Unit 2_2 Binary Tree as ADT_General Tree.pdf

Data Structures
Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423603
(An Autonomous Institute Affiliated to Savitribai Phule Pune University, Pune)
NAAC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Information Technology
(NBAAccredited)
Ms. K. D. Patil
Assistant Professor

Tree
• General Trees, Tree Terminology, Binary Trees, Use binary trees,
Conversion of general tree to binary tree, Array Based
representation of Binary Tree, Binary tree as an ADT, Binary tree
traversals - recursive and non-recursive algorithms, Construction
of tree from its traversals, Huffman coding algorithm
Data Structures Mrs. Kanchan Patil Department of Information Technology

Array Based Representation of Binary Tree
• Let’s consider a Binary tree of 7 nodes

• For the array representation of binary tree, we have to give numbering
to the corresponding nodes.
• Start from the root node and move from left to right at every level.

• we have numbered from zero you can simply place the corresponding
number in the matching index of an array.

• Now Let’s consider a Binary tree

• Make the child node of the leaf nodes as NULL

• Now number the nodes as done above for the array representation of
binary tree.

Linked List Representation of Binary Tree
• We use a double linked list to represent a binary tree. In a double linked
list, every node consists of three fields.
• First field for storing left child address, second for storing actual data and
third for storing right child address.

Linked List Representation of Binary Tree

Binary Tree as an ADT
• Binary Tree have a maximum of two children
• we can assign direct pointers to them
• The declaration of tree nodes is same as in structure to that for doubly linked lists,
in that a node is a structure including the key information plus two pointers (left and
right) to other nodes
• Binary Tree node declaration
class Node {
int value;
Node left;
Node right;
Node(int value) {
this.value = value;
right = null;
left = null;
}
}

Binary Tree as an ADT
• Binary Tree class declaration
class binary_tree
{ node left, right;
public:
btree()
{
root=NULL;
}
Isempty();
void create();
void display();
void insert(node,node);
void inorder(node);
void longestPath();
int depth(node);
void display_leaves(node temp);
node copy(node first);
void copytree();
};

General Tree
• A General Tree is a tree in which each node can have an unlimited out-degree
• Each node may have as many children as is necessary to satisfy its requirements
• It is also referred as N-array tree
• Examples:

Changing General Tree to Binary Tree
• A General Tree we can use following two relations
• Parent to Child
• Sibling to Sibling
• Rules are as follows:
• The root of the Binary Tree is the Root of the Generic Tree
• The left child of a node in the Generic Tree is the Left child of that node in the
Binary Tree
• The right sibling of any node in the Generic Tree is the Right child of that node in
the Binary Tree

Changing General Tree to Binary Tree
• Steps to Convert General Tree to Binary Tree
• Step I:
• Identify the branch from parent to its first and leftmost child
• Step II:
• Connect siblings starting with leftmost child using a branch for each siblings to
its right siblings.
• Step III:
• Remove all unneeded branches from the parent to its children. You will get the
final binary tree

Example
• Step I:
• Identify the branch from parent to its first and
leftmost child
• Step II:
• Connect siblings starting with leftmost child using
a branch for each siblings to its right siblings.
• Step III:
• Remove all unneeded branches from the parent
to its children. You will get the final binary tree

Example
• Final Binary Tree:

Quiz..

Inserting into General Trees
• To insert a node into a general tree, the user must supply the parent of the
node.
• The new node can be inserted using 3 different ways:
• FIFO insertion
• LIFO insertion
• Key sequenced insertion

• FIFO insertion:
• Insert a node at the end of the sibling list as we insert a node at the rear of
a queue

• LIFO insertion:
• Insert a node at the beginning of the sibling list

• Key sequenced insertion:
• Places the new node in key sequence among the sibling nodes
• It is most common insertion rule in general trees
• It is similar to the insertion rule in a general ordered linked list

References
• R. Lafore, “Data structures and Algorithms in Java”, Pearson education, ISBN: 9788
131718124.
• Michael Goodrich, Roberto Tamassia, Michael H. Goldwasser, “Data Structures and
Algorithms in Java”, 6th edition, wiley publication, ISBN: 978-1-118-77133-4
• R. Gilberg, B. Forouzan, “Data Structure: A Pseudo code approach with C++”, Cengage
Learning.
• Sartaj Sahni, “Data Structures, Algorithms and Applications in C++”, 2 nd Edition,
Universities Press.
• E. Horowitz, S. Sahni, S. Anderson-freed, “Fundamentals of Data Structures in C”, 2 nd
Edition, University Press, ISBN 978-81-7371-605-8.

Thank You!!!
Happy Learning!!!

Unit 2_2 Binary Tree as ADT_General Tree.pdf

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Unit 2_2 Binary Tree as ADT_General Tree.pdf