This Presentation will Clear the idea of non linear Data Structure and implementation of Tree by using array and pointer and also Explain the concept of Binary Search Tree (BST) with example
This Presentation will Clear the idea of non linear Data Structure and implementation of Tree by using array and pointer and also Explain the concept of Binary Search Tree (BST) with example
In computer science, tree traversal (also known as tree search) is a form of graph traversal and refers to the process of visiting (checking and/or updating) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well.
Class lecture of Data Structure and Algorithms and Python.
Stack, Queue, Tree, Python, Python Code, Computer Science, Data, Data Analysis, Machine Learning, Artificial Intellegence, Deep Learning, Programming, Information Technology, Psuedocide, Tree, pseudocode, Binary Tree, Binary Search Tree, implementation, Binary search, linear search, Binary search operation, real-life example of binary search, linear search operation, real-life example of linear search, example bubble sort, sorting, insertion sort example, stack implementation, queue implementation, binary tree implementation, priority queue, binary heap, binary heap implementation
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
In computer science, tree traversal (also known as tree search) is a form of graph traversal and refers to the process of visiting (checking and/or updating) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well.
Class lecture of Data Structure and Algorithms and Python.
Stack, Queue, Tree, Python, Python Code, Computer Science, Data, Data Analysis, Machine Learning, Artificial Intellegence, Deep Learning, Programming, Information Technology, Psuedocide, Tree, pseudocode, Binary Tree, Binary Search Tree, implementation, Binary search, linear search, Binary search operation, real-life example of binary search, linear search operation, real-life example of linear search, example bubble sort, sorting, insertion sort example, stack implementation, queue implementation, binary tree implementation, priority queue, binary heap, binary heap implementation
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
CW RADAR, FMCW RADAR, FMCW ALTIMETER, AND THEIR PARAMETERSveerababupersonal22
It consists of cw radar and fmcw radar ,range measurement,if amplifier and fmcw altimeterThe CW radar operates using continuous wave transmission, while the FMCW radar employs frequency-modulated continuous wave technology. Range measurement is a crucial aspect of radar systems, providing information about the distance to a target. The IF amplifier plays a key role in signal processing, amplifying intermediate frequency signals for further analysis. The FMCW altimeter utilizes frequency-modulated continuous wave technology to accurately measure altitude above a reference point.
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
Basics of Binary Tree and Binary Search Tree.pptx
1. Sanjivani Rural Education Society’s
Sanjivani College of Engineering, Kopargaon-423 603
(An Autonomous Institute, Affiliated to Savitribai Phule Pune University, Pune)
NACC ‘A’ Grade Accredited, ISO 9001:2015 Certified
Department of Computer Engineering
(NBA Accredited)
Prof.B.B.Kotame
Subject- Data Structures-II(CO214)
Unit-I Tree
2. Binary Tree
• In binary tree, every node can have at
most two branches i.e. there is no
node with degree greater than two.
• Definition:
- A binary tree is a finite set of nodes,
which is either empty or consist of a
T and two disjoint binary tree called
as left sub tree and the right sub tree.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 2
A
B C
D F
E G
3. - Difference between tree and binary tree
1. For every node may have left sub tree and right sub tree whereas in tree
sub tree doesn’t matter.
2. Binary tree can have zero nodes i.e. binary tree can be empty, which is
not in case of tree
3.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 3
A
B
A
B
In this example 1st binary tree has empty right sub tree
while second binary tree has empty left tree. if we consider
as tree then both are same only representation is different.
4. DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 4
1. Minimum number of nodes in a binary tree of height H = H + 1
Example-
To construct a binary tree of height = 4, we need at least 4 + 1 = 5 nodes.
2. Maximum number of nodes in a binary tree of height H= 2H+1 – 1
Example-
Maximum number of nodes in a binary tree of height 3
= 23+1 – 1
= 16 – 1
= 15 nodes
Properties of Binary Tree
5. 3. Total Number of leaf nodes in a Binary Tree
= Total Number of nodes with 2 children + 1
Here, Number of leaf nodes = 3, Number of nodes with 2 children = 2
• Clearly, number of leaf nodes is one greater than number of nodes with
2 children.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 5
4. Maximum number of nodes at any level ‘L’ in a binary tree= 2L
Example-
Maximum number of nodes at level-2 in a binary tree
= 22
= 4
Thus, in a binary tree, maximum number of nodes that can be present
at level-2 = 4.
6. 1. The height of a binary tree that contains n, n>=0 element is atmost n and atleast [log2(n+1)]
example: log2(n+1) if n=15
= log2 (15+1)=log(16)/log(2)
= 4 (n<= 2h-1)
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 6
7. Exercise
1. A binary tree T has n leaf nodes. The number of nodes of degree-2 in T is ______?
1.Log2n 2.n-1 3.n 4. 2n
2. In a binary tree, the number of internal nodes of degree-1 is 5 and the number of internal nodes of degree-2
is 10. The number of leaf nodes in the binary tree is ______?
1. 10 2.11 3.12 4.15
3. A binary tree T has 20 leaves. The number of nodes in T having 2 children is ______?
1. 20 2.10 3.19 4.15
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 7
8. Type of Binary Tree
1. Skewed Binary Tree: a binary tree in which every
node is having either only left sub tree or right sub
tree
2. Almost Complete Binary Tree: In a complete
binary tree, each non-leaf node compulsory has sub
tree. Also, in the last or the lowest level of this
binary tree, every node should possibly reside
on the left side. Here is the structure of a
complete binary tree:
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 8
B
C
B
C
A
B C
D F
J
E G
H I
9. DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 9
Strictly Binary Tree: if every non-terminal node in a binary tree consist of non-
empty left sub tree and right sub tree then such tree is called as strictly binary tree.
- In other words internal node will have either two children or no child at all.
A
B C
D E
F G
10. DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 10
Complete Binary Tree/Perfect Binary Tree:
• -A complete binary tree is a binary tree
that satisfies the following 2 properties-
• Every internal node has exactly 2 children.
• All the leaf nodes are at the same level.
• Complete binary tree is also called
as Perfect binary tree.
11. • Extended Binary Tree:
- Each empty sub tree is replaced by a failure node. A failure node is represented by
- Any binary tree can be converted into a extended binary tree by replacing each
empty sub tree by a failure nodes
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 11
12. Representation of Binary Tree
• To represent the binary tree in one dimensional array, we need to numbered the
nodes sequentially level by level(left to right).
• Every empty nodes are also numbered. e.g.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 12
A
C
B
G
F
E
D
7 A B C D E F G
A
C
B
G
D
G
D
13 A B C - G D - - - - - E F
13. • For complete Binary tree there is no issue, but for skew tree there is a lot of
wastage of space. e.g k depth of skew requires 2k-1 space out of only k get
occupied in array.
• Therefore another way is needed to represent the Binary tree. That is nothing but
linked representation which is an efficient way than array.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 13
14. • The code to write a tree node would be similar to what is given below. It has a data part and references
to its left and right child nodes.
In a tree, all nodes share common construct.
Binary Tree Node
17. Conversion of Tree into Binary Tree
• Children of parents added using leftmost child's right sibling relation.
DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon 17
A
C
B
G
F
E
D
H
I J
K
A
B
19. The basic operations that can be performed on a binary tree data structure, are the
following −
Insert − Inserts an element in a tree/create a tree.
Traversals − Searches an element in a tree.
Preorder Traversal − Traverses a tree in a pre-order manner.
Inorder Traversal − Traverses a tree in an in-order manner.
Postorder Traversal − Traverses a tree in a post-order manner.
Search- Search an element in tree using traversals.
Delete- delete an element from binary tree
Binary tree Basic Operations
20. Create/Insert OPERATION
• The very first insertion creates the tree. Afterwards, whenever an element is to be inserted, first locate its
proper location. Start searching from the T node, then search for the empty location in the left subtree and
insert the data. Otherwise, search for the empty location in the right subtree and insert the data.
• Algorithm:
1. Enter key to be inserted. Create node as tempNode for it.
2. Check T is NULL, if yes then make tempNode as T of tree
3. If T is not NULL then
4. Take temporary variable *ptr and set *ptr=T
5. Do
i. Ask user in which direction user wants to insert data(Left or right)
ii. if direction is Left the check following condition
21. iii. if(ptr->left==NULL) //insert node at left of tree
{
ptr->left=tempNode;
break; }
else{
ptr=ptr->left;
}
else //if user gives right direction
{
if(ptr->right==NULL)
{
ptr->right=tempNode;
break;
}
else
{
ptr=ptr->right;
}
}
iv. Do step 5 while(ptr!=NULL)
5. Repeat steps 1 to 5 until no more data to
insert.
6. Stop
22. • Btree.cpp
• Enter the element=4
• Do u want to enter more elements (y/n)y
• Enter the element=12
• in which direction(l/r)l
• Do u want to enter more elements (y/n)y
• Enter the element=34
• in which direction(l/r)l
• in which direction(l/r)?r
• Do u want to enter more elements (y/n)y
• Enter the element=1
• in which direction(l/r)r
• Do u want to enter more elements (y/n)y
• Enter the element=22
• in which direction(l/r)r
• in which direction(l/r)?r
• Do u want to enter more elements (y/n)y
• Enter the element=32
• in which direction(l/r)r
• in which direction(l/r)?l
4
12
34
1
22
32
23. Binary Tree Traversal
• Traversal is a process to visit all the nodes of a tree and print their values too. Because, all nodes are
connected via edges (links) we always start from the T (head) node.
• This process could be defined recursively.
• We cannot access a node randomly from a tree. There are three ways which we use to traverse a tree −
• In-order Traversal
• Pre-order Traversal
• Post-order Traversal
24. 1. In - Order Traversal ( LeftChild - T - RightChild )
Algorithm for inorder traversal
Step 1 : Start from the Left Subtree of T .
Step 2 : Then, visit the T.
Step 3 : Then, go to the Right Subtree.
Step 1 : Inoredr on (B) + A+(Inorder on C)
Step 2 : [B+ inorder on(D) ]+A+ (Inorder on C)
Step 3 : B + inorder on(E) + D + Inorder on( F )+ A +Inorder on (C)
Step 4 : B + E + D + F + A +Inorder on(G)+C+ Inorder on(H)
Step 4 : B + E + D + F + A +G+C+ H
Inorder Traversal : B E D F A G C H
25. 2. Pre - Order Traversal ( T - LeftChild - RightChild )
Step 1 : A + Preorder on (B) + Preorder on(C)
Step 2 : A + [B + Preorder on(D)] +Preorder on (C )
Step 3 : A + [B +[D + Preorder on(E )+Preorder on( F)]] + Preorder on (C )
Step 4: A+ B+ D+ E+ F+ [C+Preorder on(G)+Preorder on(H)]
Step 5: A + B + D+ E+ F + C+ G + H
Preorder Traversal : A B D E F C G H
Algorithm for preorder traversal
Step 1 : Start from the T and visit the T.
Step 2 : Then, go to the Left Subtree.
Step 3 : Then, go to the Right Subtree.
26. • Algorithm for post-order traversal
Step 1 : Start from the Left Subtree (Last Leaf) and visit it.
Step 2 : Then, go to the Right Subtree.
Step 3 : Then, go to the T.
Step 1 : (Postorder on (B) + Postorder on (C) + ( A)
Step 2 : [Postorder on(D)+ B]+ Postorder on (C) + ( A)
Step 2 : [[Postorder on(E)+Postorder on(F)+D]+ B]+ Postorder on (C) + ( A)
Step 3 : E + F + D + B + [[Postorder on(G)+ Postorder on(H)]+C]+A
Step 3 : E + F + D + B + G + H + C + A
Post-order Traversal : E F D B G H C A
3. Post - Order Traversal ( Left-Child – Right-Child - T )
31. Non-Recursive Preorder
• Algorithm:
1. S is an empty stack used to store NODE pointer
2. NODE *temp
3.push(root)
4. while(stack is not empty)
{
temp=pop();
print temp->data;
if temp has right child then push into stack
if temp has left child then push into stack
}
5.stop
35. Non Recursive Inorder Traversal
• Algorithm
1. S is an empty stack used to store NODE pointer
2. NODE *ptr=root
3. do
{
while(temp!=NULL)
{
push temp into stack
move temp to its left
}
pop temp
display temp->data
move temp to its right
} while(!isempty())
4. Stop
A
B C
D
38. • Algorithm
In this traversal each node is visited twice but we are supposed to dispaly
only once.
- Hence there should be some mechanism to indicate whether the node is being
visited 1st time or 2nd time.
- Display the content of the node only when it is visited for the 2nd time.
Non Recursive Postorder Traversal
39. • Algorithm:
1. S is an empty stack used to store Node
pointer
2. Node *temp= root
3. do
{
while(temp!=NULL)
s.push(temp)
temp=temp->left
4. pop from stack and assign to temp
temp=s.pop()
5. if (temp->flag==1)
print temp->data
temp=NULL
6. else
temp->flag=1
s.push(temp)
temp=temp->right
}while(!isempty()||temp!=NULL)
A
B C
D
struct BTnode
{
char data;
BTnode *left;
BTnode *right;
int flag=0;
}
41. • inorder,preorder and postorder requires stack for traversal, but there are some
traversal techniques which requires queue e.g. BFS
• This traversal is also called as Level order traversal as it visits nodes in levels
e.g.
10
5 20
15
1 7
10 5 20 1 7 15
43. • BFS is generally used for finding minimum cost edges.
• In peer to peer network, to find all neighbour nodes
44.
45. • Tree is traversed according to its depth and visited node in depthwise.
• DFS is a preorder traversal
• start from root node,move along the edge towards left node
10
5 20
15
1 7
10 5 1 7 20 15
46. • Algorithm
1. Visit the root node. push it into stack
2. Pop the node and display data.
3. if right child is not NULL,push it into stack
4. if left child is not NULL,push it into stack
5. repeat step 2-4 until stack is empty Applications:
1. Topological sorting-> for scheduling jobs
from given dependencies among jobs
2. Path finding: use stack to keep track of
the path between source vertex to
destination vertex
47. 10
5 D
F
A
B
C E
DESCRIPTION Stack OUTPUT
visit A and push(A) A
pop and display -1 A
push D
push B
B D A
pop B
display B
D A B
push C pop C and
display
D A B C
pop D
display D &push E,F
E F A B C D
pop E,display E
pop F, display F
-1 A B C D E F
48. Binary Search Tree
• When we store order data into array structure we use efficient search algorithm.e.g. Binary Search
• However, to provide efficient insertion and deletion operation,we represent a link list.
• The problem with linked list is that their search algo. which are sequential searches,very
ineffecient.
• So what we need is data structure that has efficient search algo. and at the same time efficient
insertion and deletion operation.
• Binary Search Tree provide that structure.
49. Cont...
Defination: A Binary search tree is a binary tree with following properties:
1. All keys are distincts.
2. All items in the right subtree are greater than equal to the root.
3. each subtree is itself a binary search tree.
6
17
19
10
5 20
25
10
8
5 9
22
17
19
10
5 20
12
17
8
11 15
50. BinarySearchTree(BST)
A
s
h
i
m
L
a
m
i
c
h
h
a
n
e
5
0
• A binary search tree (BST) is a binary tree that is either empty or in
which every node contains a key (value) and satisfies the following
conditions:
• All keys in the left sub-tree of the root are smaller than the key in the root
node
• All keysin the right sub-tree of the root are greater than the keyin the root
node
• Theleft and right sub-trees of the root are again binary search trees
51. BinarySearchTree(BST)
A
s
h
i
m
L
a
m
i
c
h
h
a
n
e
5
1
• Abinary search tree is basically abinary tree, and therefore it canbe
traversed in inorder, preorder andpostorder.
• If we traverse abinary search tree in inorder and print the identifiers
contained in the nodes of the tree, we get asorted list of identifiers in
ascending order.
53. DEPARTMENT OF COMPUTER ENGINEERING, Sanjivani COE, Kopargaon
53
A
B E
F
D
I
C
G
H
A
B E
F
D
I
G
C
H
A
B E
F
C
D
G
I
H
Correct
tree
Editor's Notes
1. Solution-
Using property-3, we have-
Number of degree-2 nodes
= Number of leaf nodes – 1
= n – 1 Thus, Option (B) is correct.
2. Solution-
Using property-3, we have-
Number of leaf nodes in a binary tree
= Number of degree-2 nodes + 1
= 10 + 1
= 11 Thus, Option (B) is correct.
3. Solution is 19