The document discusses binary trees and their implementation and traversal methods. It defines a binary tree as a tree where each node has at most two children. It describes the common traversal orders of binary trees as inorder, preorder and postorder. It also discusses breadth first traversal and storing binary trees using node structures. Expression trees are described as binary trees used to represent mathematical expressions where leaves are operands and internal nodes are operators.
This document discusses binary trees, including their basic definitions, traversal methods, node representations, and functions. It describes binary trees as having a root node that partitions the tree into two disjoint subsets, left and right subtrees. Traversal methods like preorder, inorder, and postorder are explained recursively. Applications of binary search trees for sorting and searching arrays are also covered.
The document discusses various tree data structures and algorithms related to binary trees. It begins with an introduction to different types of binary trees such as strict binary trees, complete binary trees, and extended binary trees. It then covers tree traversal algorithms including preorder, inorder and postorder traversal. The document also discusses representations of binary trees using arrays and linked lists. Finally, it explains algorithms for operations on binary search trees such as searching, insertion, deletion and rebalancing through rotations in AVL trees.
The document discusses different types of trees including binary trees, binary search trees, and AVL trees. It defines key tree terminology like root, child, parent, leaf nodes. It explains tree traversal methods like preorder, inorder and postorder. It also discusses operations on binary search trees like insertion and search. For AVL trees, it defines balance factors and explains single and double rotations needed to maintain balance during insertion and deletion.
Binary search trees (BSTs) are binary trees where all keys in the left subtree of a node are less than or equal to the key of that node, and all keys in the right subtree are greater than or equal to the node's key. Common BST operations include search, insertion, deletion, finding the minimum/maximum keys, and tree traversals like inorder, preorder, and postorder walks. These operations have worst-case time complexity proportional to the height of the tree.
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.
1) Tree
2) General Tree
3) Binary Tree
4) Full Binay Tree, Complete Binay Tree
5) Binary Tree Traversal (DFS & BFS)
6) Binary Search Tree
7) Reconstruction of Binay Tree
8) Expression Tree
9) Evaluation of postfix expression
10) Infix to Prefix using stack
11) Infix to Postfix using stack
12) Threaded Binary Tree
13) AVL-Tree
14) AVL-Tree Rotation
The document discusses binary trees and binary search trees. It defines key terms like root, child, parent, leaves, height, depth. It explains tree traversal methods like preorder, inorder and postorder. It then describes binary search trees and how they store keys in a way that searching, insertion and deletion can be done efficiently in O(log n) time. It discusses implementation of operations like search, insert, delete on BSTs. It introduces balanced binary search trees like AVL trees that ensure height is O(log n) through rotations during insertions and deletions.
A binary search tree (BST) is a binary tree where the value of each node is greater than all values in its left subtree and less than all values in its right subtree. This property allows efficient search, insert, and delete operations in O(logN) time. To search a BST, the algorithm starts at the root and recursively checks if the target value is equal to, less than, or greater than the value of the current node to determine if it proceeds to the left or right child. Insertion finds the appropriate position to add a new node by recursively comparing its value to ancestors' values.
This document discusses binary trees, including their basic definitions, traversal methods, node representations, and functions. It describes binary trees as having a root node that partitions the tree into two disjoint subsets, left and right subtrees. Traversal methods like preorder, inorder, and postorder are explained recursively. Applications of binary search trees for sorting and searching arrays are also covered.
The document discusses various tree data structures and algorithms related to binary trees. It begins with an introduction to different types of binary trees such as strict binary trees, complete binary trees, and extended binary trees. It then covers tree traversal algorithms including preorder, inorder and postorder traversal. The document also discusses representations of binary trees using arrays and linked lists. Finally, it explains algorithms for operations on binary search trees such as searching, insertion, deletion and rebalancing through rotations in AVL trees.
The document discusses different types of trees including binary trees, binary search trees, and AVL trees. It defines key tree terminology like root, child, parent, leaf nodes. It explains tree traversal methods like preorder, inorder and postorder. It also discusses operations on binary search trees like insertion and search. For AVL trees, it defines balance factors and explains single and double rotations needed to maintain balance during insertion and deletion.
Binary search trees (BSTs) are binary trees where all keys in the left subtree of a node are less than or equal to the key of that node, and all keys in the right subtree are greater than or equal to the node's key. Common BST operations include search, insertion, deletion, finding the minimum/maximum keys, and tree traversals like inorder, preorder, and postorder walks. These operations have worst-case time complexity proportional to the height of the tree.
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.
1) Tree
2) General Tree
3) Binary Tree
4) Full Binay Tree, Complete Binay Tree
5) Binary Tree Traversal (DFS & BFS)
6) Binary Search Tree
7) Reconstruction of Binay Tree
8) Expression Tree
9) Evaluation of postfix expression
10) Infix to Prefix using stack
11) Infix to Postfix using stack
12) Threaded Binary Tree
13) AVL-Tree
14) AVL-Tree Rotation
The document discusses binary trees and binary search trees. It defines key terms like root, child, parent, leaves, height, depth. It explains tree traversal methods like preorder, inorder and postorder. It then describes binary search trees and how they store keys in a way that searching, insertion and deletion can be done efficiently in O(log n) time. It discusses implementation of operations like search, insert, delete on BSTs. It introduces balanced binary search trees like AVL trees that ensure height is O(log n) through rotations during insertions and deletions.
A binary search tree (BST) is a binary tree where the value of each node is greater than all values in its left subtree and less than all values in its right subtree. This property allows efficient search, insert, and delete operations in O(logN) time. To search a BST, the algorithm starts at the root and recursively checks if the target value is equal to, less than, or greater than the value of the current node to determine if it proceeds to the left or right child. Insertion finds the appropriate position to add a new node by recursively comparing its value to ancestors' values.
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.
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.
The document discusses binary search trees and their implementation. It begins by defining binary trees and their properties. It then describes how binary search trees work, with the key property that for every node, all keys in its left subtree are smaller than the node's key and all keys in its right subtree are larger. It provides pseudocode for basic binary search tree operations like search, insert, delete, find minimum and maximum. Finally, it introduces AVL trees, which are self-balancing binary search trees that ensure fast lookup by keeping the height of left and right subtrees close.
The document outlines a presentation on trees and binary trees. It discusses different tree types including binary trees, complete binary trees, and binary search trees. It covers tree traversal methods like preorder, inorder and postorder traversal. It also discusses representations of binary trees using arrays and linked lists and algorithms for insertion and deletion in binary search trees.
The document discusses binary search trees and their operations. It covers definitions of binary search trees, how to search, find the minimum/maximum keys, insert and delete nodes. It then discusses AVL trees, which are self-balancing binary search trees where the heights of the left and right subtrees of every node differ by at most one. It explains rotations needed during insertions and deletions to maintain balance in AVL trees.
A binary tree is composed of nodes where each node contains a value and pointers to its left and right children. A binary tree traversal involves systematically visiting each node by traversing either breadth-first or depth-first. Breadth-first traversal visits nodes by level while depth-first traversal can be pre-order, in-order, or post-order depending on when the node is visited. Threaded binary trees reduce the number of null pointers by using them to point to other nodes for more efficient traversals.
This document discusses binary trees and their traversal. It defines binary trees, their properties such as levels and degrees of nodes. It describes different types of binary trees like complete, skewed, etc. It also explains different traversal techniques like preorder, inorder and postorder traversals and provides algorithms to implement these traversals recursively as well as using stacks. Memory representations of binary trees like sequential and linked are also summarized.
This document discusses binary search trees and efficient binary trees. It begins by explaining what a binary search tree is and how it allows for efficient searching in O(log n) time. It then discusses how to create, search, insert, delete, determine the height and number of nodes in a binary search tree. The document also covers mirrored binary trees, threaded binary trees, and AVL trees, which are self-balancing binary search trees that ensure searching remains O(log n) time.
The document discusses trees as a data structure. It begins by defining basic tree concepts such as nodes, branches, degrees of nodes, roots, leaves, internal nodes, parents, children, siblings, ancestors, descendants, paths, levels, heights, and subtrees. It then discusses binary trees specifically and their properties including traversal methods. Finally, it covers balanced binary search trees and techniques for maintaining balance such as rotations during insertions and deletions.
Tree and Binary search tree in data structure.
The complete explanation of working of trees and Binary Search Tree is given. It is discussed such a way that everyone can easily understand it. Trees have great role in the data structures.
The document provides an overview of different tree data structures including binary trees, binary search trees, AVL trees, B-trees, and B+ trees. It describes key properties such as balance factors for AVL trees and minimum/maximum node sizes for B-trees. Implementation details are given for binary trees, binary search trees, and some common tree operations like search, insert, delete. Applications of trees in indexing large datasets are also mentioned.
1. The document discusses AVL trees, which are self-balancing binary search trees. It provides examples of inserting values into an initially empty AVL tree, showing the tree after each insertion and any necessary rotations to maintain balance.
2. Deletion from an AVL tree is more complex than insertion, as it may require rotations at each level to restore balance, with a worst case of log2N rotations. The document outlines the deletion procedure and provides an example requiring multiple rotations.
1) AVL trees are self-balancing binary search trees that maintain an O(log n) search time by ensuring the heights of the two child subtrees differ by at most 1 with rotations after insertions and deletions.
2) The balance factor of a node is defined as the height of its left subtree minus the height of its right subtree, and must be -1, 0, or 1 in an AVL tree.
3) There are four types of rotations (single, double) to rebalance the tree - right-right, left-left, left-right, and right-left - depending on the balance factor violated after an insertion or deletion.
This document defines and provides examples of trees and binary trees. It begins by defining trees as hierarchical data structures with nodes and edges. It then provides definitions for terms like path, forest, ordered tree, height, and multiway tree. It specifically defines binary trees as having two children per node. The document gives examples and properties of binary trees, including full, complete, and binary search trees. It also explains linear and linked representations of binary trees and different traversal methods like preorder, postorder and inorder. Finally, it provides examples of insertion and deletion operations in binary search trees.
The document describes a course on advanced data structures. It provides information on the instructor, teaching assistant, topics to be covered including AVL and Red Black Trees, objectives of learning deletions, insertions and searches in logarithmic time. It also lists credits to other professors and researchers. The document then goes into details about balanced binary search trees, describing properties of AVL Trees and Red Black Trees to ensure the tree remains balanced during operations.
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 discusses binary trees, including their terminology, implementation, operations, and traversal methods. It lists the group members and then defines key binary tree concepts like nodes, children, parents, roots, and leaf nodes. It explains that a binary tree has at most two children per node, and describes how to implement one using linked lists. Common binary tree operations like searching, insertion, deletion, creation, and traversing are then covered with examples. The different traversal orders - preorder, inorder, postorder, and level order - are defined along with examples.
The document discusses binary trees and their representations and operations. It defines binary trees as trees where each node has at most two child nodes. It also defines complete binary trees as trees where every node has two children except leaf nodes. The document discusses array and linked representations of binary trees and various traversal operations like preorder, inorder and postorder traversals. It also provides code snippets for inserting and deleting nodes from a binary tree.
The document discusses various tree data structures, including binary trees and binary search trees. It provides definitions and examples of binary trees, their terminology like root, left/right subtrees, and tree traversal methods including preorder, inorder and postorder. It also discusses applications of binary search trees for searching, as well as operations on trees like inserting, deleting and traversing nodes.
1) Tree data structures involve nodes that can have zero or more child nodes and at most one parent node. Binary trees restrict nodes to having zero, one, or two children.
2) Binary search trees have the property that all left descendants of a node are less than the node's value and all right descendants are greater. This allows efficient searching in O(log n) time.
3) Common tree operations include insertion, deletion, and traversal. Balanced binary search trees use rotations to maintain balance during these operations.
Glamping y aguas termales: vacaciones en contacto con la naturaleza para reca...GaliWonders
Vivir la experiencia de sumergirte en aguas termales al aire libre, disfrutar de unas vistas increibles de la ciudad de Ourense y, además poder alojarte en una novedosa cabaña en mitad del bosque.
Los maestros tienen el poder de controlar a los estudiantes y soldados a través de su cuerpo y tiempo, guiándolos hacia grandes logros y tesoros a través de actividades con gran pasión.
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.
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.
The document discusses binary search trees and their implementation. It begins by defining binary trees and their properties. It then describes how binary search trees work, with the key property that for every node, all keys in its left subtree are smaller than the node's key and all keys in its right subtree are larger. It provides pseudocode for basic binary search tree operations like search, insert, delete, find minimum and maximum. Finally, it introduces AVL trees, which are self-balancing binary search trees that ensure fast lookup by keeping the height of left and right subtrees close.
The document outlines a presentation on trees and binary trees. It discusses different tree types including binary trees, complete binary trees, and binary search trees. It covers tree traversal methods like preorder, inorder and postorder traversal. It also discusses representations of binary trees using arrays and linked lists and algorithms for insertion and deletion in binary search trees.
The document discusses binary search trees and their operations. It covers definitions of binary search trees, how to search, find the minimum/maximum keys, insert and delete nodes. It then discusses AVL trees, which are self-balancing binary search trees where the heights of the left and right subtrees of every node differ by at most one. It explains rotations needed during insertions and deletions to maintain balance in AVL trees.
A binary tree is composed of nodes where each node contains a value and pointers to its left and right children. A binary tree traversal involves systematically visiting each node by traversing either breadth-first or depth-first. Breadth-first traversal visits nodes by level while depth-first traversal can be pre-order, in-order, or post-order depending on when the node is visited. Threaded binary trees reduce the number of null pointers by using them to point to other nodes for more efficient traversals.
This document discusses binary trees and their traversal. It defines binary trees, their properties such as levels and degrees of nodes. It describes different types of binary trees like complete, skewed, etc. It also explains different traversal techniques like preorder, inorder and postorder traversals and provides algorithms to implement these traversals recursively as well as using stacks. Memory representations of binary trees like sequential and linked are also summarized.
This document discusses binary search trees and efficient binary trees. It begins by explaining what a binary search tree is and how it allows for efficient searching in O(log n) time. It then discusses how to create, search, insert, delete, determine the height and number of nodes in a binary search tree. The document also covers mirrored binary trees, threaded binary trees, and AVL trees, which are self-balancing binary search trees that ensure searching remains O(log n) time.
The document discusses trees as a data structure. It begins by defining basic tree concepts such as nodes, branches, degrees of nodes, roots, leaves, internal nodes, parents, children, siblings, ancestors, descendants, paths, levels, heights, and subtrees. It then discusses binary trees specifically and their properties including traversal methods. Finally, it covers balanced binary search trees and techniques for maintaining balance such as rotations during insertions and deletions.
Tree and Binary search tree in data structure.
The complete explanation of working of trees and Binary Search Tree is given. It is discussed such a way that everyone can easily understand it. Trees have great role in the data structures.
The document provides an overview of different tree data structures including binary trees, binary search trees, AVL trees, B-trees, and B+ trees. It describes key properties such as balance factors for AVL trees and minimum/maximum node sizes for B-trees. Implementation details are given for binary trees, binary search trees, and some common tree operations like search, insert, delete. Applications of trees in indexing large datasets are also mentioned.
1. The document discusses AVL trees, which are self-balancing binary search trees. It provides examples of inserting values into an initially empty AVL tree, showing the tree after each insertion and any necessary rotations to maintain balance.
2. Deletion from an AVL tree is more complex than insertion, as it may require rotations at each level to restore balance, with a worst case of log2N rotations. The document outlines the deletion procedure and provides an example requiring multiple rotations.
1) AVL trees are self-balancing binary search trees that maintain an O(log n) search time by ensuring the heights of the two child subtrees differ by at most 1 with rotations after insertions and deletions.
2) The balance factor of a node is defined as the height of its left subtree minus the height of its right subtree, and must be -1, 0, or 1 in an AVL tree.
3) There are four types of rotations (single, double) to rebalance the tree - right-right, left-left, left-right, and right-left - depending on the balance factor violated after an insertion or deletion.
This document defines and provides examples of trees and binary trees. It begins by defining trees as hierarchical data structures with nodes and edges. It then provides definitions for terms like path, forest, ordered tree, height, and multiway tree. It specifically defines binary trees as having two children per node. The document gives examples and properties of binary trees, including full, complete, and binary search trees. It also explains linear and linked representations of binary trees and different traversal methods like preorder, postorder and inorder. Finally, it provides examples of insertion and deletion operations in binary search trees.
The document describes a course on advanced data structures. It provides information on the instructor, teaching assistant, topics to be covered including AVL and Red Black Trees, objectives of learning deletions, insertions and searches in logarithmic time. It also lists credits to other professors and researchers. The document then goes into details about balanced binary search trees, describing properties of AVL Trees and Red Black Trees to ensure the tree remains balanced during operations.
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 discusses binary trees, including their terminology, implementation, operations, and traversal methods. It lists the group members and then defines key binary tree concepts like nodes, children, parents, roots, and leaf nodes. It explains that a binary tree has at most two children per node, and describes how to implement one using linked lists. Common binary tree operations like searching, insertion, deletion, creation, and traversing are then covered with examples. The different traversal orders - preorder, inorder, postorder, and level order - are defined along with examples.
The document discusses binary trees and their representations and operations. It defines binary trees as trees where each node has at most two child nodes. It also defines complete binary trees as trees where every node has two children except leaf nodes. The document discusses array and linked representations of binary trees and various traversal operations like preorder, inorder and postorder traversals. It also provides code snippets for inserting and deleting nodes from a binary tree.
The document discusses various tree data structures, including binary trees and binary search trees. It provides definitions and examples of binary trees, their terminology like root, left/right subtrees, and tree traversal methods including preorder, inorder and postorder. It also discusses applications of binary search trees for searching, as well as operations on trees like inserting, deleting and traversing nodes.
1) Tree data structures involve nodes that can have zero or more child nodes and at most one parent node. Binary trees restrict nodes to having zero, one, or two children.
2) Binary search trees have the property that all left descendants of a node are less than the node's value and all right descendants are greater. This allows efficient searching in O(log n) time.
3) Common tree operations include insertion, deletion, and traversal. Balanced binary search trees use rotations to maintain balance during these operations.
Glamping y aguas termales: vacaciones en contacto con la naturaleza para reca...GaliWonders
Vivir la experiencia de sumergirte en aguas termales al aire libre, disfrutar de unas vistas increibles de la ciudad de Ourense y, además poder alojarte en una novedosa cabaña en mitad del bosque.
Los maestros tienen el poder de controlar a los estudiantes y soldados a través de su cuerpo y tiempo, guiándolos hacia grandes logros y tesoros a través de actividades con gran pasión.
O documento apresenta diversas citações sobre a relação entre humanos e cães. Em três frases ou menos, o documento resume que cães são animais leais e amorosos que trazem alegria para as pessoas, e que a relação entre eles é baseada no afeto e na confiança mútua.
Este documento describe la magnitud del problema de las enfermedades crónicas en Chile. Las enfermedades crónicas afectan predominantemente a los adultos mayores y representan un desafío importante para la salud pública. Las tres principales causas de muerte en Chile son las enfermedades cardiovasculares, los tumores malignos y los traumatismos. Las enfermedades crónicas más comunes incluyen las cardiovasculares, el cáncer, la diabetes y las enfermedades pulmonares y mentales.
El documento presenta una actividad interactiva en la que los usuarios pueden mover el mouse sobre los personajes para obtener más información sobre ellos.
Las dificultades en el aprendizaje se refieren a cinco grupos: problemas escolares, bajo rendimiento escolar, dificultades específicas de aprendizaje, trastorno por déficit de atención con hiperactividad, y discapacidad intelectual límite. Los problemas escolares se manifiestan como dificultades en los aprendizajes y adaptación escolar, afectando de modo leve y puntual el aprendizaje. Las características incluyen rendimiento por debajo de la capacidad y alteraciones en procesos psicoló
Assemblea constitutiva Palamós i Sant Joan per l'AutodeterminacióPere Minobas Suquet
La plataforma ciutadana Palamós i Sant Joan per l’Autodeterminació, es va reunir ahir dia 6 de novembre de 2009 a la biblioteca Lluís Barceló i Bou per dur a terme l’assemblea constitutiva d’aquesta.
A l’acte hi van assistir un centenar de persones mostrant així el seu interès, oferint la col·laboració i suport necessaris per poder dur a terme el referèndum.
Este documento describe el proceso psicosocial del envejecimiento desde tres perspectivas: comunicarse, elegir según creencias y valores, y autorrealización. Cada perspectiva analiza los aspectos físicos, psíquicos y sociales del envejecimiento y cómo estos permiten o promueven dicho proceso. También define el envejecimiento desde las perspectivas de Harman y Streheler, describiendo los cambios físicos, psíquicos y biológicos asociados con la edad.
The document advertises a conference package from the Park Inn Cardiff City Centre hotel. It offers a 50% discount on day delegate rates for multiple bookings as part of its "Fifty-Fifty" campaign. The day delegate rate includes tea/coffee, a 2-course lunch buffet, meeting room hire, AV equipment, stationery, and discounted parking. It also notes the hotel's recently refurbished meeting rooms and provides details on their capacities.
This document provides an introduction to using Puppet including quick primers on its basic concepts like resources, classes, nodes, and data parameters. It also gives examples of useful Puppet commands and demonstrates how to configure sudoers permissions on different operating systems using Puppet manifests and inheriting classes. References for additional Puppet documentation and guides are provided at the end.
El documento describe el tercer sector y sus diferentes clasificaciones. El tercer sector está conformado por organizaciones sin fines de lucro que buscan contribuir al bienestar social. Se clasifican en población civil (asociaciones civiles, fundaciones, instituciones de beneficencia privada), sector privado, sector gubernamental, sector religioso y organizaciones internacionales.
El documento describe brevemente la historia y los tipos de estadística. Explica que la estadística descriptiva se dedica a analizar y representar datos, mientras que la estadística inferencial comprende métodos para deducir propiedades de una población. Además, resume que las civilizaciones antiguas ya recolectaban y analizaban datos, y que la estadística moderna se desarrolló principalmente durante los siglos XVIII y XIX.
Este documento plantea tres preguntas sobre posibles relaciones entre variables: si existe relación entre el tipo de centro educativo y elegir enfermería como primera opción, si existe relación entre elegir enfermería como primera opción y el sexo, y si existe relación entre el gasto mensual en el móvil y el sexo.
The document discusses binary search trees and their properties. It explains that a binary search tree is a binary tree where every node's left subtree contains values less than the node's value and the right subtree contains greater values. Operations like search, insert, delete can be done in O(h) time where h is the height of the tree. The height is O(log n) for balanced trees but can be O(n) for unbalanced trees. The document also provides examples of using a binary search tree to sort a set of numbers in O(n log n) time by building the BST and doing an inorder traversal.
The document discusses binary search trees and different ways to traverse them. It explains that traversing a binary search tree can be done in preorder, inorder, or postorder fashion by recursively visiting the left child, then the node, then the right child in different orders. Searching for a value in a balanced binary search tree takes O(log n) time, while searching an unsorted linked list takes O(n) time.
Content of slide
Tree
Binary tree Implementation
Binary Search Tree
BST Operations
Traversal
Insertion
Deletion
Types of BST
Complexity in BST
Applications of BST
The document discusses various tree traversal algorithms and operations on binary trees. It explains breadth-first traversal, depth-first traversal including preorder, inorder and postorder. It also covers searching, inserting and checking if two trees are the same in binary trees. Other topics covered include finding the size, height, root-to-leaf sums, checking if a tree is a binary search tree, and level order traversal. Iterative algorithms for postorder, preorder and inorder traversal using stacks are also presented.
The document discusses trees and graphs data structures. It begins with introducing different types of trees like binary trees, binary search trees, threaded binary trees, and their various traversal algorithms like inorder, preorder and postorder traversals. It then discusses tree operations like copying trees, testing for equality. It also covers the satisfiability problem and how binary trees can be used to represent logical expressions to solve this problem. Finally, it discusses threaded binary trees where null links in a binary tree are replaced with threads, and how this allows for efficient inorder traversal in linear time.
Trees are hierarchical data structures that can represent relationships between data items. They are useful for representing organizational charts, file systems, and programming environments. Key tree concepts include the root node, internal and leaf nodes, ancestors and descendants, subtrees, depth, height, and degree. Common tree operations include traversing the tree using preorder, inorder, and postorder traversal methods, evaluating expression trees, and using trees for data compression through Huffman coding. Huffman coding assigns variable-length binary codes to characters based on their frequency, allowing more common characters to have shorter codes to reduce the overall file size.
This document discusses trees and graphs as tree-like data structures. It defines key terminology used for trees like nodes, edges, roots, and leaves. It also describes different types of trees like binary search trees and balanced trees. The document provides examples of implementing tree data structures recursively using class definitions. It explains algorithms for traversing trees, specifically depth-first search (DFS) and breadth-first search (BFS). DFS is demonstrated step-by-step on a sample tree. The document also briefly mentions graphs as another tree-like structure.
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
This document introduces binary trees and provides a series of practice problems of increasing difficulty related to binary trees. It begins with an introduction to binary tree structure and terminology. It then provides 14 binary tree problems with descriptions and hints for solving each problem. The problems involve tasks like counting nodes, finding minimum/maximum values, printing trees in different orders, checking for paths with a given sum, and printing all root-to-leaf paths. Sample solutions are provided in subsequent sections in C/C++ and Java languages.
The document discusses binary tree traversal methods. It defines key binary tree terminology like nodes, edges, root, and provides examples of different types of binary trees like strictly binary, complete, and almost complete binary trees. It also explains the three common traversal techniques for binary search trees - in-order, pre-order and post-order traversals - and provides pseudocode algorithms and examples for each traversal method.
This document introduces binary trees and provides sample code for basic operations like lookups and inserts. It discusses the structure of binary trees, with nodes containing left/right pointers and data. Binary search trees require that all left subtree nodes are less than the parent and right greater. Sample C/C++ code is given for lookup and insert functions that demonstrate the recursive traversal and modification of the tree. The document aims to prepare the reader to solve practice problems of increasing difficulty involving binary trees and pointers.
Tree Leetcode - Interview Questions - Easy CollectionsSunil Yadav
The document discusses 4 common interview questions involving binary tree data structures:
1. Maximum Depth of Binary Tree, which finds the maximum number of nodes along the longest path from the root to a leaf node.
2. Validate Binary Search Tree, which checks if a binary tree satisfies the properties of a binary search tree.
3. Binary Tree Level Order Traversal, which returns the nodes of a binary tree level by level from left to right in a 2D list.
4. Convert Sorted Array to Binary Search Tree, which constructs a height-balanced binary search tree from a given sorted array.
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 binary tree representation and traversal methods. It provides two main representations of binary trees - array and linked representations. It also describes different types of binary trees like full, complete, left-skewed, and right-skewed trees. The document then explains three common traversal techniques for binary trees - inorder, preorder, and postorder traversals. Algorithms and code snippets are given for each traversal. Finally, applications of binary tree traversals are discussed along with expression trees and converting infix to postfix notation using a stack.
The document discusses tree data structures and binary trees. It provides definitions for key tree terminology like root, child, parent, leaf nodes, and discusses tree traversal methods like preorder, inorder, and postorder traversal. It also covers implementing binary trees using linked lists and building binary search trees with functions for insertion, searching, and deletion of nodes.
The document discusses different types of binary tree traversal including inorder, preorder, and postorder traversal. It provides C code examples to perform each type of traversal on a binary search tree. The code inserts nodes into the tree, then performs the specified traversal by recursively navigating the tree and printing out the node values at each step according to the traversal type. Sample output is shown for building a binary search tree and performing various traversals on it by selecting options from a menu.
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
Web-IT Support and Consulting - dBase exportsDirk Cludts
The document describes a multi-step process for converting multiple dBase files to CSV format for easier use in Excel and SQL Server. It involves using VBA macros in Excel to:
1) Define source and destination folders and file settings like delimiters
2) Loop through all files in the source folder, opening and exporting the data to individual CSV files in the destination folder
3) Close the files and move to the next one until all are converted
Running the macro will automatically convert hundreds of dBase files to CSV in one go. The document provides detailed code explanations and instructions.
Web-IT Support and Consulting - bulk dBase (DBF) exports via Microsoft Excel ...Dirk Cludts
If you're working with dBase files and want them to migrate to MS SQL Server or export them into CSV files? If so, this handy white paper will be important for you.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...PECB
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2. Binary Trees
Tree with no node having more than two children.
A finite set of nodes, one of which is designated as the root.
The root node may have at most two sub-trees, each of which
is also a binary tree.The two sub-trees of a given node are
ordered and we refer to them as left child and the right child.
Respectively.
3. Binary Trees
Nodes in a binary tree may
have zero, one or two
children.
The maximum number of
nodes at a given level/depth i
is
2i-1 for i ≥ 1
(Considering the level/depth of root
node as i = 1)
A
B C
D E F
G H
4. Binary Trees
The maximum number of
nodes for an entire
binary tree of depth k is.
2k-1 for k ≥ 1
A full binary tree of
depth k is a binary tree
with 2k-1 nodes.
That is the maximum
number of nodes a binary
tree can have.
A
B C
D E F
G H
Max. No of Node = 15
6. Binary Tree Implementation
ElementVariable will serve as our data field.
Left and Right points to the two sub-trees.
Value NULL indicates the absence of a sub-tree.
Root points at the root node of the tree.
Root == NULL indicates an empty tree.
7. Binary Tree Traversal
Visiting each node exactly once, is calledTraversal.
When positioned at any given node a traversal function
may
Continue down to left sub-tree or
Continue down to right sub-tree or
Or process the current node
Still leaves open the question of when we should process
the data item.
8. Binary Tree Traversal
To process the data item we have the following options.
Visit the node before moving down the left sub-tree.
(Preorder)
Visit the node after traversing the left sub-tree but before
traversing the right sub-tree. (Inorder)
Visit the after traversing both sub-trees. (PostOrder)
9. Binary Tree Traversal
InorderTraversal
1. Move down the tree as far left as possible
2. Visit the current node
3. Backup one node in the tree and visit it.
4. Move down the right sub-tree of the node visited in step 3.
5. Repeat the step 1 to 5 until all nodes have been processed.
65. Expression Trees
Is a BinaryTree.
Leaves of an expression tree are operand, such as
constants or variable names.
Other nodes contain the operators.
66. Expression Trees
We can evaluate and expression tree by applying the
operator at the root to the values obtained by recursively
evaluating the left and right sub-trees.
(a + b * c) +((d * e + f) *g)
*
b c
a
+
d e
*
+
f
*
g
+
74. Expression Trees
Postfix Expression to ExpressionTree
a b + c d e + * *
a
b
a, b are operands push pointers to
their nodes in the stack
75. Expression Trees
Postfix Expression to ExpressionTree
a b + c d e + * *
a b
+ operator , pop the last two
pointers, create a new expression
tree. Push pointer to its root back in
stack.
+
76. Expression Trees
Postfix Expression to ExpressionTree
a b + c d e + * *
a b
push pointers to the nodes of the
operands c, d & e
+
c
d
e
77. Expression Trees
Postfix Expression to ExpressionTree
a b + c d e + * *
a b
+ operator , pop the last two
pointers, create a new expression
tree. Push pointer to its root back in
stack.
+
c
d e
+
78. Expression Trees
Postfix Expression to ExpressionTree
a b + c d e + * *
a b
* operator , pop the last two
pointers, create a new expression
tree. Push pointer to its root back in
stack.
+
c
d e
+
*
79. Expression Trees
Postfix Expression to ExpressionTree
a b + c d e + * *
a b
* operator again, pop the last two
pointers, create a new expression
tree. Push pointer to its root back in
stack.
+
c
d e
+
*
*
80. Binary Search Trees
A binary tree , used for searching.
Each node in the tree is assigned a key value.
Keys are assumed as distinct.
81. Binary Search Trees
For every node X in
the tree
Left Sub-tree key
values < X < Right
Sub-tree key values.
4
3 5
1
2
7 9
8
10
11
12
13
6
84. Binary Search Tree Implementation
FindValue
Requires returning a pointer to the node in treeT that has the
key value.
IfT is Null return NULL, if the key stored at T is X, we can
returnT. Otherwise depending on the less than and greater
than relationship we can traverse the tree recursively either on
the left sub tree or the right subtree.
86. Binary Search Tree Implementation
Find MinimumValue
Get us the minimum or smallest key value in the tree.
For Find Minimum, start at the root and go left as long as there
is a left child.
87. Binary Tree Implementation
Position FindMin(SearchTree T)
{
if (T == NULL)
{
return NULL;
}else
if (TLeft == NULL)
{
return T;
}else
Return FindMin(TLeft);
}
88. Binary Search Tree Implementation
Find MaximumValue
Get us the maximum or largest key value in the tree.
For Find Maximum start at the root and go right as long as
there is a right child.
89. Binary Tree Implementation
Position FindMax(SearchTree T)
{
if (T == NULL)
{
return NULL;
}else
if (TRight == NULL)
{
return T;
}else
Return FindMin(TRight);
}
90. Binary Search Tree Implementation
Insert (Duplication Not Allowed)
Proceed down the tree in similar fashion as we did in Find
Function.
Insert X at the last spot on the path traversed.
92. Binary Search Tree Implementation
Delete
If the node is a leaf , it can be deleted immediately.
If the node has one child, the node can be deleted after its
parent adjust a pointer to bypass the node.
If the node has two children, replace the data of this node with
the smallest data of the right sub-tree and recursively delete
that node.
99. Binary Search Tree Implementation
SearchTree Delete(ElementType X, SearchTree T)
{
Position TempCell
if (T == NULL)
{
Error(“Element Not Found”);
}else
if (X < TElement)
{
TLeft = Delete(X,TLeft);
} else
if (X > TElement)
{
TRight = Delete(X,TRight);
} else
// contd. On next page
}
100. Binary Search Tree Implementation
SearchTree Delete(ElementType X, SearchTree T)
{….
If (TLeft && TRight) // left and right child //
{
TmpCell = FindMin(TRight);
TElement = TmpCellElement;
TRight = Delete(TElement, TRight);
}
Else
{
TmpCell = T;
If (TLeft == NULL) // leaves , no children //
{
T = TRight;
}else if (TRight == NULL)
{
T = TLeft;
}
Free(TmpCell);
}
return T;
}
101. AVL Trees
Binary search tree with a balance condition.
The balance condition must be easy to maintain and it
ensures that the dept of the tree is O(log n).
Idea is to acquire same height on the left and right sub-
trees.
Prevent a worst case running time of O(n). i.e. a left-iest
or right-iest tree.A tree structure looking like a linear list.
102. AVL Trees
Balanced Condition
left height(n) = 0 if n has no left child.
= 1 + height(left child(n)) for all other nodes.
right height(n) = 0 if n has no right child.
= 1 + height(right child(n)) for all other nodes.
Balance(n) = right height(n) – left height(n)
103. AVL Trees
Balance condition indicates the relative height of its right
sub-tree compares to its left.
If the balance is positive the right sub-tree has greater
depth than the left sub-tree.
If the balance is negative the left sub-tree has greater
depth than the right sub-tree.
A binary tree is an AVL tree if and only if every node in
the tree has a balance of -1 , 0 or +1.
104. AVL Trees
x
2
5
0 0
1
0 0 0 0
1 1
2
51
0 0 1 0
1 2
4
0 0
balance = right height – left height
= 0 - 0 (AVL Tree)
balance = right height – left height
= 2 – 1 = 1 (AVL Tree)
balance = right height – left height
= 1 – 1 = 0 (AVL Tree)
106. AVL Trees
Height of the two child sub-trees of any node differ by at
most one; therefore it is also said to be height-balanced.
Searching, Insert and Delete all take O(log n) in both
average and worst cases.Where n is the number of nodes
in the tree prior to the operation.
Insertions and deletions may require the tree to be
rebalanced by one or more tree rotation.
Node with balance factor 1,0 or -1 is considered
balanced.
Node with any other balance factor is called unbalance
and need to be rotated or rebalanced.
124. AVL Tree Insertion
Trace the path from the root node to a leaf node.
Insert the new node.
Retrace the path back up to the root, adjusting balances
along the way.
If a nodes balance is out of the bound condition i.e.
-1 > balance >1. rotate and rebalance.
125. AVL Tree Insertion
Rotation
Singly Rotation
It preserves the Ordered property of the tree.
It restores all nodes to appropriate AVL balance.
Preserves the Inorder traversal of the tree i.e. Inorder traversal will
access nodes in the same order after transformation.
Only modify three pointers to accomplish the rebalancing.
126. AVL Trees Implementation
Singly Rotation ( Left and Right )
Right Rotation of Root Q results in Q stepping down a
hierarchy. P becomes Root with Q as right child and right child
of P becomes left child of Q.