B-Trees are tree data structures used to store data on disk storage. They allow for efficient retrieval of data compared to binary trees when using disk storage due to reduced height. B-Trees group data into nodes that can have multiple children, reducing the height needed compared to binary trees. Keys are inserted by adding to leaf nodes or splitting nodes and promoting middle keys. Deletion involves removing from leaf nodes, borrowing/promoting keys, or joining nodes.
Binary search trees (BSTs) are data structures that allow for efficient searching, insertion, and deletion. Nodes in a BST are organized so that all left descendants of a node are less than the node's value and all right descendants are greater. This property allows values to be found, inserted, or deleted in O(log n) time on average. Searching involves recursively checking if the target value is less than or greater than the current node's value. Insertion follows the search process and adds the new node in the appropriate place. Deletion handles three cases: removing a leaf, node with one child, or node with two children.
Presentation On Binary Search Tree using Linked List Concept which includes Traversing the tree in Inorder, Preorder and Postorder Methods and also searching the element in the Tree
- A red-black tree is a self-balancing binary search tree where each node is colored red or black. It maintains the properties that the black height of each path is equal and there are no adjacent red nodes, ensuring O(log n) time for operations.
- Common operations like insertion, deletion, and searching on a red-black tree work similarly to a binary search tree but may require rotations and color changes to maintain the red-black properties.
- Red-black trees are widely used in applications that require efficient search structures for frequently updated data like process memory management and functional programming data structures.
BTrees - Great alternative to Red Black, AVL and other BSTsAmrinder Arora
BTrees - designed by Rudolf Bayer and Ed McCreight - fundamental data structure in computer science. Great alternative to BSTs. Very appropriate for disk based access.
Binary trees are a non-linear data structure where each node has zero, one, or two child nodes. They are commonly used to represent hierarchical relationships. A binary tree has a root node at the top with child nodes below it. Binary trees can be empty or consist of a root node and left and right subtrees, which are also binary trees. They allow for efficient search, insert, and delete operations and can be represented using arrays or linked lists.
Splay trees are self-balancing binary search trees that provide fast access both in worst-case amortized time (O(log n)) and in practice due to their locality properties. When a node is accessed, it is rotated to the root through a series of zig-zag and zig-zig rotations, improving locality for future accesses. This helps frequently accessed nodes rise to the top of the tree over time. Splay trees also support efficient split and join operations through splaying, which makes them useful for tasks like range queries and dictionary operations.
This document provides an overview of B-trees, which are balanced search trees used to store large datasets efficiently on disk. It discusses the key properties of B-trees, including their height, minimum node size of t keys, and ability to reduce disk accesses. The basic operations of insertion and deletion are explained through examples, along with the process of splitting or merging nodes when they become too full or empty. B-trees allow searching in O(log n) time and are commonly used in databases and file systems to enable fast indexed retrieval of data.
B-Trees are tree data structures used to store data on disk storage. They allow for efficient retrieval of data compared to binary trees when using disk storage due to reduced height. B-Trees group data into nodes that can have multiple children, reducing the height needed compared to binary trees. Keys are inserted by adding to leaf nodes or splitting nodes and promoting middle keys. Deletion involves removing from leaf nodes, borrowing/promoting keys, or joining nodes.
Binary search trees (BSTs) are data structures that allow for efficient searching, insertion, and deletion. Nodes in a BST are organized so that all left descendants of a node are less than the node's value and all right descendants are greater. This property allows values to be found, inserted, or deleted in O(log n) time on average. Searching involves recursively checking if the target value is less than or greater than the current node's value. Insertion follows the search process and adds the new node in the appropriate place. Deletion handles three cases: removing a leaf, node with one child, or node with two children.
Presentation On Binary Search Tree using Linked List Concept which includes Traversing the tree in Inorder, Preorder and Postorder Methods and also searching the element in the Tree
- A red-black tree is a self-balancing binary search tree where each node is colored red or black. It maintains the properties that the black height of each path is equal and there are no adjacent red nodes, ensuring O(log n) time for operations.
- Common operations like insertion, deletion, and searching on a red-black tree work similarly to a binary search tree but may require rotations and color changes to maintain the red-black properties.
- Red-black trees are widely used in applications that require efficient search structures for frequently updated data like process memory management and functional programming data structures.
BTrees - Great alternative to Red Black, AVL and other BSTsAmrinder Arora
BTrees - designed by Rudolf Bayer and Ed McCreight - fundamental data structure in computer science. Great alternative to BSTs. Very appropriate for disk based access.
Binary trees are a non-linear data structure where each node has zero, one, or two child nodes. They are commonly used to represent hierarchical relationships. A binary tree has a root node at the top with child nodes below it. Binary trees can be empty or consist of a root node and left and right subtrees, which are also binary trees. They allow for efficient search, insert, and delete operations and can be represented using arrays or linked lists.
Splay trees are self-balancing binary search trees that provide fast access both in worst-case amortized time (O(log n)) and in practice due to their locality properties. When a node is accessed, it is rotated to the root through a series of zig-zag and zig-zig rotations, improving locality for future accesses. This helps frequently accessed nodes rise to the top of the tree over time. Splay trees also support efficient split and join operations through splaying, which makes them useful for tasks like range queries and dictionary operations.
This document provides an overview of B-trees, which are balanced search trees used to store large datasets efficiently on disk. It discusses the key properties of B-trees, including their height, minimum node size of t keys, and ability to reduce disk accesses. The basic operations of insertion and deletion are explained through examples, along with the process of splitting or merging nodes when they become too full or empty. B-trees allow searching in O(log n) time and are commonly used in databases and file systems to enable fast indexed retrieval of data.
Binary trees are a data structure where each node has at most two children. A binary tree node contains data and pointers to its left and right child nodes. Binary search trees are a type of binary tree where nodes are organized in a manner that allows for efficient searches, insertions, and deletions of nodes. The key operations on binary search trees are searching for a node, inserting a new node, and deleting an existing node through various algorithms that traverse the tree. Common traversals of binary trees include preorder, inorder, and postorder traversals.
The document describes m-way search trees, B-trees, heaps, and their related operations. An m-way search tree is a tree where each node has at most m child nodes and keys are arranged in ascending order. B-trees are similar but ensure the number of child nodes falls in a range and all leaf nodes are at the same depth. Common operations like searching, insertion, and deletion are explained for each with examples. Heaps store data in a complete binary tree structure where a node's value is greater than its children's values.
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.
B-trees and B+-trees are balanced tree data structures used to store and retrieve data in databases. B-trees allow for rapid searching through an upside-down tree structure. B+-trees are optimized for disk storage, with data only stored in leaf nodes and internal nodes containing keys. Both support efficient insertion and deletion while maintaining balance, through splitting and merging nodes as needed. Examples demonstrate inserting and deleting values in B-trees and B+-trees of a given order.
A presentation on prim's and kruskal's algorithmGaurav Kolekar
This slides are for a presentation on Prim's and Kruskal's algorithm. Where I have tried to explain how both the algorithms work, their similarities and their differences.
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.
B-trees are multiway search trees used to store large datasets on disk. They reduce the height of the tree compared to binary trees, lowering the number of disk accesses needed for operations like search. A B-tree of order m has internal nodes with up to m children, keeps the leaves at the same level, and remains balanced during insertions and deletions which may involve splitting and merging nodes as well as promoting keys. B-trees are efficient for disk-based data structures due to their ability to group adjacent records into each node transfer.
The document discusses minimum spanning trees (MST) and two algorithms for finding them: Prim's algorithm and Kruskal's algorithm. Prim's algorithm operates by building the MST one vertex at a time, starting from an arbitrary root vertex and at each step adding the cheapest connection to another vertex not yet included. Kruskal's algorithm finds the MST by sorting the edges by weight and sequentially adding edges that connect different components without creating cycles.
The document discusses B+ trees, which are self-balancing search trees used to store data in databases. It defines B+ trees, provides examples, and explains how to perform common operations like searching, insertion, and deletion on B+ trees in a way that maintains the tree's balanced structure. Key aspects are that B+ trees allow fast searching, maintain balance during operations, and improve performance over other tree structures for large databases.
This document discusses stacks and queues as linear data structures. It defines stacks as last-in, first-out (LIFO) collections where the last item added is the first removed. Queues are first-in, first-out (FIFO) collections where the first item added is the first removed. Common stack and queue operations like push, pop, insert, and remove are presented along with algorithms and examples. Applications of stacks and queues in areas like expression evaluation, string reversal, and scheduling are also covered.
Binary search trees are binary trees where all left descendants of a node are less than the node's value and all right descendants are greater. This structure allows for efficient search, insertion, and deletion operations. The document provides definitions and examples of binary search tree properties and operations like creation, traversal, searching, insertion, deletion, and finding minimum and maximum values. Applications include dynamically maintaining a sorted dataset to enable efficient search, insertion, and deletion.
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...
Skip list is data structure that possesses the concept of the expressway in terms of basic operation like insertion, deletion and searching. It guarantees approximate cost of this operation should not go beyond O(log n).
The document discusses page replacement algorithms used in virtual memory management. It introduces the concept of page replacement that occurs during a page fault when a requested page is not in main memory. The main goals of page replacement algorithms are to reduce page faults. The document describes three common algorithms - FIFO, Optimal, and LRU - and provides examples of how each works to replace pages.
Linked lists are linear data structures where elements are linked using pointers. The three main types are singly, doubly, and circular linked lists. Linked lists allow dynamic memory allocation and fast insertion/deletion compared to arrays but slower access. A linked list contains nodes, each with a data field and pointer to the next node. Basic operations on linked lists include insertion, deletion, traversal, and search. Doubly linked lists include pointers to both the next and previous nodes.
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.
What is Normalization in Database Management System (DBMS) ?
What is the history of the system of normalization?
Types of Normalizations,
and why this is needed all details in the presentation.
presentation on binary search trees for the subject analysis and design of algorithms, helpful to especially GTU students and computer and IT engineers
This document discusses binary trees. It defines a binary tree as a structure containing nodes with two self-referenced fields - a left reference and a right reference. Each node can have at most two child nodes. It provides examples of common binary tree terminology like root, internal nodes, leaves, siblings, depth, and height. It also describes different ways to represent binary trees using arrays or links and their tradeoffs. Complete binary trees are discussed as an optimal structure with height proportional to log of number of nodes.
This document defines and provides examples of B-trees, which are multi-way search trees used to store data in databases. B-trees allow for fast searches, insertions, and deletions. The key points are:
1. B-trees are m-way trees where each node can have up to m children. They maintain sorted keys and partition data to keep leaves at the same level.
2. An example demonstrates a 5-way B-tree containing 26 items. The process of constructing a B-tree by inserting keys one by one is also shown step-by-step.
3. Deletion from a B-tree can involve removing a key from a leaf, borrowing/prom
The document discusses the motivation for using B-trees to store large datasets that do not fit into main memory. It notes that while binary search trees provide logarithmic-time performance, disk access times are significantly slower than memory. B-trees are designed to group related data together to minimize disk I/O and improve performance. The document defines B-trees as m-way search trees where nodes can have up to m children, leaves are on the same level, and operations like insertion and deletion involve splitting or merging nodes to balance the tree.
Binary trees are a data structure where each node has at most two children. A binary tree node contains data and pointers to its left and right child nodes. Binary search trees are a type of binary tree where nodes are organized in a manner that allows for efficient searches, insertions, and deletions of nodes. The key operations on binary search trees are searching for a node, inserting a new node, and deleting an existing node through various algorithms that traverse the tree. Common traversals of binary trees include preorder, inorder, and postorder traversals.
The document describes m-way search trees, B-trees, heaps, and their related operations. An m-way search tree is a tree where each node has at most m child nodes and keys are arranged in ascending order. B-trees are similar but ensure the number of child nodes falls in a range and all leaf nodes are at the same depth. Common operations like searching, insertion, and deletion are explained for each with examples. Heaps store data in a complete binary tree structure where a node's value is greater than its children's values.
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.
B-trees and B+-trees are balanced tree data structures used to store and retrieve data in databases. B-trees allow for rapid searching through an upside-down tree structure. B+-trees are optimized for disk storage, with data only stored in leaf nodes and internal nodes containing keys. Both support efficient insertion and deletion while maintaining balance, through splitting and merging nodes as needed. Examples demonstrate inserting and deleting values in B-trees and B+-trees of a given order.
A presentation on prim's and kruskal's algorithmGaurav Kolekar
This slides are for a presentation on Prim's and Kruskal's algorithm. Where I have tried to explain how both the algorithms work, their similarities and their differences.
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.
B-trees are multiway search trees used to store large datasets on disk. They reduce the height of the tree compared to binary trees, lowering the number of disk accesses needed for operations like search. A B-tree of order m has internal nodes with up to m children, keeps the leaves at the same level, and remains balanced during insertions and deletions which may involve splitting and merging nodes as well as promoting keys. B-trees are efficient for disk-based data structures due to their ability to group adjacent records into each node transfer.
The document discusses minimum spanning trees (MST) and two algorithms for finding them: Prim's algorithm and Kruskal's algorithm. Prim's algorithm operates by building the MST one vertex at a time, starting from an arbitrary root vertex and at each step adding the cheapest connection to another vertex not yet included. Kruskal's algorithm finds the MST by sorting the edges by weight and sequentially adding edges that connect different components without creating cycles.
The document discusses B+ trees, which are self-balancing search trees used to store data in databases. It defines B+ trees, provides examples, and explains how to perform common operations like searching, insertion, and deletion on B+ trees in a way that maintains the tree's balanced structure. Key aspects are that B+ trees allow fast searching, maintain balance during operations, and improve performance over other tree structures for large databases.
This document discusses stacks and queues as linear data structures. It defines stacks as last-in, first-out (LIFO) collections where the last item added is the first removed. Queues are first-in, first-out (FIFO) collections where the first item added is the first removed. Common stack and queue operations like push, pop, insert, and remove are presented along with algorithms and examples. Applications of stacks and queues in areas like expression evaluation, string reversal, and scheduling are also covered.
Binary search trees are binary trees where all left descendants of a node are less than the node's value and all right descendants are greater. This structure allows for efficient search, insertion, and deletion operations. The document provides definitions and examples of binary search tree properties and operations like creation, traversal, searching, insertion, deletion, and finding minimum and maximum values. Applications include dynamically maintaining a sorted dataset to enable efficient search, insertion, and deletion.
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...
Skip list is data structure that possesses the concept of the expressway in terms of basic operation like insertion, deletion and searching. It guarantees approximate cost of this operation should not go beyond O(log n).
The document discusses page replacement algorithms used in virtual memory management. It introduces the concept of page replacement that occurs during a page fault when a requested page is not in main memory. The main goals of page replacement algorithms are to reduce page faults. The document describes three common algorithms - FIFO, Optimal, and LRU - and provides examples of how each works to replace pages.
Linked lists are linear data structures where elements are linked using pointers. The three main types are singly, doubly, and circular linked lists. Linked lists allow dynamic memory allocation and fast insertion/deletion compared to arrays but slower access. A linked list contains nodes, each with a data field and pointer to the next node. Basic operations on linked lists include insertion, deletion, traversal, and search. Doubly linked lists include pointers to both the next and previous nodes.
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.
What is Normalization in Database Management System (DBMS) ?
What is the history of the system of normalization?
Types of Normalizations,
and why this is needed all details in the presentation.
presentation on binary search trees for the subject analysis and design of algorithms, helpful to especially GTU students and computer and IT engineers
This document discusses binary trees. It defines a binary tree as a structure containing nodes with two self-referenced fields - a left reference and a right reference. Each node can have at most two child nodes. It provides examples of common binary tree terminology like root, internal nodes, leaves, siblings, depth, and height. It also describes different ways to represent binary trees using arrays or links and their tradeoffs. Complete binary trees are discussed as an optimal structure with height proportional to log of number of nodes.
This document defines and provides examples of B-trees, which are multi-way search trees used to store data in databases. B-trees allow for fast searches, insertions, and deletions. The key points are:
1. B-trees are m-way trees where each node can have up to m children. They maintain sorted keys and partition data to keep leaves at the same level.
2. An example demonstrates a 5-way B-tree containing 26 items. The process of constructing a B-tree by inserting keys one by one is also shown step-by-step.
3. Deletion from a B-tree can involve removing a key from a leaf, borrowing/prom
The document discusses the motivation for using B-trees to store large datasets that do not fit into main memory. It notes that while binary search trees provide logarithmic-time performance, disk access times are significantly slower than memory. B-trees are designed to group related data together to minimize disk I/O and improve performance. The document defines B-trees as m-way search trees where nodes can have up to m children, leaves are on the same level, and operations like insertion and deletion involve splitting or merging nodes to balance the tree.
16807097.ppt b tree are a good data structureSadiaSharmin40
The document discusses B-trees, which are tree data structures used to store large datasets on disk. B-trees allow for faster retrieval of data compared to binary search trees when data exceeds main memory. B-trees differ from binary search trees in that internal nodes can have more than two child nodes and store multiple key-value pairs. The document outlines the rules for B-tree structure and provides examples of inserting and removing elements from a B-tree while maintaining its balanced structure.
B-trees are multi-way tree data structures used to store large datasets, such as an index, that are too large to fit in memory. B-trees reduce the number of disk accesses needed compared to binary trees by allowing nodes to have more than two child nodes. Keys in non-leaf nodes partition the keys in child nodes, all leaves are at the same level, and nodes are kept at least half full. Insertion and deletion may cause nodes to split or merge to maintain these properties.
1. Disk access times are much slower than CPU instruction times, so minimizing disk accesses is important for performance.
2. B-trees address this issue by allowing nodes to have multiple children, reducing the height of the tree and thus the number of required disk accesses to retrieve data.
3. Keys are inserted into B-trees by adding them to leaves and splitting nodes as they become full, and deleted by removing from leaves or borrowing/promoting keys from siblings if needed to maintain minimum occupancy.
The document discusses B-trees, which are tree data structures used to store large data sets that cannot fit into main memory. B-trees allow for fast retrieval of data by balancing search trees across multiple disk blocks. They work by having internal nodes with up to m children, with leaf nodes containing keys in sorted order. This balancing allows B-trees to provide fast access and search times even for very large datasets spanning multiple disk drives.
B-trees are tree data structures that allow efficient retrieval of records in large datasets that exceed the capacity of main memory. B-trees allow nodes to have more than two child nodes, reducing the height of the tree and therefore the number of disk accesses needed for search, insert and delete operations compared to binary search trees. B-trees maintain the properties that all leaves are at the same depth, internal nodes have a minimum number of child nodes, and leaf nodes have a maximum number of records. This provides fast access and updates while keeping the tree balanced during operations.
The document defines and provides an example of a B-tree, which is a tree data structure used to store sorted data. It then walks through constructing a B-tree of order 5 by inserting keys in order. The keys are inserted into leaf nodes, and if a leaf becomes too full, it is split and the middle key is promoted. This may cause parent nodes to split as well, all the way up to the root. The root will also split if needed, increasing the height of the tree. The document concludes by listing keys to insert into an empty B-tree as an exercise.
B-trees are multi-way tree data structures used to store large datasets, such as indexes, that cannot fit in memory. B-trees reduce the number of disk accesses needed for operations by allowing nodes to have more than two child nodes. The height of B-trees is smaller than balanced binary trees over the same data, improving efficiency. Keys in non-leaf B-tree nodes partition keys in child nodes, and all leaves are at the same level. Insertion and removal may cause nodes to split or join to maintain these properties.
The document discusses B trees and B+ trees. B trees are multi-way search trees where each node can have up to m children and keys are balanced across nodes. B+ trees are a variant where records are stored only at leaf nodes and interior nodes store keys to allow efficient data retrieval, insertion and removal. B+ trees typically store leaf nodes on disk and internal nodes in memory for large datasets.
The document discusses trees and tree data structures. It provides details on heap data structures and algorithms for inserting and deleting elements from a heap. It also covers B-trees, including their definition, properties, and algorithms for constructing, inserting, and removing elements from a B-tree. B-trees are designed to improve search efficiency for large datasets stored on disk compared to binary search trees.
This document discusses B-trees, which are self-balancing search trees where all leaves are at the same level. It provides examples of constructing a B-tree by inserting keys in order, and describes how insertion and deletion operations are performed. Advantages of B-trees are that they are self-balancing and nodes at all leaf levels are equal. Disadvantages are that insertion and deletion algorithms are more complex than other search trees.
The document presents information on B-trees. It begins by defining B-trees as balanced search trees designed for storage systems that read and write large blocks of data like disks. B-trees generalize binary search trees by allowing nodes to have more than two children. They were invented to index large datasets that could not fit entirely in main memory. The document then discusses properties of B-trees like their minimum and maximum number of keys per node, search, insertion and deletion algorithms, and provides examples of constructing a B-tree.
This document describes operations on a B-tree including insertion, deletion, splitting and merging of nodes. It shows a B-tree initially containing 26 items in a balanced structure with all leaves at the same level. Keys are added to the leaf nodes, causing splits that promote keys up the tree and rebalance the structure. Deletion is demonstrated by borrowing or merging with neighboring nodes, or demoting and promoting keys when underflow occurs.
B-Trees are tree data structures that allow efficient retrieval of records from disk storage. They work by grouping records into pages that can be read from disk with a single access. This reduces the number of disk accesses needed compared to other tree structures when data exceeds main memory. B-Trees maintain balance by allowing nodes to have a flexible number of children within a minimum and maximum range. Keys are inserted by splitting full nodes and promoting middle keys, and deleted by borrowing from siblings or merging nodes.
B-Trees and B+ Trees are data structures used to store large amounts of data on disks when it cannot all fit in main memory. They allow for efficient multilevel indexing and reduce disk access times compared to other balanced trees like AVL trees by keeping the tree height low. B-Trees have multiple keys in each node and store data pointers in internal and leaf nodes, while B+ Trees only store data pointers in leaf nodes. B+ Trees provide faster searches and easier insertion/deletion compared to B-Trees. Both are commonly used in database systems and file systems to efficiently organize and retrieve large blocks of indexed data from secondary storage.
The document describes multi-way B-trees, which generalize binary search trees by allowing nodes to have multiple children. B-trees address the problem of storing large datasets that do not fit in memory by minimizing disk accesses during operations like search, insert, and delete. They achieve this through branching nodes with multiple children to reduce height, keeping leaves at the same depth, and performing splits and merges to balance the tree during modifications.
A B-tree is a tree data structure that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time. The key properties of a B-tree are that non-leaf nodes can have between m/2 to m children, leaf nodes have at most m-1 keys, and all leaves are at the same depth. An example 5-order B-tree is shown containing 26 keys partitioned among nodes. The process of inserting and deleting keys may involve splitting or merging nodes to maintain the B-tree properties.
A B-tree is a tree data structure that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time. The key properties of a B-tree are that non-leaf nodes can have between m/2 to m children, leaf nodes have at most m-1 keys, and all leaves are at the same depth. An example 5-order B-tree is shown containing 26 keys partitioned among nodes. Insertion may cause leaf node splitting and splitting can propagate up the tree, requiring new root nodes. Deletion removes keys from leaves or replaces with predecessors/successors. The maximum number of keys in an order m, height h B-tree is mh+1
Indexed sequential files provide both indexed and sequential access to records in a file. Records are organized into blocks, and a B+ tree index structure is used to index the blocks. This allows both efficient indexed access via the B+ tree as well as sequential access by scanning blocks. B+ trees support insertion and deletion of records through localized splitting, merging, and redistribution of blocks and index nodes to maintain balance and efficiency.
This document contains a program list for a data structures course using C programming language. It outlines various programs to implement arrays, both 1D and 2D, searching and sorting techniques on arrays, stacks, queues, and linked lists. There are over 30 individual programs covering traversing, inserting, deleting, merging, searching, and sorting operations on these various data structures. The course is for third semester BCA students and will be taught by faculty member Ashok Kumar.
Binary search trees have the following key properties:
1. Each node contains a value
2. The value of each left descendant is smaller than the node's value
3. The value of each right descendant is larger than the node's value
They allow for efficient insertion, deletion, and search operations in O(log n) time by maintaining this ordering property as the tree is modified.
this ppt is on the topic of system security. there are some topic which are introduce very nicely.there are some commont topic introduce in the
1. firewall
2.antivirus
3.malware
and IOT
these are the sub topic..
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.
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.
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 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.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
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How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
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.
South African Journal of Science: Writing with integrity workshop (2024)
B trees
1. Definition of a B-tree
• A B-tree of order m is an m-way tree (i.e., a tree where each
node may have up to m children) in which:
1. the number of keys in each non-leaf node is one less than the number
of its children and these keys partition the keys in the children in the
fashion of a search tree
2. all leaves are on the same level
3. all non-leaf nodes except the root have at least m / 2 children
4. the root is either a leaf node, or it has from two to m children
5. a leaf node contains no more than m – 1 keys
• The number m should always be odd
2. An example B-Tree
51 6242
6 12
26
55 60 7064 9045
1 2 4 7 8 13 15 18 25
27 29 46 48 53
A B-tree of order 5
containing 26 items
Note that all the leaves are at the same levelNote that all the leaves are at the same level
3. • Suppose we start with an empty B-tree and keys arrive in the
following order:1 12 8 2 25 6 14 28 17 7 52 16 48 68
3 26 29 53 55 45
• We want to construct a B-tree of order 5
• The first four items go into the root:
• To put the fifth item in the root would violate condition 5
• Therefore, when 25 arrives, pick the middle key to make a
new root
Constructing a B-tree
12128811 22
4. Constructing a B-tree
Add 25 to the tree
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
12128811 22 2525
Exceeds Order.
Promote middle and
split.
13. Inserting into a B-Tree
• Attempt to insert the new key into a leaf
• If this would result in that leaf becoming too big, split the leaf
into two, promoting the middle key to the leaf’s parent
• If this would result in the parent becoming too big, split the
parent into two, promoting the middle key
• This strategy might have to be repeated all the way to the top
• If necessary, the root is split in two and the middle key is
promoted to a new root, making the tree one level higher
14. Exercise in Inserting a B-Tree
• Insert the following keys to a 5-way B-tree:
• 3, 7, 9, 23, 45, 1, 5, 14, 25, 24, 13, 11, 8, 19, 4, 31, 35, 56
16. Removal from a B-tree
• During insertion, the key always goes into a leaf. For deletion
we wish to remove from a leaf. There are three possible ways
we can do this:
• 1 - If the key is already in a leaf node, and removing it doesn’t
cause that leaf node to have too few keys, then simply remove
the key to be deleted.
• 2 - If the key is not in a leaf then it is guaranteed (by the
nature of a B-tree) that its predecessor or successor will be in
a leaf -- in this case can we delete the key and promote the
predecessor or successor key to the non-leaf deleted key’s
position.
17. Removal from a B-tree (2)
• If (1) or (2) lead to a leaf node containing less than the
minimum number of keys then we have to look at the siblings
immediately adjacent to the leaf in question:
– 3: if one of them has more than the min’ number of keys then we can
promote one of its keys to the parent and take the parent key into our
lacking leaf
– 4: if neither of them has more than the min’ number of keys then the
lacking leaf and one of its neighbours can be combined with their
shared parent (the opposite of promoting a key) and the new leaf will
have the correct number of keys; if this step leave the parent with too
few keys then we repeat the process up to the root itself, if required
18. Type #1: Simple leaf deletion
1212 2929 5252
22 77 99 1515 2222 5656 6969 72723131 4343
Delete 2: Since there are enough
keys in the node, just delete it
Assuming a 5-way
B-Tree, as before...
Note when printed: this slide is animated
19. Type #2: Simple non-leaf deletion
1212 2929 5252
77 99 1515 2222 5656 6969 72723131 4343
Delete 52
Borrow the predecessor
or (in this case) successor
5656
Note when printed: this slide is animated
Delete : 52
20. Type #4: Too few keys in node and
its siblings
1212 2929 5656
77 99 1515 2222 6969 72723131 4343
Delete 72
Delete 72: Too few keys!
Join back together
Note when printed: this slide is animated
21. Type #4: Too few keys in node and
its siblings
1212 2929
77 99 1515 2222 696956563131 4343
Note when printed: this slide is animated
22. Type #3: Enough siblings
1212 2929
77 99 1515 2222 696956563131 4343
Delete 22
Demote root key and
promote leaf key
Note when printed: this slide is animated
Delete: 22
23. Type #3: Enough siblings
1212
292977 99 1515
3131
696956564343
Note when printed: this slide is animated
24. Exercise in Removal from a B-Tree
• Given 5-way B-tree created by these data (last exercise):
• 3, 7, 9, 23, 45, 1, 5, 14, 25, 24, 13, 11, 8, 19, 4, 31, 35, 56
• Add these further keys: 2, 6,12
• Delete these keys: 4, 5, 7, 3, 14