This document discusses binary trees and binary search trees. It covers binary tree definitions, traversal algorithms, binary search trees, and balanced binary search trees called AVL trees. Specifically, it explores recursive and non-recursive traversal algorithms, insertion and deletion operations in binary search trees, and rotations needed to balance AVL trees during insertion and deletion.
This document discusses trees and binary trees. It covers tree definitions, properties, traversals, and common algorithms. Specifically for binary trees, it discusses their implementation, operations like insertion and deletion, and binary search trees. BSTs allow for efficient search, insertion, and deletion in O(h) time where h is the tree height. Balanced BSTs like red-black trees maintain h as O(log n) to guarantee efficient performance.
This document discusses trees and binary trees. It covers tree definitions, properties, traversals, and common algorithms. Specifically for binary trees, it discusses their implementation, operations like insertion and deletion, and binary search trees. BSTs allow for efficient search, insertion, and deletion in O(h) time where h is the tree height. Balanced BSTs like red-black trees maintain h as O(log n) to guarantee efficient performance.
This document provides an introduction to data structures and algorithms in C programming. It discusses linear and non-linear data structures like arrays, stacks, queues, linked lists, trees, graphs, and binary search trees. It describes their characteristics and common operations. Specifically, it provides details on stacks and queues, including implementations and applications. Algorithms for common stack operations like push and pop are given. The document also introduces object-oriented programming concepts like classes, objects, inheritance, encapsulation, and polymorphism. Finally, it discusses abstract data types and provides an example stack abstract data type with algorithms for push, pop and display operations.
This document covers different data structures including arrays, lists, stacks, queues, and trees. It describes the basic operations and applications of each structure. For trees specifically, it defines common tree terminology, covers tree traversal methods like preorder and postorder, and describes binary trees and their properties. It provides examples of using trees to represent arithmetic expressions and decision processes.
- Binary trees are a data structure where each element has up to two children, allowing elements to be organized in a hierarchical tree-like structure. This allows items to be stored and searched more efficiently than linear data structures like linked lists.
- Searching and inserting items into a balanced binary tree takes O(log n) time, where n is the number of nodes, as each operation requires traversing a branching path proportional to the log of the number of elements. For large n, this provides much faster access than the O(n) time required to search a linked list.
- Binary trees can be traversed in different orders like in-order, pre-order and post-order to process or output the elements
This document discusses different types of tree data structures, including binary trees and binary search trees. It provides descriptions of key tree terminology like root, parent, child, leaf nodes, and different tree traversal methods. The document also covers operations on binary search trees like insertion, searching, and deletion. It provides pseudocode examples for these BST operations and discusses handling different cases that can occur during node deletion. Finally, it briefly introduces AVL trees and the concept of balance factors and rotations needed to maintain the balanced tree property.
This document provides an introduction to trees as a non-linear data structure. It discusses key terms like root, parent, child, leaf nodes. It also covers different types of trees like binary trees and binary search trees. Tree traversal algorithms like preorder, inorder and postorder are explained along with pseudocode. Finally, it briefly discusses applications of trees and the Huffman algorithm for data compression.
This document discusses trees and binary trees. It covers tree definitions, properties, traversals, and common algorithms. Specifically for binary trees, it discusses their implementation, operations like insertion and deletion, and binary search trees. BSTs allow for efficient search, insertion, and deletion in O(h) time where h is the tree height. Balanced BSTs like red-black trees maintain h as O(log n) to guarantee efficient performance.
This document discusses trees and binary trees. It covers tree definitions, properties, traversals, and common algorithms. Specifically for binary trees, it discusses their implementation, operations like insertion and deletion, and binary search trees. BSTs allow for efficient search, insertion, and deletion in O(h) time where h is the tree height. Balanced BSTs like red-black trees maintain h as O(log n) to guarantee efficient performance.
This document provides an introduction to data structures and algorithms in C programming. It discusses linear and non-linear data structures like arrays, stacks, queues, linked lists, trees, graphs, and binary search trees. It describes their characteristics and common operations. Specifically, it provides details on stacks and queues, including implementations and applications. Algorithms for common stack operations like push and pop are given. The document also introduces object-oriented programming concepts like classes, objects, inheritance, encapsulation, and polymorphism. Finally, it discusses abstract data types and provides an example stack abstract data type with algorithms for push, pop and display operations.
This document covers different data structures including arrays, lists, stacks, queues, and trees. It describes the basic operations and applications of each structure. For trees specifically, it defines common tree terminology, covers tree traversal methods like preorder and postorder, and describes binary trees and their properties. It provides examples of using trees to represent arithmetic expressions and decision processes.
- Binary trees are a data structure where each element has up to two children, allowing elements to be organized in a hierarchical tree-like structure. This allows items to be stored and searched more efficiently than linear data structures like linked lists.
- Searching and inserting items into a balanced binary tree takes O(log n) time, where n is the number of nodes, as each operation requires traversing a branching path proportional to the log of the number of elements. For large n, this provides much faster access than the O(n) time required to search a linked list.
- Binary trees can be traversed in different orders like in-order, pre-order and post-order to process or output the elements
This document discusses different types of tree data structures, including binary trees and binary search trees. It provides descriptions of key tree terminology like root, parent, child, leaf nodes, and different tree traversal methods. The document also covers operations on binary search trees like insertion, searching, and deletion. It provides pseudocode examples for these BST operations and discusses handling different cases that can occur during node deletion. Finally, it briefly introduces AVL trees and the concept of balance factors and rotations needed to maintain the balanced tree property.
This document provides an introduction to trees as a non-linear data structure. It discusses key terms like root, parent, child, leaf nodes. It also covers different types of trees like binary trees and binary search trees. Tree traversal algorithms like preorder, inorder and postorder are explained along with pseudocode. Finally, it briefly discusses applications of trees and the Huffman algorithm for data compression.
This chapter discusses various searching and hashing algorithms. It covers sequential search which has order n performance, binary search which improves on sequential search with order log2n performance by dividing the search space in half each iteration, and hashing which maps keys to table locations using a hash function and has near constant order 1 performance on average. The chapter explores implementing ordered lists that allow for efficient binary search, and resolving collisions that occur in hashing through open addressing or chaining techniques.
lecture10 date structure types of graph and terminologyKamranAli649587
The document discusses tree traversal techniques and heaps. It begins by explaining tree traversal concepts and the three common traversal techniques: preorder, inorder, and postorder. It then discusses heaps, which are almost complete binary trees where the key of each node is less than or equal to its children's keys. Heaps support efficient insertion and deletion of minimum elements in logarithmic time and are used to implement priority queues. Code implementations of binary trees, tree traversals, heaps, and their operations like insertion and deletion are also provided.
The document discusses various tree data structures including binary trees and their terminology. It defines a tree as a set of nodes connected by links/branches where one node is designated as the root. Key terms discussed include child, parent, leaf, root, and level. The document also covers different ways to represent trees using arrays and linked lists and how to traverse trees using preorder, inorder, and postorder traversal algorithms.
Christoph Koch is a professor of Computer Science at EPFL, specializing in data management. Until 2010, he was an Associate Professor in the Department of Computer Science at Cornell University. Previously to this, from 2005 to 2007, he was an Associate Professor of Computer Science at Saarland University. Earlier, he obtained his PhD in Artificial Intelligence from TU Vienna and CERN (2001), was a postdoctoral researcher at TU Vienna and the University of Edinburgh (2001-2003), and an assistant professor at TU Vienna (2003-2005). He has won Best Paper Awards at PODS 2002, ICALP 2005, and SIGMOD 2011, an Outrageous Ideas and Vision Paper Award at CIDR 2013, a Google Research Award (in 2009), and an ERC Grant (in 2011). He is a PI of the FET Flagship Human Brain Project and of NCCR MARVEL, a new Swiss national research center for materials research. He (co-)chaired the program committees of DBPL 2005, WebDB 2008, ICDE 2011, VLDB 2013, and was PC vice-chair of ICDE 2008 and ICDE 2009. He has served on the editorial board of ACM Transactions on Internet Technology and as Editor-in-Chief of PVLDB.
This document provides an overview of trees and graphs as data structures. It discusses binary trees, including their implementation and operations like searching. Binary search trees are described, with examples of insertion and searching. Graphs are then introduced, including undirected and directed graphs. Graph representations in Python are shown. Examples of an undirected weighted graph, minimal spanning tree, and shortest paths are provided. Finally, it notes some common graph algorithms.
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.
The document discusses recursion, including recursive definitions, algorithms, and functions. It provides examples of recursively defined problems like factorials, Fibonacci numbers, and the Tower of Hanoi. Recursive functions are used to implement algorithms to solve these problems by reducing the problem into smaller instances until a base case is reached. Both advantages and disadvantages of the recursive approach are discussed, as well as considerations for choosing between recursion and iteration.
The document discusses data structures and algorithms. It begins by defining data structures as organized data and allowed operations. It then discusses arrays, linked lists, binary trees, and their implementations. Arrays allow fast access but fixed size, while linked lists and trees can grow dynamically but have slower access. Binary tree operations like search, insert, and delete have logarithmic time complexity due to the tree height being logarithmic in the number of nodes. The document provides examples of various data structure implementations and traversals.
Introduction to data structure by anil duttAnil Dutt
This document provides an introduction and overview of common data structures including linked lists, stacks, queues, trees, and graphs. It defines each structure and describes their basic operations and implementations. Linked lists allow insertions and deletions anywhere and come in singly and doubly linked varieties. Stacks and queues follow last-in, first-out and first-in, first-out rules respectively. Binary trees enable fast searching and sorting of data. Graphs represent relationships between nodes connected by edges.
1. Hash tables are good for random access of elements but not sequential access. When records need to be accessed sequentially, hashing can be problematic because elements are stored in random locations instead of consecutively.
2. To find the successor of a node in a binary search tree, we take the right child. This operation has a runtime complexity of O(1).
3. When comparing operations like insertion, deletion, and searching between different data structures, arrays generally have the best performance for insertion and searching, while linked lists have better performance for deletion and allow for easy insertion/deletion anywhere. Binary search trees fall between these two.
The document describes different types of editors used in HDL design including schematic and layout editors.
Schematic editors allow designers to capture circuit connectivity and hierarchy using libraries of component symbols. Layout editors allow designers to specify the physical structure of a design using geometric shapes.
Both editor types provide file and display commands, drawing tools to create and edit circuit elements, and data structures like linked lists and quad trees to store and query design information.
The document discusses collaborations between 6 students on the topics of data structures trees and graphs. It provides information on binary trees, binary search trees, tree and graph implementations and common graph algorithms like Dijkstra's algorithm. Examples of trees, graphs and Dijkstra's algorithm are shown.
The document discusses binary trees and binary search trees. It defines key concepts like nodes, children, parents, leaves, height, and tree traversal. It explains that binary search trees allow searching, insertion, and deletion in O(log N) time by enforcing the property that all left descendants of a node are less than the node and all right descendants are greater. The operations of searching, insertion, deletion and their time complexities are outlined for binary search trees.
The document discusses binary trees, including their basic terminology, properties, representations, traversal methods, and common operations. It provides algorithms for inserting nodes, deleting nodes, and merging two binary trees. The key points covered are:
- Binary trees have a root node, child nodes, and properties like maximum/minimum number of nodes based on height.
- They can be represented sequentially using arrays or non-sequentially using linked lists.
- Common traversal orders are preorder, inorder, and postorder.
- Operations include insertion, deletion, traversal, and merging two trees into one larger tree.
- Algorithms are presented for inserting nodes using linked lists and merging two trees by combining their nodes.
Query compilation in Impala involves parsing the SQL, semantic analysis to validate the query, planning to generate an executable query plan, and finally executing the query. The query planner considers different join orders and strategies like broadcast joins and partitioned joins to minimize data transfer during query execution based on table and column statistics. The explain output provides details on how the query will be executed in a distributed fashion across nodes.
The document discusses different tree traversal algorithms including depth-first search (DFS) and breadth-first search (BFS). It describes three DFS traversal methods - preorder, inorder, and postorder - and provides recursive and non-recursive algorithms for implementing each. BFS traversal is also covered, which processes all nodes level-by-level using a queue. Examples and applications of the various tree traversal techniques are presented.
This document discusses data structures and binary trees. It begins with basic terminology used in trees such as root, node, degree, levels, and traversal methods. It then explains different types of binary trees including strictly binary trees and complete binary trees. Next, it covers binary tree representations using arrays and linked lists. Finally, it discusses operations that can be performed on binary search trees including insertion, searching, deletion, and traversing nodes using preorder, inorder and postorder traversal methods.
This document discusses augmenting data structures by adding additional information and operations while maintaining efficiency. It describes augmenting red-black trees to support efficient retrieval of order statistics and ranks by adding a size field to nodes. Interval trees are also covered, which store intervals in a red-black tree sorted by low endpoint while maintaining the maximum endpoint in each subtree, enabling efficient search for overlapping intervals. The key to augmentation is showing the new information can be maintained through basic operations like insertion and deletion without affecting overall asymptotic runtime.
This document discusses binary search trees and balanced binary search trees like AVL trees. It begins with an overview of binary search trees and their properties. It then introduces the concept of balance factors and describes how AVL trees maintain a balance factor between -1 and 1 for every node through rotations. The document provides examples of single and double rotations performed during insertion to rebalance the tree. It concludes with an algorithm for inserting a node into an AVL tree that searches back up the tree to perform necessary rotations after an insertion causes imbalance.
The document discusses heaps and their implementation and applications. It defines heaps as binary trees that satisfy the heap property, where each node is greater than or equal to its children (for min-heaps) or less than or equal (for max-heaps). Heaps can be implemented efficiently using arrays, allowing for fast insertion, deletion, and finding the maximum/minimum element. The document outlines heap operations and provides examples of heap construction. Common applications of heaps discussed are priority queues, selection algorithms, and heapsort.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
This chapter discusses various searching and hashing algorithms. It covers sequential search which has order n performance, binary search which improves on sequential search with order log2n performance by dividing the search space in half each iteration, and hashing which maps keys to table locations using a hash function and has near constant order 1 performance on average. The chapter explores implementing ordered lists that allow for efficient binary search, and resolving collisions that occur in hashing through open addressing or chaining techniques.
lecture10 date structure types of graph and terminologyKamranAli649587
The document discusses tree traversal techniques and heaps. It begins by explaining tree traversal concepts and the three common traversal techniques: preorder, inorder, and postorder. It then discusses heaps, which are almost complete binary trees where the key of each node is less than or equal to its children's keys. Heaps support efficient insertion and deletion of minimum elements in logarithmic time and are used to implement priority queues. Code implementations of binary trees, tree traversals, heaps, and their operations like insertion and deletion are also provided.
The document discusses various tree data structures including binary trees and their terminology. It defines a tree as a set of nodes connected by links/branches where one node is designated as the root. Key terms discussed include child, parent, leaf, root, and level. The document also covers different ways to represent trees using arrays and linked lists and how to traverse trees using preorder, inorder, and postorder traversal algorithms.
Christoph Koch is a professor of Computer Science at EPFL, specializing in data management. Until 2010, he was an Associate Professor in the Department of Computer Science at Cornell University. Previously to this, from 2005 to 2007, he was an Associate Professor of Computer Science at Saarland University. Earlier, he obtained his PhD in Artificial Intelligence from TU Vienna and CERN (2001), was a postdoctoral researcher at TU Vienna and the University of Edinburgh (2001-2003), and an assistant professor at TU Vienna (2003-2005). He has won Best Paper Awards at PODS 2002, ICALP 2005, and SIGMOD 2011, an Outrageous Ideas and Vision Paper Award at CIDR 2013, a Google Research Award (in 2009), and an ERC Grant (in 2011). He is a PI of the FET Flagship Human Brain Project and of NCCR MARVEL, a new Swiss national research center for materials research. He (co-)chaired the program committees of DBPL 2005, WebDB 2008, ICDE 2011, VLDB 2013, and was PC vice-chair of ICDE 2008 and ICDE 2009. He has served on the editorial board of ACM Transactions on Internet Technology and as Editor-in-Chief of PVLDB.
This document provides an overview of trees and graphs as data structures. It discusses binary trees, including their implementation and operations like searching. Binary search trees are described, with examples of insertion and searching. Graphs are then introduced, including undirected and directed graphs. Graph representations in Python are shown. Examples of an undirected weighted graph, minimal spanning tree, and shortest paths are provided. Finally, it notes some common graph algorithms.
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.
The document discusses recursion, including recursive definitions, algorithms, and functions. It provides examples of recursively defined problems like factorials, Fibonacci numbers, and the Tower of Hanoi. Recursive functions are used to implement algorithms to solve these problems by reducing the problem into smaller instances until a base case is reached. Both advantages and disadvantages of the recursive approach are discussed, as well as considerations for choosing between recursion and iteration.
The document discusses data structures and algorithms. It begins by defining data structures as organized data and allowed operations. It then discusses arrays, linked lists, binary trees, and their implementations. Arrays allow fast access but fixed size, while linked lists and trees can grow dynamically but have slower access. Binary tree operations like search, insert, and delete have logarithmic time complexity due to the tree height being logarithmic in the number of nodes. The document provides examples of various data structure implementations and traversals.
Introduction to data structure by anil duttAnil Dutt
This document provides an introduction and overview of common data structures including linked lists, stacks, queues, trees, and graphs. It defines each structure and describes their basic operations and implementations. Linked lists allow insertions and deletions anywhere and come in singly and doubly linked varieties. Stacks and queues follow last-in, first-out and first-in, first-out rules respectively. Binary trees enable fast searching and sorting of data. Graphs represent relationships between nodes connected by edges.
1. Hash tables are good for random access of elements but not sequential access. When records need to be accessed sequentially, hashing can be problematic because elements are stored in random locations instead of consecutively.
2. To find the successor of a node in a binary search tree, we take the right child. This operation has a runtime complexity of O(1).
3. When comparing operations like insertion, deletion, and searching between different data structures, arrays generally have the best performance for insertion and searching, while linked lists have better performance for deletion and allow for easy insertion/deletion anywhere. Binary search trees fall between these two.
The document describes different types of editors used in HDL design including schematic and layout editors.
Schematic editors allow designers to capture circuit connectivity and hierarchy using libraries of component symbols. Layout editors allow designers to specify the physical structure of a design using geometric shapes.
Both editor types provide file and display commands, drawing tools to create and edit circuit elements, and data structures like linked lists and quad trees to store and query design information.
The document discusses collaborations between 6 students on the topics of data structures trees and graphs. It provides information on binary trees, binary search trees, tree and graph implementations and common graph algorithms like Dijkstra's algorithm. Examples of trees, graphs and Dijkstra's algorithm are shown.
The document discusses binary trees and binary search trees. It defines key concepts like nodes, children, parents, leaves, height, and tree traversal. It explains that binary search trees allow searching, insertion, and deletion in O(log N) time by enforcing the property that all left descendants of a node are less than the node and all right descendants are greater. The operations of searching, insertion, deletion and their time complexities are outlined for binary search trees.
The document discusses binary trees, including their basic terminology, properties, representations, traversal methods, and common operations. It provides algorithms for inserting nodes, deleting nodes, and merging two binary trees. The key points covered are:
- Binary trees have a root node, child nodes, and properties like maximum/minimum number of nodes based on height.
- They can be represented sequentially using arrays or non-sequentially using linked lists.
- Common traversal orders are preorder, inorder, and postorder.
- Operations include insertion, deletion, traversal, and merging two trees into one larger tree.
- Algorithms are presented for inserting nodes using linked lists and merging two trees by combining their nodes.
Query compilation in Impala involves parsing the SQL, semantic analysis to validate the query, planning to generate an executable query plan, and finally executing the query. The query planner considers different join orders and strategies like broadcast joins and partitioned joins to minimize data transfer during query execution based on table and column statistics. The explain output provides details on how the query will be executed in a distributed fashion across nodes.
The document discusses different tree traversal algorithms including depth-first search (DFS) and breadth-first search (BFS). It describes three DFS traversal methods - preorder, inorder, and postorder - and provides recursive and non-recursive algorithms for implementing each. BFS traversal is also covered, which processes all nodes level-by-level using a queue. Examples and applications of the various tree traversal techniques are presented.
This document discusses data structures and binary trees. It begins with basic terminology used in trees such as root, node, degree, levels, and traversal methods. It then explains different types of binary trees including strictly binary trees and complete binary trees. Next, it covers binary tree representations using arrays and linked lists. Finally, it discusses operations that can be performed on binary search trees including insertion, searching, deletion, and traversing nodes using preorder, inorder and postorder traversal methods.
This document discusses augmenting data structures by adding additional information and operations while maintaining efficiency. It describes augmenting red-black trees to support efficient retrieval of order statistics and ranks by adding a size field to nodes. Interval trees are also covered, which store intervals in a red-black tree sorted by low endpoint while maintaining the maximum endpoint in each subtree, enabling efficient search for overlapping intervals. The key to augmentation is showing the new information can be maintained through basic operations like insertion and deletion without affecting overall asymptotic runtime.
This document discusses binary search trees and balanced binary search trees like AVL trees. It begins with an overview of binary search trees and their properties. It then introduces the concept of balance factors and describes how AVL trees maintain a balance factor between -1 and 1 for every node through rotations. The document provides examples of single and double rotations performed during insertion to rebalance the tree. It concludes with an algorithm for inserting a node into an AVL tree that searches back up the tree to perform necessary rotations after an insertion causes imbalance.
The document discusses heaps and their implementation and applications. It defines heaps as binary trees that satisfy the heap property, where each node is greater than or equal to its children (for min-heaps) or less than or equal (for max-heaps). Heaps can be implemented efficiently using arrays, allowing for fast insertion, deletion, and finding the maximum/minimum element. The document outlines heap operations and provides examples of heap construction. Common applications of heaps discussed are priority queues, selection algorithms, and heapsort.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Low power architecture of logic gates using adiabatic techniquesnooriasukmaningtyas
The growing significance of portable systems to limit power consumption in ultra-large-scale-integration chips of very high density, has recently led to rapid and inventive progresses in low-power design. The most effective technique is adiabatic logic circuit design in energy-efficient hardware. This paper presents two adiabatic approaches for the design of low power circuits, modified positive feedback adiabatic logic (modified PFAL) and the other is direct current diode based positive feedback adiabatic logic (DC-DB PFAL). Logic gates are the preliminary components in any digital circuit design. By improving the performance of basic gates, one can improvise the whole system performance. In this paper proposed circuit design of the low power architecture of OR/NOR, AND/NAND, and XOR/XNOR gates are presented using the said approaches and their results are analyzed for powerdissipation, delay, power-delay-product and rise time and compared with the other adiabatic techniques along with the conventional complementary metal oxide semiconductor (CMOS) designs reported in the literature. It has been found that the designs with DC-DB PFAL technique outperform with the percentage improvement of 65% for NOR gate and 7% for NAND gate and 34% for XNOR gate over the modified PFAL techniques at 10 MHz respectively.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
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.
2. Data Structures Using C++ 2
Chapter Objectives
• Learn about binary trees
• Explore various binary tree traversal algorithms
• Learn how to organize data in a binary search tree
• Discover how to insert and delete items in a binary
search tree
• Explore nonrecursive binary tree traversal
algorithms
• Learn about AVL (height-balanced) trees
3. Data Structures Using C++ 3
Binary Trees
• Definition: A binary tree, T, is either empty
or such that:
– T has a special node called the root node;
– T has two sets of nodes, LT and RT, called the
left subtree and right subtree of T, respectively;
– LT and RT are binary trees
9. Data Structures Using C++ 9
Binary Trees
Following struct defines the node of a binary tree:
template<class elemType>
struct nodeType
{
elemType info;
nodeType<elemType> *llink;
nodeType<elemType> *rlink;
};
10. Data Structures Using C++ 10
Nodes
• For each node:
– Data is stored in info
– The pointer to the left child is stored in llink
– The pointer to the right child is stored in rlink
12. Data Structures Using C++ 12
Binary Tree Definitions
• Leaf: node that has no left and right
children
• Parent: node with at least one child node
• Level of a node: number of branches on the
path from root to node
• Height of a binary tree: number of nodes no
the longest path from root to node
13. Data Structures Using C++ 13
Height of a Binary Tree
Recursive algorithm to find height of binary
tree:
(height(p) denotes height of binary tree with
root p):
if(p is NULL)
height(p) = 0
else
height(p) = 1 + max(height(p->llink), height(p-
>rlink))
14. Data Structures Using C++ 14
Height of a Binary Tree
Function to implement above algorithm:
template<class elemType>
int height(nodeType<elemType> *p)
{
if(p == NULL)
return 0;
else
return 1 + max(height(p->llink),
height(p->rlink));
}
15. Data Structures Using C++ 15
Copy Tree
• Useful operation on binary trees is to
make identical copy of binary tree
• Use function copyTree when we
overload assignment operator and
implement copy constructor
16. Data Structures Using C++ 16
Copy Tree
template<class elemType>
void copyTree(nodeType<elemType>* &copiedTreeRoot,
nodeType<elemType>* otherTreeRoot)
{
if(otherTreeRoot == NULL)
copiedTreeRoot = NULL;
else
{
copiedTreeRoot = new nodeType<elemType>;
copiedTreeRoot->info = otherTreeRoot->info;
copyTree(copiedTreeRoot->llink, otherTreeRoot->llink);
copyTree(copiedTreeRoot->rlink, otherTreeRoot->rlink);
}
}//end copyTree
17. Data Structures Using C++ 17
Binary Tree Traversal
• Must start with the root, then
– Visit the node first or
– Visit the subtrees first
• Three different traversals
– Inorder
– Preorder
– Postorder
18. Data Structures Using C++ 18
Traversals
• Inorder
– Traverse the left subtree
– Visit the node
– Traverse the right subtree
• Preorder
– Visit the node
– Traverse the left subtree
– Traverse the right subtree
19. Data Structures Using C++ 19
Traversals
• Postorder
– Traverse the left subtree
– Traverse the right subtree
– Visit the node
23. Data Structures Using C++ 23
Implementing Binary Trees:
class binaryTreeType Functions
• Public
– isEmpty
– inorderTraversal
– preorderTraversal
– postorderTraversal
– treeHeight
– treeNodeCount
– treeLeavesCount
– destroyTree
• Private
• copyTree
• Destroy
• Inorder, preorder,
postorder
• Height
• Max
• nodeCount
• leavesCount
24. Data Structures Using C++ 24
Binary Search Trees
• Data in each node
– Larger than the data in its left child
– Smaller than the data in its right child
• A binary search tree,t, is either empty or:
– T has a special node called the root node
– T has two sets of nodes, LT and RT, called the left
subtree and right subtree of T, respectively
– Key in root node larger than every key in left subtree
and smaller than every key in right subtree
– LT and RT are binary search trees
26. Data Structures Using C++ 26
Operations Performed on Binary
Search Trees
• Determine whether the binary search tree is
empty
• Search the binary search tree for a particular
item
• Insert an item in the binary search tree
• Delete an item from the binary search tree
27. Data Structures Using C++ 27
Operations Performed on Binary
Search Trees
• Find the height of the binary search tree
• Find the number of nodes in the binary
search tree
• Find the number of leaves in the binary
search tree
• Traverse the binary search tree
• Copy the binary search tree
29. Data Structures Using C++ 29
Binary Search Tree Analysis
• Theorem: Let T be a binary search tree with n
nodes, where n > 0.The average number of nodes
visited in a search of T is approximately 1.39log2n
• Number of comparisons required to determine
whether x is in T is one more than the number of
comparisons required to insert x in T
• Number of comparisons required to insert x in T
same as the number of comparisons made in
unsuccessful search, reflecting that x is not in T
30. Data Structures Using C++ 30
Binary Search Tree Analysis
It follows that:
It is also known that:
Solving Equations (11-1) and (11-2)
32. Data Structures Using C++ 32
Nonrecursive Inorder Traversal:
General Algorithm
1. current = root; //start traversing the binary tree at
// the root node
2. while(current is not NULL or stack is nonempty)
if(current is not NULL)
{
push current onto stack;
current = current->llink;
}
else
{
pop stack into current;
visit current; //visit the node
current = current->rlink; //move to the
//right child
}
33. Data Structures Using C++ 33
Nonrecursive Preorder Traversal:
General Algorithm
1. current = root; //start the traversal at the root node
2. while(current is not NULL or stack is nonempty)
if(current is not NULL)
{
visit current;
push current onto stack;
current = current->llink;
}
else
{
pop stack into current;
current = current->rlink; //prepare to visit
//the right subtree
}
34. Data Structures Using C++ 34
Nonrecursive Postorder Traversal
1. current = root; //start traversal at root node
2. v = 0;
3. if(current is NULL)
the binary tree is empty
4. if(current is not NULL)
a. push current into stack;
b. push 1 onto stack;
c. current = current->llink;
d. while(stack is not empty)
if(current is not NULL and v is 0)
{
push current and 1 onto stack;
current = current->llink;
}
35. Data Structures Using C++ 35
Nonrecursive Postorder Traversal
(Continued)
else
{
pop stack into current and v;
if(v == 1)
{
push current and 2 onto stack;
current = current->rlink;
v = 0;
}
else
visit current;
}
36. Data Structures Using C++ 36
AVL (Height-balanced Trees)
• A perfectly balanced binary tree is a binary
tree such that:
– The height of the left and right subtrees of the
root are equal
– The left and right subtrees of the root are
perfectly balanced binary trees
38. Data Structures Using C++ 38
AVL (Height-balanced Trees)
• An AVL tree (or height-balanced tree) is a
binary search tree such that:
– The height of the left and right subtrees of the
root differ by at most 1
– The left and right subtrees of the root are AVL
trees
46. Data Structures Using C++ 46
AVL Tree Rotations
• Reconstruction procedure: rotating tree
• left rotation and right rotation
• Suppose that the rotation occurs at node x
• Left rotation: certain nodes from the right subtree of x
move to its left subtree; the root of the right subtree of x
becomes the new root of the reconstructed subtree
• Right rotation at x: certain nodes from the left subtree of x
move to its right subtree; the root of the left subtree of x
becomes the new root of the reconstructed subtree
53. Data Structures Using C++ 53
Deletion From AVL Trees
• Case 1: the node to be deleted is a leaf
• Case 2: the node to be deleted has no right
child, that is, its right subtree is empty
• Case 3: the node to be deleted has no left
child, that is, its left subtree is empty
• Case 4: the node to be deleted has a left
child and a right child
54. Data Structures Using C++ 54
Analysis: AVL Trees
Consider all the possible AVL trees of height h. Let Th be an
AVL tree of height h such that Th has the fewest number of
nodes. Let Thl denote the left subtree of Th and Thr denote the
right subtree of Th. Then:
where | Th | denotes the number of nodes in Th.
55. Data Structures Using C++ 55
Analysis: AVL Trees
Suppose that Thl is of height h – 1 and Thr is of height h – 2.
Thl is an AVL tree of height h – 1 such that Thl has the fewest
number of nodes among all AVL trees of height h – 1. Thr is
an AVL tree of height h – 2 that has the fewest number of
nodes among all AVL trees of height h – 2. Thl is of the form
Th -1 and Thr is of the form Th -2. Hence:
56. Data Structures Using C++ 56
Analysis: AVL Trees
Let Fh+2 = |Th | + 1. Then:
Called a Fibonacci sequence; solution to Fh is given by:
Hence
From this it can be concluded that
57. Data Structures Using C++ 57
Chapter Summary
• Binary trees
• Binary search trees
• Recursive traversal algorithms
• Nonrecursive traversal algorithms
• AVL trees