These slides are about Splay Tree .
From these slides u can learn Basics of splay tree by definition and its examples.At the end its Advantages And Disadvantages.
Tree and graph data structures are used to represent hierarchical data. A tree has nodes connected by edges in a parent-child relationship where each node can have zero or more children but only one parent, forming a rooted tree. Common tree types include binary trees where each node has at most two children, binary search trees where the left child is less than the parent which is less than the right child, and B-trees where nodes can have multiple children. Trees are traversed using in-order, pre-order and post-order algorithms.
A tree is a hierarchical data structure where items are arranged in a sorted sequence. It represents relationships between data items. A tree has a root node at the top with child nodes branching out connected by edges. Each node stores data and links to other nodes. The level of a node indicates its depth from the root with the root being level 0. Siblings are nodes that share the same parent. Leaf nodes have no children while non-terminal nodes have children. The degree of a node is the number of subtrees extending from it.
This document discusses trees as a data structure. It defines trees as structures containing nodes where each node can have zero or more children and at most one parent. Binary trees are defined as trees where each node has at most two children. The document discusses tree terminology like root, leaf, and height. It also covers binary search trees and their properties for storing and searching data, as well as algorithms for inserting and deleting nodes. Finally, it briefly discusses other types of trees like balanced search trees and parse trees.
The document defines trees and graphs, their terminology, and applications. It describes trees as undirected graphs where any two vertices are connected by a single path. Binary search trees allow for fast insertion and removal and are designed for fast searching. Trees can be traversed in pre-order, in-order, and post-order. They have applications in file systems, AI, compiler design, and text processing. Graphs consist of nodes and edges, and can be directed or undirected. Graphs have applications in maps, networks, VLSI design, and the internet.
The document provides information about B+ trees and height balancing trees. It begins with an introduction to B+ trees, describing their properties, representation, advantages over B-trees, and algorithms for insertion and deletion. It then covers key points about B+ trees, provides examples of height balanced trees like AVL trees and 2-3-4 trees, and gives pseudocode for operations on these trees like calculating balancing factors. The document concludes with solved problems on B+ trees.
1. Trees are non-linear data structures that represent hierarchical relationships. They consist of nodes connected by edges, with one node designated as the root.
2. Trees can be represented using arrays or linked lists. Array representation requires knowing the height of the tree in advance, while linked lists do not waste memory but have slower access times.
3. Common tree terminology includes root, leaf nodes, internal nodes, siblings, ancestors, descendants, depth, height, and subtrees. Binary trees restrict nodes to at most two children each.
Tree is a non-linear data structure that can represent hierarchical relationships. It consists of nodes connected by edges. The root node has child nodes, and nodes may be leaf nodes or have child nodes themselves. Binary trees restrict nodes to having at most two children. General trees can be converted to binary trees by making the first child the left child and next siblings the right child. Binary trees can be built from input data by comparing values to determine left or right placement, or from traversal operations.
Tree and graph data structures are used to represent hierarchical data. A tree has nodes connected by edges in a parent-child relationship where each node can have zero or more children but only one parent, forming a rooted tree. Common tree types include binary trees where each node has at most two children, binary search trees where the left child is less than the parent which is less than the right child, and B-trees where nodes can have multiple children. Trees are traversed using in-order, pre-order and post-order algorithms.
A tree is a hierarchical data structure where items are arranged in a sorted sequence. It represents relationships between data items. A tree has a root node at the top with child nodes branching out connected by edges. Each node stores data and links to other nodes. The level of a node indicates its depth from the root with the root being level 0. Siblings are nodes that share the same parent. Leaf nodes have no children while non-terminal nodes have children. The degree of a node is the number of subtrees extending from it.
This document discusses trees as a data structure. It defines trees as structures containing nodes where each node can have zero or more children and at most one parent. Binary trees are defined as trees where each node has at most two children. The document discusses tree terminology like root, leaf, and height. It also covers binary search trees and their properties for storing and searching data, as well as algorithms for inserting and deleting nodes. Finally, it briefly discusses other types of trees like balanced search trees and parse trees.
The document defines trees and graphs, their terminology, and applications. It describes trees as undirected graphs where any two vertices are connected by a single path. Binary search trees allow for fast insertion and removal and are designed for fast searching. Trees can be traversed in pre-order, in-order, and post-order. They have applications in file systems, AI, compiler design, and text processing. Graphs consist of nodes and edges, and can be directed or undirected. Graphs have applications in maps, networks, VLSI design, and the internet.
The document provides information about B+ trees and height balancing trees. It begins with an introduction to B+ trees, describing their properties, representation, advantages over B-trees, and algorithms for insertion and deletion. It then covers key points about B+ trees, provides examples of height balanced trees like AVL trees and 2-3-4 trees, and gives pseudocode for operations on these trees like calculating balancing factors. The document concludes with solved problems on B+ trees.
1. Trees are non-linear data structures that represent hierarchical relationships. They consist of nodes connected by edges, with one node designated as the root.
2. Trees can be represented using arrays or linked lists. Array representation requires knowing the height of the tree in advance, while linked lists do not waste memory but have slower access times.
3. Common tree terminology includes root, leaf nodes, internal nodes, siblings, ancestors, descendants, depth, height, and subtrees. Binary trees restrict nodes to at most two children each.
Tree is a non-linear data structure that can represent hierarchical relationships. It consists of nodes connected by edges. The root node has child nodes, and nodes may be leaf nodes or have child nodes themselves. Binary trees restrict nodes to having at most two children. General trees can be converted to binary trees by making the first child the left child and next siblings the right child. Binary trees can be built from input data by comparing values to determine left or right placement, or from traversal operations.
This document provides an overview of representing graphs and Dijkstra's algorithm in Prolog. It discusses different ways to represent graphs in Prolog, including using edge clauses, a graph term, and an adjacency list. It then explains Dijkstra's algorithm for finding the shortest path between nodes in a graph and provides pseudocode for implementing it in Prolog using rules for operations like finding the minimum value and merging lists.
This PPT is all about the Tree basic on fundamentals of B and B+ Tree with it's Various (Search,Insert and Delete) Operations performed on it and their Examples...
This document discusses trees as a data structure. It defines key tree terminology like root, leaf nodes, ancestors and descendants. It describes different tree representations and traversal techniques including preorder, inorder and postorder sequences. It also covers different types of binary trees and basic tree operations like insertion, deletion and searching. Common applications of trees include representing arithmetic expressions, decision processes and priority queues.
A singly linked list is a linear data structure composed of nodes, where each node contains a data element and a link to the next node. The first node is referenced by a pointer called the head. Each node's link points to the next node in the list, with the last node's link pointing to null. Operations like insertion and deletion on singly linked lists can be performed by updating the links between nodes in constant time regardless of the list's size.
Each node in a doubly linked list contains two pointers - one pointing to the next node and one pointing to the previous node. This allows traversal in both directions through the list. A doubly linked list supports common operations like insertion and deletion at both ends of the list as well as anywhere in the list by updating the relevant pointer fields of the nodes. While requiring more space per node, doubly linked lists allow easy traversal backwards through the list and reversing of the list.
The document discusses various searching and sorting algorithms. It describes linear search, binary search, and interpolation search for searching unsorted and sorted lists. It also explains different sorting algorithms like bubble sort, selection sort, insertion sort, quicksort, shellsort, heap sort, and merge sort. Linear search searches sequentially while binary search uses divide and conquer. Sorting algorithms like bubble sort, selection sort, and insertion sort are in-place and have quadratic time complexity in the worst case. Quicksort, mergesort, and heapsort generally have better performance.
The document discusses graph traversal algorithms breadth-first search (BFS) and depth-first search (DFS). It provides examples of how BFS and DFS work, including pseudocode for algorithms. It also discusses applications of BFS such as finding shortest paths and detecting bipartitions. Applications of DFS include finding connected components and topological sorting.
The document defines and describes various graph concepts and data structures used to represent graphs. It defines a graph as a collection of nodes and edges, and distinguishes between directed and undirected graphs. It then describes common graph terminology like adjacent/incident nodes, subgraphs, paths, cycles, connected/strongly connected components, trees, and degrees. Finally, it discusses two common ways to represent graphs - the adjacency matrix and adjacency list representations, noting their storage requirements and ability to add/remove nodes.
Binary trees are a non-linear data structure where each node has at most two children, used to represent hierarchical relationships, with nodes connected through parent-child links and traversed through preorder, inorder, and postorder methods; they can be represented through arrays or linked lists and support common operations like search, insert, and delete through comparing node values and restructuring child pointers.
The document discusses red-black trees, which are self-balancing binary search trees. It describes the basic operations on dynamic sets like search, insert, and delete. It then explains the properties and structure of red-black trees, including that they ensure height is O(log n) through coloring nodes red or black. The insert and fixup algorithms are shown to maintain these properties and run in O(log n) time, providing efficient search tree operations.
This document discusses binary search trees (BST), including:
- The definition and properties of a BST, with nodes organized based on key values.
- Common BST operations like insertion, deletion, and searching in logarithmic time.
- Advantages of BSTs like efficient searching and working compared to arrays/lists.
- Applications of BSTs in databases, dictionaries, and evaluating expressions.
- Visual examples of searching, inserting, and deleting nodes from a BST.
The document discusses tree data structures and binary search trees. It defines key tree terminology like root, internal and leaf nodes. It explains tree traversal algorithms like preorder, inorder and postorder traversal using recursion and iteration. It also describes operations on binary search trees like searching, inserting and deleting nodes. The complexity of these BST operations is provided. Algorithms to find the inorder predecessor and successor of a node in a BST are presented.
Here are the answers to the assessment questions:
1. 2
2. 1
3. 4
4. 4
The key aspects of a splay tree are that accessing a node causes it to be rotated to the root, decreasing its future access time. This self-organizing behavior is what gives splay trees their efficiency.
The document discusses red-black trees, which are a type of self-balancing binary search tree. Red-black trees were invented in 1972 by Rudolf Bayer as a way to maintain the balancing of binary search trees during insertion and deletion operations. They support common binary search tree operations like search, insert, and delete in O(log n) time on average and worst case. The document outlines the properties and balancing operations used to maintain a red-black tree during insertions and deletions.
The document discusses red-black trees, which are binary search trees augmented with node colors to guarantee a height of O(log n). It first defines the properties of red-black trees, then proves their height is O(log n), and finally describes insertion and deletion operations. The key points are that nodes can be red or black, insertion can violate properties so recoloring is needed, and rotations are used to restructure the tree during insertion and deletion while maintaining the red-black properties.
Selection sort is a sorting algorithm that finds the smallest element in an unsorted list and swaps it with the first element, then finds the next smallest element and swaps it with the second element, continuing in this way until the list is fully sorted. It works by iterating through the list, finding the minimum element, and swapping it into its correct place at each step.
A doubly linked list allows traversal in both directions by storing references to both the next and previous nodes. Each node contains two references - a next link pointing to the next node and a prev link pointing to the previous node. This allows for quick insertion and removal at both ends as well as the middle of the list. Sentinel nodes are added at the beginning and end to simplify programming, with the header pointing forward and the trailer pointing backward.
1) Introduction to Trees.
2) Basic terminologies
3) Binary tree
4) Binary tree types
5) Binary tree representation
6) Binary search tree
7) Creation of a binary tree
8) Operations on binary search tree Trees
non linear data structure -introduction of treeSiddhi Viradiya
The document defines trees and binary trees. A tree consists of nodes connected by branches, with one root node and zero or more subtrees. A binary tree restricts each node to have at most two children. The document discusses tree terminology like root, child, parent, leaf nodes. It also covers tree traversal methods like preorder, inorder and postorder. Finally, it shows how to construct a binary tree from its traversals.
The document discusses stacks, which are a fundamental data structure used in programs. It defines a stack as a linear list of items where additions and deletions are restricted to one end, called the top. Common stack operations include push, which adds an element to the top, and pop, which removes an element from the top. Stacks have applications in parsing expressions, reversing strings, implementing depth-first search algorithms, and calculating arithmetic expressions in prefix and postfix notation. Stacks can be implemented using static arrays or dynamic arrays/linked lists.
This document discusses splay trees, a type of self-balancing binary search tree where frequently accessed elements are moved closer to the root through rotations. Splay trees provide O(log n) time for search, insert, and delete operations while being simpler to implement than other self-balancing trees. When an element is accessed in a splay tree, it is "splayed" or rotated to the root through zig, zig-zig, or zig-zag steps depending on its position. Splay trees prioritize frequently accessed elements but may become unbalanced if all elements are accessed sequentially. The document provides examples of splaying tree rotations and constructs splay trees for two example sequences.
In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.
This document provides an overview of representing graphs and Dijkstra's algorithm in Prolog. It discusses different ways to represent graphs in Prolog, including using edge clauses, a graph term, and an adjacency list. It then explains Dijkstra's algorithm for finding the shortest path between nodes in a graph and provides pseudocode for implementing it in Prolog using rules for operations like finding the minimum value and merging lists.
This PPT is all about the Tree basic on fundamentals of B and B+ Tree with it's Various (Search,Insert and Delete) Operations performed on it and their Examples...
This document discusses trees as a data structure. It defines key tree terminology like root, leaf nodes, ancestors and descendants. It describes different tree representations and traversal techniques including preorder, inorder and postorder sequences. It also covers different types of binary trees and basic tree operations like insertion, deletion and searching. Common applications of trees include representing arithmetic expressions, decision processes and priority queues.
A singly linked list is a linear data structure composed of nodes, where each node contains a data element and a link to the next node. The first node is referenced by a pointer called the head. Each node's link points to the next node in the list, with the last node's link pointing to null. Operations like insertion and deletion on singly linked lists can be performed by updating the links between nodes in constant time regardless of the list's size.
Each node in a doubly linked list contains two pointers - one pointing to the next node and one pointing to the previous node. This allows traversal in both directions through the list. A doubly linked list supports common operations like insertion and deletion at both ends of the list as well as anywhere in the list by updating the relevant pointer fields of the nodes. While requiring more space per node, doubly linked lists allow easy traversal backwards through the list and reversing of the list.
The document discusses various searching and sorting algorithms. It describes linear search, binary search, and interpolation search for searching unsorted and sorted lists. It also explains different sorting algorithms like bubble sort, selection sort, insertion sort, quicksort, shellsort, heap sort, and merge sort. Linear search searches sequentially while binary search uses divide and conquer. Sorting algorithms like bubble sort, selection sort, and insertion sort are in-place and have quadratic time complexity in the worst case. Quicksort, mergesort, and heapsort generally have better performance.
The document discusses graph traversal algorithms breadth-first search (BFS) and depth-first search (DFS). It provides examples of how BFS and DFS work, including pseudocode for algorithms. It also discusses applications of BFS such as finding shortest paths and detecting bipartitions. Applications of DFS include finding connected components and topological sorting.
The document defines and describes various graph concepts and data structures used to represent graphs. It defines a graph as a collection of nodes and edges, and distinguishes between directed and undirected graphs. It then describes common graph terminology like adjacent/incident nodes, subgraphs, paths, cycles, connected/strongly connected components, trees, and degrees. Finally, it discusses two common ways to represent graphs - the adjacency matrix and adjacency list representations, noting their storage requirements and ability to add/remove nodes.
Binary trees are a non-linear data structure where each node has at most two children, used to represent hierarchical relationships, with nodes connected through parent-child links and traversed through preorder, inorder, and postorder methods; they can be represented through arrays or linked lists and support common operations like search, insert, and delete through comparing node values and restructuring child pointers.
The document discusses red-black trees, which are self-balancing binary search trees. It describes the basic operations on dynamic sets like search, insert, and delete. It then explains the properties and structure of red-black trees, including that they ensure height is O(log n) through coloring nodes red or black. The insert and fixup algorithms are shown to maintain these properties and run in O(log n) time, providing efficient search tree operations.
This document discusses binary search trees (BST), including:
- The definition and properties of a BST, with nodes organized based on key values.
- Common BST operations like insertion, deletion, and searching in logarithmic time.
- Advantages of BSTs like efficient searching and working compared to arrays/lists.
- Applications of BSTs in databases, dictionaries, and evaluating expressions.
- Visual examples of searching, inserting, and deleting nodes from a BST.
The document discusses tree data structures and binary search trees. It defines key tree terminology like root, internal and leaf nodes. It explains tree traversal algorithms like preorder, inorder and postorder traversal using recursion and iteration. It also describes operations on binary search trees like searching, inserting and deleting nodes. The complexity of these BST operations is provided. Algorithms to find the inorder predecessor and successor of a node in a BST are presented.
Here are the answers to the assessment questions:
1. 2
2. 1
3. 4
4. 4
The key aspects of a splay tree are that accessing a node causes it to be rotated to the root, decreasing its future access time. This self-organizing behavior is what gives splay trees their efficiency.
The document discusses red-black trees, which are a type of self-balancing binary search tree. Red-black trees were invented in 1972 by Rudolf Bayer as a way to maintain the balancing of binary search trees during insertion and deletion operations. They support common binary search tree operations like search, insert, and delete in O(log n) time on average and worst case. The document outlines the properties and balancing operations used to maintain a red-black tree during insertions and deletions.
The document discusses red-black trees, which are binary search trees augmented with node colors to guarantee a height of O(log n). It first defines the properties of red-black trees, then proves their height is O(log n), and finally describes insertion and deletion operations. The key points are that nodes can be red or black, insertion can violate properties so recoloring is needed, and rotations are used to restructure the tree during insertion and deletion while maintaining the red-black properties.
Selection sort is a sorting algorithm that finds the smallest element in an unsorted list and swaps it with the first element, then finds the next smallest element and swaps it with the second element, continuing in this way until the list is fully sorted. It works by iterating through the list, finding the minimum element, and swapping it into its correct place at each step.
A doubly linked list allows traversal in both directions by storing references to both the next and previous nodes. Each node contains two references - a next link pointing to the next node and a prev link pointing to the previous node. This allows for quick insertion and removal at both ends as well as the middle of the list. Sentinel nodes are added at the beginning and end to simplify programming, with the header pointing forward and the trailer pointing backward.
1) Introduction to Trees.
2) Basic terminologies
3) Binary tree
4) Binary tree types
5) Binary tree representation
6) Binary search tree
7) Creation of a binary tree
8) Operations on binary search tree Trees
non linear data structure -introduction of treeSiddhi Viradiya
The document defines trees and binary trees. A tree consists of nodes connected by branches, with one root node and zero or more subtrees. A binary tree restricts each node to have at most two children. The document discusses tree terminology like root, child, parent, leaf nodes. It also covers tree traversal methods like preorder, inorder and postorder. Finally, it shows how to construct a binary tree from its traversals.
The document discusses stacks, which are a fundamental data structure used in programs. It defines a stack as a linear list of items where additions and deletions are restricted to one end, called the top. Common stack operations include push, which adds an element to the top, and pop, which removes an element from the top. Stacks have applications in parsing expressions, reversing strings, implementing depth-first search algorithms, and calculating arithmetic expressions in prefix and postfix notation. Stacks can be implemented using static arrays or dynamic arrays/linked lists.
This document discusses splay trees, a type of self-balancing binary search tree where frequently accessed elements are moved closer to the root through rotations. Splay trees provide O(log n) time for search, insert, and delete operations while being simpler to implement than other self-balancing trees. When an element is accessed in a splay tree, it is "splayed" or rotated to the root through zig, zig-zig, or zig-zag steps depending on its position. Splay trees prioritize frequently accessed elements but may become unbalanced if all elements are accessed sequentially. The document provides examples of splaying tree rotations and constructs splay trees for two example sequences.
In computer science, a tree is a widely used abstract data type (ADT)—or data structure implementing this ADT—that simulates a hierarchical tree structure, with a root value and subtrees of children with a parent node, represented as a set of linked nodes.
Splay trees are a self-adjusting binary search tree data structure. They perform basic operations like insertion, lookup, and removal in O(log n) amortized time by splaying nodes up the tree after access. This has the effect of moving frequently accessed nodes closer to the root over time. The document discusses the differences between splay trees and AVL trees, how splaying is done through different rotation cases, and how amortized analysis shows splay trees have O(log n) performance on average across operations.
Splay trees are a type of self-adjusting binary search tree that optimizes access to frequently used elements. They have the potential to achieve better than O(log n) time bounds due to splaying operations that rotate frequently accessed nodes toward the root. There are two approaches to splaying - bottom-up splaying which uses three rotation cases (zig, zig-zag, zig-zig) to move a node to the root, and top-down splaying which starts at the top and recombines subtrees. Splay trees are used for operations like find, delete minimum, and removal through these splaying techniques.
The document discusses trees as fundamental data structures that combine advantages of ordered arrays and linked lists by allowing fast searching, insertion, and deletion. It defines key tree terminology like root, parent, child, leaf nodes, subtrees, traversal, levels, and properties. Specific algorithms covered include minimum spanning trees and Kruskal's algorithm for finding a minimum spanning tree in a graph by greedily adding the lowest weight edge that connects two components.
This document provides information about different tree data structures including binary trees, binary search trees, AVL trees, red-black trees, splay trees, and B-trees. Binary search trees allow for fast searching and maintain an ordered structure. AVL and red-black trees are self-balancing binary search trees that ensure fast search, insert, and delete times by keeping the tree balanced. B-trees are multiway search trees that allow for efficient storage and retrieval of data in databases and file systems.
The document discusses heap trees, which are tree-based data structures where all nodes follow a specific ordering. There are two main types: max-heaps, where the root node has the greatest value of its children, and min-heaps, where the root node has the minimum value. Heaps are often stored as arrays for efficient implementation of operations like insertion, deletion, and merging in logarithmic time. Common applications of heaps include priority queues, sorting algorithms, and finding order statistics.
Splay trees are self-balancing binary search trees where recently accessed elements can be accessed quickly. Operations like insertion, search, and deletion are combined with a basic operation called splaying that rearranges the tree to place the accessed node at the root. This provides an amortized time complexity of O(log(n)) for operations. Splaying is performed using zig, zig-zig, and zig-zag steps depending on whether the node and its parent are the left or right child of their parent nodes. Insertion searches for a node then splays it to the root, while search splays a found node or returns null if not found. Deletion splays the tree to the parent of a deleted node or
Trees are fundamental data structures that combine advantages of ordered arrays and linked lists. They consist of nodes connected by edges, where nodes often represent entities and edges represent relationships between nodes. Common tree operations include traversing to visit all nodes in order, searching for a node by its key, and inserting or deleting nodes. These operations have O(log N) time complexity where N is the number of nodes. Binary trees restrict each node to at most two children while Huffman trees are used to compress data by assigning variable-length binary codes to characters based on their frequency.
Splay trees by NIKHIL ARORA (www.internetnotes.in)nikhilarora2211
Splay trees are self-adjusting binary search trees that improve access speed for frequently accessed nodes. They achieve this by moving recently accessed nodes closer to the root through rotations. The splay tree algorithm was developed in 1985 and offers logarithmic-time performance on average. It is well-suited for applications like network routing that see frequent repeats of certain data accesses. Splay trees perform surgery on the tree through six different rotation operations called splaying steps. The appropriate step depends on whether the node has a grandparent and its position relative to its parent and grandparent.
This document discusses various non-linear data structures including AVL trees, splay trees, B-trees, and red-black trees. It provides information on their properties, rotations, insertion, deletion, and search operations. AVL trees are self-balancing binary search trees that balance after each insertion or deletion. Splay trees dynamically balance trees by rotating nodes to the root after access. B-trees are balanced m-way search trees used for external storage, with nodes containing multiple sorted keys. Red-black trees are self-balancing binary search trees that use color attributes to balance rotations.
The presentation discusses splay trees and Euler tour trees. It defines a splay tree as a self-balancing binary search tree that rearranges elements recently accessed to the root through rotations. Splay trees have faster access times than other self-balancing trees like AVL and red-black trees. The presentation covers splay tree operations like search, insert, delete and the zig, zig-zag, and zig-zig splay steps. It also discusses Euler tour trees, which were invented by Euler and are used for dynamic connectivity problems by representing trees as node sequences.
Search tree,Tree and binary tree and heap treezia eagle
This document contains definitions and explanations of search trees and heaps. It defines search trees as data structures used for locating specific keys within a set where each node's key must be greater than keys in its left subtree and less than keys in its right subtree. It provides examples of constructing and performing operations on binary search trees like insertion, searching, and deletion. It defines heaps as binary trees that follow the shape and order property, with max heaps having each node greater than its children and min heaps having each node less than its children. It explains representing heaps in arrays and operations like deleting and inserting elements through reheapifying.
This document discusses binary trees and binary search trees. It defines key tree terms like root, child, parent, leaf nodes. It explains tree traversal methods like preorder, inorder and postorder. It also covers basic BST operations like insertion, search and deletion of nodes. Code snippets are provided to implement these operations and traversal methods on a sample binary search tree. Examples of traversing a sample tree in different orders are given.
This document discusses tree data structures and binary search trees. It begins with definitions of trees and their components like nodes, edges, and root/child relationships. It then covers tree traversals like preorder, inorder and postorder. Next, it defines binary search trees and their properties for storing and retrieving data efficiently. It provides examples of inserting, searching for, and deleting nodes from binary search trees. Searching and insertion are straightforward, while deletion has three cases depending on the number of child nodes.
Leveraging Generative AI to Drive Nonprofit InnovationTechSoup
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
This presentation was provided by Racquel Jemison, Ph.D., Christina MacLaughlin, Ph.D., and Paulomi Majumder. Ph.D., all of the American Chemical Society, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
3. The splay tree was invented by Daniel
Sleator and Robert Tarjan in 1985.[1]
A splay tree is a self-adjusting binary search tree with the
additional property that recently accessed elements are
quick to access again. ., splay trees perform better than
other search trees, even when the specific pattern of the
sequence is unknown
All normal operations on a binary search tree are combined
with one basic operation, called splaying.
oSplaying the tree for a certain element rearranges the
tree so that the element is placed at the root of the tree.
Presented By: M.Shahbaz
5. Splaying
When a node x is accessed, a splay operation is performed on x to move
it to the root. To perform a splay operation we carry out a sequence
of splay steps, each of which movesx closer to the root. By performing a
splay operation on the node of interest after every access, the recently
accessed nodes are kept near the root and the tree remains roughly
balanced, so that we achieve the desired amortized time bounds.
Each particular step depends on three factors:
Whether x is the left or right child of its parent node, p,
whether p is the root or not, and if not
whether p is the left or right child of its parent, g (the grandparent of x)..
Presented By: M.Shahbaz
7. Zig rotation:
this step is done when p is the root. The tree is rotated
on the edge between x and p. Zig steps exist to deal
with the parity issue and will be done only as the last
step in a splay operation and only when x has odd depth
at the beginning of the operation.
Presented By: M.Shahbaz
8. this step is done when p is not the root and x and p are either both right
children or are both left children. The picture below shows the case
where x and p are both left children. The tree is rotated on the edge
joining p with its parent g, then rotated on the edge joining x with p.
Note that zig-zig steps are the only thing that differentiate splay trees
from the rotate to root method introduced by Allen and Munro prior to
the introduction of splay trees.
Presented By: M.Shahbaz
9. this step is done when p is not the root and x is a right child
and p is a left child or vice versa. The tree is rotated on the edge
between p and x, and then rotated on the resulting edge
between x and g.
Presented By: M.Shahbaz
10. Starts the same as a BST with the new node
created at the a leaf. The new leaf node is
splayed until it becomes the root.
Splaying also occurs on
unsuccessful searches. The last
item on the access path is splayed
in this case.
Presented By: M.Shahbaz
12. • First access the node to force it to percolate
to the root.
• Remove the root.
• Determine the largest item in the left subtree
and rotate it to the root of the left subtree
which results in the left subtree new root
having no right child.
• The right subtree is then added as the right
child of the new root.
Presented By: M.Shahbaz
14. Good performance for a splay tree depends on the fact
that it is self-optimizing, in that frequently accessed nodes
will move nearer to the root where they can be accessed
more quickly. The worst-case height—though unlikely—is
O(n), with the average being O(log n).
Having frequently used nodes near the root is an
advantage for many practical applications (also see Locality
of reference), and is particularly useful for
implementing caches and garbage collection algorithms
Small memory footprint: Splay trees do not need to store
any bookkeeping data.
Presented By: M.Shahbaz
15. The most significant disadvantage of splay trees is that the
height of a splay tree can be linear.
The representation of splay trees can change even when
they are accessed in a 'read-only' manner (i.e.
by find operations). This complicates the use of such splay
trees in a multi-threaded environment.
Specifically, extra management is needed if multiple threads
are allowed to perform find operations concurrently. This
also makes them unsuitable for general use in purely
functional programming, although even there they can be
used in limited ways to implement priority queues.
Presented By: M.Shahbaz