of the new INFO with the existing
INFO.
Change the left or right pointer of the node under
which the new node has been inserted.
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15. Implementing Binary Tree
Manipulating Tree Structures (Contd..)
The graphical representation of an insertion is as
follows:
Before Insertion
After Insertion
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16. Implementing Binary Tree
Searching in a Binary Tree
Since the binary tree contains the stored data, the
search will be made along one subtree only until a
specific INFO is located.
The logic for searching is as foliows (assume that
SEARCH _INFO is the data to be located, ROOT has
the address of the root node and PTR is a pointer of
type tree_tag):
Set PTR to ROOT.
Ask for SEARCH INFO.
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17. Implementing Binary Tree
Searching in a Binary Tree (Contd..)
While PTR != NULL do step 4.
Compare SEARCH_INFO with INFO of the node to
which PTR is pointing.
If SEARCH_INFO = INFO of node, exit from loop
and do step 5.
If SEARCH-INFO INFO of node, set PTR to the
right pointer of the node.
If SEARCH_INFO INFO of node, set PTR to the
left pointer of the node.
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18. Implementing Binary Tree
Searching in a Binary Tree(Contd..)
Report that the SEARCH_WFO exists in case PTR
!=NULL (in which case the loop was exited
because the SEARCH _INFO was located) or that
the SEARCH_INFO does not exist in case PTR =
NULL.
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19. Implementing Binary Tree
Traversing a Binary Tree
Inorder method can be used to traverse the
binary tree. The procedure to traverse is as
follows:
Traverse the left subtree of ROOT in inorder
until a NULL pointer is encountered.
Display the contents
Traverse the right subtree of ROOT in
inorder until a NULL pointer is encountered.
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20. Implementing Binary Tree
Deletion of a Node from a Binary Tree
It involve changing of pointers.
When a node is to be deleted, its left and /or right
subtrees have to be linked to the rest of the tree
otherwise all this data will be lost.
The situations that may arise during deletion are as
follows:
The node to be deleted has no subtrees.
The node to be deleted has only one subtree.
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21. Implementing Binary Tree
Deletion of a Node from a Binary
Tree(Contd..)
The node to be deleted has both subtrees.
The root node is being deleted
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22. Implementing Binary Tree
Problem Statement 5.D.1
Create an invoice data entry program, which performs
following operations:
Accept Data and store it in a binary tree
Display Information from a tree
Modify Rate and Qty for a specific item
Delete information from the tree
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23. Implementing Binary Tree
Summary
In this lesson, you learned that:
A tree is a data structure used to represent data
containing a hierarchical relation between its
elements. For example, the UNIX file system, which
has a hierarchical structure, can be represented using
a tree
Data in a tree is stored in nodes. Each node contains
INFO (data) and addresses of the nodes to which it
points
A tree begin from a root node
The height of a tree is the number of layers in the tree
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24. Implementing Binary Tree
Summary (Contd..)
A node with subtrees is referred to as a parent node.
A node with no subtrees is referred to as a terminal
node
Trees are defined using structures
A binary tree is a type of a tree in which each node
may have a maximum of two nodes under it, which
are referred to as subtrees. Thus a node may have a
left subtree and/or a right subtree.
Binary sorted trees store the data in a manner such
that all right subtrees (i.e. subtrees to the right of a
parent node) have INFO larger in value than their
parent nodes and the left subtrees have INFO smaller
than their parent nodes
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25. Implementing Binary Tree
Summary (Contd..)
Insertion in a binary sorted tree involves comparing
the new INFO with the existing INFO in the tree, in
order to insert the new data in the appropriate place.
Searching in a binary sorted tree involves comparing
the search INFO with the INFO in the node pointed
at by a pointer PTR, which is initially made to point to
the root node.
Traversal in a binary sorted tree is done recursively
using the inorder method.
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26. Implementing Binary Tree
Summary (Contd..)
There are four cases to be considered while deleting
a node from a binary tree:
The node has no subtrees
The node has a subtree to its left only
The node has a subtree to its right only
The node has two subtrees
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