The document discusses different types of trees and graphs as data structures. It defines trees as hierarchical data structures that can represent information in a flexible manner. Binary search trees allow rapid retrieval of data based on keys. Different types of trees are discussed including binary trees, ordered trees, rooted trees, and complete trees. Graphs are also covered as structures that can represent relationships between data items and support applications like social networks. Common graph terms like nodes, edges, directed/undirected graphs, and connectivity are defined.
This document discusses trees and their applications in discrete mathematics. It begins with an introduction to trees, including defining different types of trees such as rooted trees, m-ary trees, and binary trees. It then covers applications of trees such as binary search trees, decision trees, and game trees. Next, it discusses different tree traversal algorithms like preorder, inorder, and postorder traversal and how they can be used to represent expressions. Finally, it provides examples of evaluating expressions represented as trees.
Tries are a data structure for storing strings that allow for fast pattern matching. A trie is a tree where each edge represents a character and each path from the root node to a leaf spells out a key. Standard tries insert strings by adding nodes for each character. Compressed tries reduce redundant nodes by compressing chains. Suffix tries store all suffixes of a text in a compressed trie to enable quick string queries. Tries support faster insertion and lookup compared to hash tables, with no collisions between keys.
In computer science, a tree is a widely used abstract data type (ADT) or data structure implementing this ADT that simulates a hierarchical tree structure, with a root value and subtrees of children, represented as a set of linked nodes.
The document defines a tree as a set of nodes with a root node and zero or more subtrees. It discusses terminology like degree, parent, child, and sibling nodes. Trees can be represented sequentially or linked. Binary trees restrict nodes to having at most two children. Binary search trees require that all left descendants of a node are less than the node and all right descendants are greater. The document describes traversing binary trees using inorder, preorder, and postorder traversal.
This document discusses trees as a data structure. It defines key tree terminology like root, leaf nodes, ancestors and descendants. It describes different tree representations and traversal techniques including preorder, inorder and postorder sequences. It also covers different types of binary trees and basic tree operations like insertion, deletion and searching. Common applications of trees include representing arithmetic expressions, decision processes and priority queues.
Tree is a non-linear data structure that can represent hierarchical relationships. It consists of nodes connected by edges. The root node has child nodes, and nodes may be leaf nodes or have child nodes themselves. Binary trees restrict nodes to having at most two children. General trees can be converted to binary trees by making the first child the left child and next siblings the right child. Binary trees can be built from input data by comparing values to determine left or right placement, or from traversal operations.
This document 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.
This document discusses binary search trees (BSTs). It defines BSTs as binary trees where all left descendants of a node are less than the node's value and all right descendants are greater. It describes how to implement a BST using linked nodes, and how to perform operations like insertion, searching, and different traversal orders through the tree. The document is presented by Mahmoud Rafeek Al-farra and contains details on representing, inserting into, searching, and traversing BSTs implemented as a concrete Java class.
This document discusses trees and their applications in discrete mathematics. It begins with an introduction to trees, including defining different types of trees such as rooted trees, m-ary trees, and binary trees. It then covers applications of trees such as binary search trees, decision trees, and game trees. Next, it discusses different tree traversal algorithms like preorder, inorder, and postorder traversal and how they can be used to represent expressions. Finally, it provides examples of evaluating expressions represented as trees.
Tries are a data structure for storing strings that allow for fast pattern matching. A trie is a tree where each edge represents a character and each path from the root node to a leaf spells out a key. Standard tries insert strings by adding nodes for each character. Compressed tries reduce redundant nodes by compressing chains. Suffix tries store all suffixes of a text in a compressed trie to enable quick string queries. Tries support faster insertion and lookup compared to hash tables, with no collisions between keys.
In computer science, a tree is a widely used abstract data type (ADT) or data structure implementing this ADT that simulates a hierarchical tree structure, with a root value and subtrees of children, represented as a set of linked nodes.
The document defines a tree as a set of nodes with a root node and zero or more subtrees. It discusses terminology like degree, parent, child, and sibling nodes. Trees can be represented sequentially or linked. Binary trees restrict nodes to having at most two children. Binary search trees require that all left descendants of a node are less than the node and all right descendants are greater. The document describes traversing binary trees using inorder, preorder, and postorder traversal.
This document discusses trees as a data structure. It defines key tree terminology like root, leaf nodes, ancestors and descendants. It describes different tree representations and traversal techniques including preorder, inorder and postorder sequences. It also covers different types of binary trees and basic tree operations like insertion, deletion and searching. Common applications of trees include representing arithmetic expressions, decision processes and priority queues.
Tree is a non-linear data structure that can represent hierarchical relationships. It consists of nodes connected by edges. The root node has child nodes, and nodes may be leaf nodes or have child nodes themselves. Binary trees restrict nodes to having at most two children. General trees can be converted to binary trees by making the first child the left child and next siblings the right child. Binary trees can be built from input data by comparing values to determine left or right placement, or from traversal operations.
This document 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.
This document discusses binary search trees (BSTs). It defines BSTs as binary trees where all left descendants of a node are less than the node's value and all right descendants are greater. It describes how to implement a BST using linked nodes, and how to perform operations like insertion, searching, and different traversal orders through the tree. The document is presented by Mahmoud Rafeek Al-farra and contains details on representing, inserting into, searching, and traversing BSTs implemented as a concrete Java class.
1) Trees are hierarchical data structures that store data in nodes connected by edges. They are useful for representing hierarchical relationships.
2) Binary search trees allow quick search, insertion, and deletion of nodes due to the organizational property that the value of each node is greater than all nodes in its left subtree and less than all nodes in its right subtree.
3) Common tree traversal algorithms include preorder, inorder, and postorder traversals, which visit nodes in different orders depending on whether the left/right children or root is visited first.
Sorting
Performance parameters
Insertion Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Shell Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Tree and graph data structures are used to represent hierarchical data. A tree has nodes connected by edges in a parent-child relationship where each node can have zero or more children but only one parent, forming a rooted tree. Common tree types include binary trees where each node has at most two children, binary search trees where the left child is less than the parent which is less than the right child, and B-trees where nodes can have multiple children. Trees are traversed using in-order, pre-order and post-order algorithms.
The document discusses tree data structures and binary search trees. It defines key tree terminology like root, internal and leaf nodes. It explains tree traversal algorithms like preorder, inorder and postorder traversal using recursion and iteration. It also describes operations on binary search trees like searching, inserting and deleting nodes. The complexity of these BST operations is provided. Algorithms to find the inorder predecessor and successor of a node in a BST are presented.
Graphs are one of the most important non-linear data structures that represent relationships between elements. Graphs can be classified as directed or undirected. Common graph representations include adjacency lists and matrices. Graph algorithms like depth-first search, breadth-first search, minimum spanning trees (using Prim's and Kruskal's algorithms), and shortest paths (using Dijkstra's algorithm) are used to traverse and analyze graph structures.
The document discusses graph traversal algorithms breadth-first search (BFS) and depth-first search (DFS). It provides examples of how BFS and DFS work, including pseudocode for algorithms. It also discusses applications of BFS such as finding shortest paths and detecting bipartitions. Applications of DFS include finding connected components and topological sorting.
A tree is a hierarchical data structure where items are arranged in a sorted sequence. It represents relationships between data items. A tree has a root node at the top with child nodes branching out connected by edges. Each node stores data and links to other nodes. The level of a node indicates its depth from the root with the root being level 0. Siblings are nodes that share the same parent. Leaf nodes have no children while non-terminal nodes have children. The degree of a node is the number of subtrees extending from it.
The document discusses general trees, which are a type of tree data structure where each node can have zero or more children. It defines a general tree, lists some key properties like the number of nodes, height, root, leaves, and ancestors. The document also provides examples of different types of trees including binary trees, balanced trees, unbalanced trees, red-black trees, and B-trees. It briefly mentions simulating a general tree and implementing tree data structures in programming.
The document defines and describes various graph concepts and data structures used to represent graphs. It defines a graph as a collection of nodes and edges, and distinguishes between directed and undirected graphs. It then describes common graph terminology like adjacent/incident nodes, subgraphs, paths, cycles, connected/strongly connected components, trees, and degrees. Finally, it discusses two common ways to represent graphs - the adjacency matrix and adjacency list representations, noting their storage requirements and ability to add/remove nodes.
Trees and Graphs in data structures and AlgorithmsBHARATH KUMAR
The document discusses tree data structures and binary search trees. It defines key concepts related to trees including root, parent, child, leaf nodes, internal nodes, height, depth, and traversal methods. It then describes properties of binary trees including full, complete, and perfect binary trees. Binary search trees are defined as having left and right subtrees containing only nodes with keys less than or greater than the parent node's key. Basic binary search tree operations like search, insert, and traversal methods are also outlined. Sample C code for traversing a binary tree using preorder, inorder, and postorder methods is provided.
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 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.
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.
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.
Content of slide
Tree
Binary tree Implementation
Binary Search Tree
BST Operations
Traversal
Insertion
Deletion
Types of BST
Complexity in BST
Applications of BST
non linear data structure -introduction of treeSiddhi Viradiya
The document defines trees and binary trees. A tree consists of nodes connected by branches, with one root node and zero or more subtrees. A binary tree restricts each node to have at most two children. The document discusses tree terminology like root, child, parent, leaf nodes. It also covers tree traversal methods like preorder, inorder and postorder. Finally, it shows how to construct a binary tree from its traversals.
The document discusses abstract data types (ADTs) and several common data structures, including stacks, queues, linked lists, trees, and their applications. An ADT defines a data type and operations on that data type without specifying how those operations are implemented. Common programming languages define simple ADTs like integers, while more complex ADTs like lists, stacks and queues must be explicitly defined. The key operations and applications of each data structure are described.
Trees are hierarchical data structures composed of nodes connected by edges. A tree has a root node with child nodes below it. Leaf nodes have no children, while internal nodes have children. Binary trees restrict nodes to having 0, 1, or 2 children. Binary search trees organize nodes so that all left descendants of a node are less than or equal to the node and all right descendants are greater than or equal. Common tree operations include insertion, searching, and deletion.
6. Linked list - Data Structures using C++ by Varsha Patilwidespreadpromotion
The document discusses linked lists as a dynamic data structure. It defines a linked list as a collection of data elements called nodes that together represent a sequence. Each node contains a data field for the element and a link to the next node. This allows elements to be added or removed without reorganizing the entire structure. The document covers different types of linked lists including singly linked, doubly linked, circular, and their applications for storing polynomials and implementing stacks. It also discusses operations like traversal, insertion, and deletion of nodes.
9. Searching & Sorting - Data Structures using C++ by Varsha Patilwidespreadpromotion
The document discusses various searching and sorting algorithms. It covers sequential search, binary search, Fibonacci search, hashed search, indexed sequential search and their time complexities. Sorting algorithms like bubble sort, insertion sort, selection sort are explained along with their analysis. Internal sorting techniques like quicksort, heapsort, radix sort and bucket sort are also mentioned. The document provides details on sorting methods, order, stability and efficiency.
1) Trees are hierarchical data structures that store data in nodes connected by edges. They are useful for representing hierarchical relationships.
2) Binary search trees allow quick search, insertion, and deletion of nodes due to the organizational property that the value of each node is greater than all nodes in its left subtree and less than all nodes in its right subtree.
3) Common tree traversal algorithms include preorder, inorder, and postorder traversals, which visit nodes in different orders depending on whether the left/right children or root is visited first.
Sorting
Performance parameters
Insertion Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Shell Sort
Technique
Algorithm
Performance with examples
Applications
Example Program
Tree and graph data structures are used to represent hierarchical data. A tree has nodes connected by edges in a parent-child relationship where each node can have zero or more children but only one parent, forming a rooted tree. Common tree types include binary trees where each node has at most two children, binary search trees where the left child is less than the parent which is less than the right child, and B-trees where nodes can have multiple children. Trees are traversed using in-order, pre-order and post-order algorithms.
The document discusses tree data structures and binary search trees. It defines key tree terminology like root, internal and leaf nodes. It explains tree traversal algorithms like preorder, inorder and postorder traversal using recursion and iteration. It also describes operations on binary search trees like searching, inserting and deleting nodes. The complexity of these BST operations is provided. Algorithms to find the inorder predecessor and successor of a node in a BST are presented.
Graphs are one of the most important non-linear data structures that represent relationships between elements. Graphs can be classified as directed or undirected. Common graph representations include adjacency lists and matrices. Graph algorithms like depth-first search, breadth-first search, minimum spanning trees (using Prim's and Kruskal's algorithms), and shortest paths (using Dijkstra's algorithm) are used to traverse and analyze graph structures.
The document discusses graph traversal algorithms breadth-first search (BFS) and depth-first search (DFS). It provides examples of how BFS and DFS work, including pseudocode for algorithms. It also discusses applications of BFS such as finding shortest paths and detecting bipartitions. Applications of DFS include finding connected components and topological sorting.
A tree is a hierarchical data structure where items are arranged in a sorted sequence. It represents relationships between data items. A tree has a root node at the top with child nodes branching out connected by edges. Each node stores data and links to other nodes. The level of a node indicates its depth from the root with the root being level 0. Siblings are nodes that share the same parent. Leaf nodes have no children while non-terminal nodes have children. The degree of a node is the number of subtrees extending from it.
The document discusses general trees, which are a type of tree data structure where each node can have zero or more children. It defines a general tree, lists some key properties like the number of nodes, height, root, leaves, and ancestors. The document also provides examples of different types of trees including binary trees, balanced trees, unbalanced trees, red-black trees, and B-trees. It briefly mentions simulating a general tree and implementing tree data structures in programming.
The document defines and describes various graph concepts and data structures used to represent graphs. It defines a graph as a collection of nodes and edges, and distinguishes between directed and undirected graphs. It then describes common graph terminology like adjacent/incident nodes, subgraphs, paths, cycles, connected/strongly connected components, trees, and degrees. Finally, it discusses two common ways to represent graphs - the adjacency matrix and adjacency list representations, noting their storage requirements and ability to add/remove nodes.
Trees and Graphs in data structures and AlgorithmsBHARATH KUMAR
The document discusses tree data structures and binary search trees. It defines key concepts related to trees including root, parent, child, leaf nodes, internal nodes, height, depth, and traversal methods. It then describes properties of binary trees including full, complete, and perfect binary trees. Binary search trees are defined as having left and right subtrees containing only nodes with keys less than or greater than the parent node's key. Basic binary search tree operations like search, insert, and traversal methods are also outlined. Sample C code for traversing a binary tree using preorder, inorder, and postorder methods is provided.
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 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.
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.
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.
Content of slide
Tree
Binary tree Implementation
Binary Search Tree
BST Operations
Traversal
Insertion
Deletion
Types of BST
Complexity in BST
Applications of BST
non linear data structure -introduction of treeSiddhi Viradiya
The document defines trees and binary trees. A tree consists of nodes connected by branches, with one root node and zero or more subtrees. A binary tree restricts each node to have at most two children. The document discusses tree terminology like root, child, parent, leaf nodes. It also covers tree traversal methods like preorder, inorder and postorder. Finally, it shows how to construct a binary tree from its traversals.
The document discusses abstract data types (ADTs) and several common data structures, including stacks, queues, linked lists, trees, and their applications. An ADT defines a data type and operations on that data type without specifying how those operations are implemented. Common programming languages define simple ADTs like integers, while more complex ADTs like lists, stacks and queues must be explicitly defined. The key operations and applications of each data structure are described.
Trees are hierarchical data structures composed of nodes connected by edges. A tree has a root node with child nodes below it. Leaf nodes have no children, while internal nodes have children. Binary trees restrict nodes to having 0, 1, or 2 children. Binary search trees organize nodes so that all left descendants of a node are less than or equal to the node and all right descendants are greater than or equal. Common tree operations include insertion, searching, and deletion.
6. Linked list - Data Structures using C++ by Varsha Patilwidespreadpromotion
The document discusses linked lists as a dynamic data structure. It defines a linked list as a collection of data elements called nodes that together represent a sequence. Each node contains a data field for the element and a link to the next node. This allows elements to be added or removed without reorganizing the entire structure. The document covers different types of linked lists including singly linked, doubly linked, circular, and their applications for storing polynomials and implementing stacks. It also discusses operations like traversal, insertion, and deletion of nodes.
9. Searching & Sorting - Data Structures using C++ by Varsha Patilwidespreadpromotion
The document discusses various searching and sorting algorithms. It covers sequential search, binary search, Fibonacci search, hashed search, indexed sequential search and their time complexities. Sorting algorithms like bubble sort, insertion sort, selection sort are explained along with their analysis. Internal sorting techniques like quicksort, heapsort, radix sort and bucket sort are also mentioned. The document provides details on sorting methods, order, stability and efficiency.
This document discusses queues and their implementation using data structures in C++. It covers:
1) Defining queues and their operations of insertion at the rear and deletion at the front.
2) Implementing queues using arrays and avoiding their drawbacks using circular queues.
3) Other applications that use queues like simulation, job scheduling, and priority queues.
4) Different queue implementations like multi-queue, deque, and priority queue data structures.
10. Search Tree - Data Structures using C++ by Varsha Patilwidespreadpromotion
The document discusses binary search trees and their variants. It explains that search trees are important for algorithm design and it is desirable to minimize the search time of each node. There are static and dynamic binary search trees, with the latter adjusting its structure during access. AVL trees are a type of self-balancing binary search tree where rotations are used to rebalance the tree after insertions or deletions and ensure the heights of subtrees differ by at most one. Compilers use symbol tables implemented as search trees to track variables in source code.
1. Fundamental Concept - Data Structures using C++ by Varsha Patilwidespreadpromotion
This document provides an overview of key concepts related to data structures and algorithms using C++. It discusses fundamental topics like data types, data objects, abstract data types, and data structures. It also covers algorithms, including their characteristics, design tools like pseudocode and flowcharts, and complexity analysis using Big O notation. Finally, it introduces software engineering concepts like the software development life cycle and its main phases of analysis, design, implementation, testing and verification.
The document discusses stacks and their applications. It describes stacks as last-in, first-out data structures and covers stack operations like push and pop. Common uses of stacks include expression evaluation, recursion, reversing data structures, and printing job queues. The document also discusses time and space complexity analysis of algorithms, conversion between infix, postfix and prefix notation, and software engineering principles like the software development life cycle.
The document discusses hashing techniques for data structures. It describes how hashing is used to store and retrieve records from a hash table using a key and hash function. When two keys hash to the same location (collision), different collision resolution strategies can be used like open addressing, separate chaining, and bucket hashing. Open addressing methods like linear probing and quadratic probing search for the next empty location to store collided records. Separate chaining stores collided records in linked lists at hash table locations.
The document discusses various searching and sorting algorithms. It describes linear search, binary search, selection sort, bubble sort, and heapsort. For each algorithm, it provides pseudocode examples and analyzes their performance in terms of number of comparisons required in the worst case. Linear search requires N comparisons in the worst case, while binary search requires log N comparisons. Selection sort and bubble sort both require approximately N^2 comparisons, while heapsort requires 1.5NlogN comparisons.
Discrete Mathematics S. Lipschutz, M. Lipson And V. H. Patilwidespreadpromotion
This document provides a summary of Scilab codes that correspond to examples from the textbook "Discrete Mathematics" by S. Lipschutz, M. Lipson And V. H. Patil. It includes a list of 73 Scilab codes organized by chapter in the textbook. Each code is associated with an example from the corresponding chapter in the textbook. The codes cover topics in set theory, functions, vectors, matrices, counting, probability, graphs, properties of integers, algebraic systems, Boolean algebra, and recurrence relations.
The document provides an overview of common data structures including lists, stacks, queues, trees, and hash tables. It describes each data structure, how it can be implemented both statically and dynamically, and how to use the core Java classes like ArrayList, Stack, LinkedList, and HashMap that implement these structures. Key points covered include common operations for each structure, examples of using the Java classes, and applications like finding prime numbers in a range or matching brackets in an expression.
The document discusses recursion in computer programming. It defines recursion as a function that calls itself or is called by another function. It categorizes different types of recursion such as direct, indirect, linear, tree, and tail recursion. It explains how recursive functions work by using a stack to store information from each function call. Examples of recursively-defined problems like factorials and Fibonacci numbers are provided. Guidelines for writing recursive functions and solving problems recursively are also outlined.
2. Linear Data Structure Using Arrays - Data Structures using C++ by Varsha P...widespreadpromotion
This document discusses arrays and ordered lists as linear data structures. It describes arrays as a collection of homogeneous data elements that allow direct access via indexes. The key properties of arrays include sequential storage of elements, random access, and calculation of element addresses based on base address and offsets. The document also covers array implementation in C++, one-dimensional and two-dimensional arrays, row-major and column-major representations, and the use of arrays to represent polynomials, strings and sparse matrices. Finally, it provides a brief introduction to ordered lists and their representation as linear data structures.
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.
Data structures allow for the organization and storage of data. There are linear and non-linear data structures. Linear structures include arrays, stacks, queues, and linked lists. Arrays store elements in contiguous memory locations. Stacks and queues follow first-in last-out and first-in first-out rules respectively. Linked lists connect nodes using pointers. Non-linear structures include trees and graphs which emulate hierarchical and network-like connections. Common operations on data structures include traversing, searching, insertion, and deletion.
មេរៀនៈ Data Structure and Algorithm in C/C++Ngeam Soly
This document provides an introduction to a lecture on data structures and algorithms. It discusses the lecturer's contact information and expectations for reading ahead of lectures. It then covers topics that will be discussed in the course, including programs and programming, introduction to programming, crafting programs effectively, what makes a good program, and why data structures and algorithms are important subjects. The document provides an overview of what will be covered in the course.
Database structure Structures Link list and trees and Recurison complete Adnan abid
Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete
Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete Database structure Structures Link list and trees and Recurison complete
Introduction to data structures and AlgorithmDhaval Kaneria
This document provides an introduction to algorithms and data structures. It defines algorithms as step-by-step processes to solve problems and discusses their properties, including being unambiguous, composed of a finite number of steps, and terminating. The document outlines the development process for algorithms and discusses their time and space complexity, noting worst-case, average-case, and best-case scenarios. Examples of iterative and recursive algorithms for calculating factorials are provided to illustrate time and space complexity analyses.
It is a presentation on some Searching and Sorting Techniques for Computer Science.
It consists of the following techniques:
Sequential Search
Binary Search
Selection Sort
Bubble Sort
Insertion Sort
The binary search is faster than the sequential search. The complexity of binary search is O(log n) whereas the complexity of a sequential search is O(n). Stacks are used to evaluate algebraic or arithmetic expressions using prefix or postfix notations. Heap sort involves creating a max heap from the array and then replacing the root with the last element and rebuilding the heap for the remaining elements, repeating this process to sort the entire array.
This document provides information about Dream Valley College for Girls Centre for Educational Excellence. It includes an index and presentation on data structures covering topics like arrays, linked lists, queues, trees, and graphs. The presentation was presented by Harish Sir and includes definitions, examples, and diagrams to explain each data structure concept.
13. Indexing MTrees - Data Structures using C++ by Varsha Patilwidespreadpromotion
This document discusses various data structures and file organization techniques. It covers indexing techniques like B-trees and tries, as well as file organization methods like sequential and hashed indexes. Specific data structures covered include B-trees, B+-trees, tries, splay trees, red-black trees, and KD-trees. Operations for searching, inserting and deleting records in these tree structures are also outlined.
The document discusses heaps and their implementation and applications. It defines heaps as binary trees that satisfy the heap property, where each node is greater than or equal to its children (for min-heaps) or less than or equal (for max-heaps). Heaps can be implemented efficiently using arrays, allowing for fast insertion, deletion, and finding the maximum/minimum element. The document outlines heap operations and provides examples of heap construction. Common applications of heaps discussed are priority queues, selection algorithms, and heapsort.
The document discusses abstract data types (ADTs) and the standard template library (STL) in C++. It covers:
- ADTs allow programmers to use data types without knowing implementation details.
- The STL includes containers, iterators, and algorithms to simplify storing and processing data. It is part of the C++ standard library.
- The STL contains various containers like vectors, lists, queues, and maps that make code reuse easier. Algorithms like sort can be directly applied to containers.
The document discusses collaborations between 6 students on the topics of data structures trees and graphs. It provides information on binary trees, binary search trees, tree and graph implementations and common graph algorithms like Dijkstra's algorithm. Examples of trees, graphs and Dijkstra's algorithm are shown.
The document discusses height balanced binary trees. A height balanced binary tree is one where, for each node, the heights of the left and right subtrees differ by no more than 1. An AVL tree is a type of height balanced binary tree. The document provides an example of a height balanced tree that is not completely balanced. It also gives a formula to calculate the maximum number of nodes in a balanced binary tree of height h as 2h-1 - 1 internal nodes plus up to 2h leaf nodes.
Here are the steps to construct the binary search tree from the given pre-order and in-order traversals:
1. The root node is the first element of pre-order traversal, which is 'a'.
2. Search for 'a' in in-order traversal. Elements before 'a' are in left subtree and elements after are in right subtree.
3. Recursively construct left subtree with pre-order elements 'b,c,d' and in-order elements 'c,d,b'.
4. Recursively construct right subtree with pre-order elements 'e,g,h,j' and in-order elements 'h,g,j,e'.
for sbi so Ds c c++ unix rdbms sql cn osalisha230390
This document contains 35 questions related to data structures and algorithms. It covers topics like data structures used in different areas like databases, networks and hierarchies. Other topics covered include trees, graphs, sorting, hashing and file structures. Sample problems are given related to these topics to test understanding.
The document discusses trees and binary trees as data structures. It defines what a tree is, including parts like the root, parent, child, leaf nodes. It then defines binary trees as trees where each node has no more than two children. Binary search trees are introduced as binary trees where all left descendants of a node are less than or equal to the node and all right descendants are greater. The document concludes by discussing how to build a binary search tree class with Node objects.
Common Use of Tree as a Data Structure
ADVANCE
1. Nodes
2. Parent Nodes & Child Nodes
3. Leaf Nodes
4. Root Node
5. Sub Tree
6. Level of a tree:
7. m-ary Tree
8. Binary Tree (BT)
9. Complete and Full Binary Tree
10. Traversal
11. Binary Search Tree (BST)
12. Inorder Traversal – Left_ParentNode_Right
13. Postorder Traversal – Left_Right_ParentNode
14. Preorder Traversal – ParentNode_Left_Right
15. Binary Search Tree (BST)
16. BST - Insert, Delete
The document discusses representing electrical circuits as graphs for computer simulation. It describes that a circuit can be expressed as a directed graph consisting of branches that connect at nodes. For large circuits, a computer program needs the circuit expressed as fundamental matrices including the node-incidence matrix, basic cutset matrix, and basic loop matrix. These matrices provide a standard form for the program to analyze the graph representation of the circuit.
16. Algo analysis & Design - Data Structures using C++ by Varsha Patilwidespreadpromotion
This document discusses various algorithms and data structures including divide-and-conquer, greedy algorithms, dynamic programming, pattern matching, and tries. It provides examples of each technique and describes how to determine when a problem can be solved using each approach. The key characteristics of different trie variants like standard, compressed, and suffix tries are also outlined. Overall, the document presents fundamental algorithm design strategies and data structures.
IRJET- Study of Topological Analogies of Perfect Difference Network and Compl...IRJET Journal
This document analyzes the topological properties of complete graphs and perfect difference networks (PDNs). It shows that a complete graph can be derived from a system of perfect difference sets (PDSs) by taking the union of the PDN and the graph of missing links. Specifically:
1) The total number of missing links in a complete graph derived from a PDS system of order n is (n2 - n)/2.
2) The total number of links in a complete graph is equal to the total number of links in the corresponding PDN plus the missing links.
3) A complete graph can be constructed by combining the PDN derived from a PDS with the graph of the missing links
1) The document is an assignment submission on data structures covering queues, linked lists, and trees.
2) It discusses the concepts of queues including FIFO operations, applications such as call centers, and implementations using arrays or linked lists.
3) Linked lists are described as dynamic structures that connect nodes through pointers and are used for stacks, queues, and graphs. Common types include singly, doubly, and circular linked lists.
4) Trees are hierarchical structures where each node has a maximum of two children. Binary trees, their terminology, types such as full and balanced binary trees, and advantages are outlined.
EVOLUTIONARY CENTRALITY AND MAXIMAL CLIQUES IN MOBILE SOCIAL NETWORKSijcsit
This paper introduces an evolutionary approach to enhance the process of finding central nodes in mobile networks. This can provide essential information and important applications in mobile and social networks. This evolutionary approach considers the dynamics of the network and takes into consideration the central nodes from previous time slots. We also study the applicability of maximal cliques algorithms in mobile social networks and how it can be used to find the central nodes based on the discovered maximal cliques. The experimental results are promising and show a significant enhancement in finding the central nodes.
This document provides information about tree data structures. It defines key tree terminology like root, parent, child, leaf node, internal node, subtree, and siblings. It also describes different types of trees like binary trees, binary search trees, threaded binary trees, and heaps. Common tree traversal algorithms like preorder, inorder, and postorder are explained. Priority queues and their representations using heaps are also discussed.
This document discusses graphs and their representation in code. It defines graphs as consisting of vertices and edges, with edges specified as pairs of vertices. It distinguishes between directed and undirected graphs. Key graph terms like paths, cycles, and connectivity are defined. Real-world systems that can be modeled as graphs are given as an example. The document then discusses representing vertices and edges in code, choosing an adjacency matrix to represent the edges in the graph.
1. The document outlines the key topics and concepts covered in a 6-week data structures and algorithms course, including common data structures like arrays, linked lists, stacks, queues, binary trees, and graphs.
2. It provides details on different types of data structures, operations, advantages and disadvantages of each structure. Example applications are also discussed.
3. The reasons for choosing to learn data structures and algorithms are given as preparing for other programming languages and computer science topics, learning algorithm design, and gaining practical knowledge through live video lectures.
This document defines key terms related to trees as data structures. It discusses different implementations of trees using links and arrays, and different traversal methods for trees including preorder, inorder, postorder, and levelorder traversal. It also provides examples of binary tree implementations using classes for tree nodes and the tree itself.
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