computer notes - Data Structures - 1
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The document discusses data structures and their implementation in C++. It covers topics like the need for data structures to organize data efficiently, commonly used data structures like arrays, linked lists, stacks and queues, selecting appropriate data structures based on algorithm requirements, and implementing dynamic arrays in C++ using pointers and the new operator.
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The document discusses equivalence relations and the union-find algorithm. It defines what makes a binary relation an equivalence relation by having the properties of reflexivity, symmetry, and transitivity. It gives examples like electrical connectivity being an equivalence relation. The union-find algorithm can be used to dynamically determine if elements are in the same equivalence class based on the given relations, by performing find and union operations in time proportional to m+n for m finds and n-1 unions.
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The document discusses divide and conquer algorithms for sorting, specifically mergesort and quicksort. It explains that mergesort works by recursively splitting a list in half, sorting the halves, and then merging the sorted halves together. Quicksort works by picking a pivot value and partitioning the list into elements less than and greater than the pivot, before recursively sorting the sublists. Both algorithms run in O(n log n) time.
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The document discusses various aspects of balanced binary search trees, including:
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computer notes - Data Structures - 33
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computer notes - Data Structures - 31
Union-find data structures can be used to efficiently generate random mazes. A maze can be represented as a grid of cells where each cell is initially isolated by walls. Removing walls corresponds to union operations, joining the cells' sets. A maze is generated by randomly performing unions until the entrance and exit cells are in the same set, connected by a path through the maze.
computer notes - Data Structures - 34
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computer notes - Data Structures - 38
The document discusses three elementary sorting algorithms: selection sort, insertion sort, and bubble sort. It explains their basic mechanisms, provides examples, and analyzes their time complexities. Selection sort and bubble sort have a worst-case time complexity of O(n2) because they require iterating through the entire array multiple times. Insertion sort's worst-case is also O(n2) as it may require shifting over elements each iteration. The document then introduces the idea of divide and conquer algorithms like merge sort which can achieve optimal O(n log n) time complexity.
computer notes - Data Structures - 21
The document describes various tree rotation operations used to rebalance binary search trees, including single and double rotations. Single rotations include single right rotation and single left rotation, which rotate the tree around a single node. Double rotations first perform a single rotation on one child then a single rotation on the original node, such as double right-left rotation and double left-right rotation.
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The document discusses different ways to implement tables or dictionaries using data structures like arrays, linked lists, and skip lists. It explains that tables consist of rows and columns of data with fields/keys that uniquely identify each entry. Arrays allow fast searching if sorted but slow insertion/deletion. Linked lists allow fast insertion/deletion but slow searching. Skip lists combine fast search of sorted data structures with fast insertion/deletion of unsorted structures.
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The document discusses algorithms and data structures. It begins by introducing common data structures like arrays, stacks, queues, trees, and hash tables. It then explains that data structures allow for organizing data in a way that can be efficiently processed and accessed. The document concludes by stating that the choice of data structure depends on effectively representing real-world relationships while allowing simple processing of the data.
Introduction to Data Structures, Data Structures using C.pptx
P.Poongothai
Kristu Jayanti College (Autonomous)
Lec1
This document discusses data structures and their role in organizing data efficiently for computer programs. It defines key concepts like abstract data types, algorithms, and problems. It also provides examples to illustrate selecting the appropriate data structure based on the operations and constraints of a problem. A banking application is used to demonstrate how hash tables are suitable because they allow extremely fast searching by account numbers while also supporting efficient insertion and deletion. B-trees are shown to be better than hash tables for a city database because they enable fast range queries in addition to exact searches. Overall, the document emphasizes that each data structure has costs and benefits, and a careful analysis is needed to determine the best structure for a given problem.
EE-232-LEC-01 Data_structures.pptx
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Data structures and algorithms short note (version 14).pd
The document provides an introduction to data structures and algorithms. It discusses why data structures are needed, common measurements of efficiency, and the costs of algorithms. It defines abstract and concrete data structures, and provides examples of stacks and queues as abstract data types that can be implemented using concrete data structures like arrays. It also discusses algorithms for operations like sorting, searching, insertion and removal. Overall, the document serves as an introductory overview of key concepts in data structures and algorithms.
algo 1.ppt
This document introduces key concepts related to data structures and algorithms. It defines objectives like introducing commonly used data structures and selecting the best one for a given problem. It describes how abstraction is used to model problems and define abstract data types independently of programming languages. Data structures provide a physical implementation of abstract data types by organizing data in memory. Algorithms manipulate data structures to transform their state and produce outputs. Properties like finiteness, definiteness, correctness, and efficiency are discussed for algorithms. Measuring an algorithm's theoretical efficiency using asymptotic analysis is introduced.
Chapter 1 Introduction to Data Structures and Algorithms.pdf
Data structures provide an efficient way to store and organize data in a computer so that it can be used efficiently. They allow programmers to handle data in an enhanced way, improving software performance. There are linear data structures like arrays and linked lists, and non-linear structures like trees and graphs. Common operations on data structures include insertion, deletion, searching, sorting, and merging. Asymptotic analysis is used to define the time complexity of algorithms in the average, best, and worst cases.
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Lecture1 data structure(introduction)
Selecting Data Structure
Data Structure Philosophy
Abstract Data Types
Logical vs. Physical Form
Programs
Algorithm Properties
References
Introduction to Data Structure
Data may be organized in many different ways; the logical or mathematical model of a particular organization of data is called "Data Structure". The choice of a particular data model depends on two considerations:
It must be rich enough in structure to reflect the actual relationships of the data in the real world.
The structure should be simple enough that one can effectively process the data when necessary.
Data Structure Operations
The particular data structure that one chooses for a given situation depends largely on the nature of specific operations to be performed.
The following are the four major operations associated with any data structure:
i. Traversing : Accessing each record exactly once so that certain items in the record may be processed.
ii. Searching : Finding the location of the record with a given key value, or finding the locations of all records which satisfy one or more conditions.
iii. Inserting : Adding a new record to the structure.
iv. Deleting : Removing a record from the structure.
Primitive and Composite Data Types
Primitive Data Types are Basic data types of any language. In most computers these are native to the machine's hardware.
Some Primitive data types are:
Integer
Bca2020 data structure and algorithm
This document provides information about getting fully solved assignments from an assignment help service. It includes contact information for the service via email or phone call. It also provides a sample assignment question from the subject of Data Structure and Algorithm for BCA semester 2. The sample assignment includes 6 questions ranging from explaining common data structure operations and algorithms like insertion sort to defining concepts like NP-completeness, queues, and the greedy method strategy. Students are encouraged to contact the provided email or phone number to receive solved assignments.
DS-UNIT 1 FINAL (2).pptx
This document provides an introduction and overview of data structures and dynamic memory allocation in C programming. It defines key terminology related to data structures like data, records, files, attributes, and fields. It also describes different types of data structures like primitive, non-primitive, homogeneous, non-homogeneous, static, and dynamic data structures. The document explains the need for data structures and their advantages and disadvantages. It also discusses operations that can be performed on data structures and introduces dynamic memory allocation using functions like malloc(), calloc(), free(), and realloc(). Finally, it provides a brief introduction to recursion as a programming concept.
Data Structures_Introduction
This document provides an introduction and overview of data structures and dynamic memory allocation in C programming. It defines key terminology related to data structures like data, records, files, attributes, and fields. It also describes different types of data structures like primitive, non-primitive, homogeneous, non-homogeneous, static, and dynamic data structures. The document explains the need for data structures and their advantages and disadvantages. It then covers dynamic memory allocation using functions like malloc(), calloc(), realloc(), and free() in C. Finally, it provides a brief introduction to recursion as a process of repeating items in a self-similar way by allowing a function to call itself.
Similar to computer notes - Data Structures - 1 (20)
Introduction to Data Structures, Data Structures using C.pptx
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Data structures and algorithms short note (version 14).pd
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computer notes - Data Structures - 30
The document discusses different techniques for improving the efficiency of union-find algorithms, including union-by-size, path compression, and union-by-height. Union-by-size works by making the root of the smaller tree the child of the larger tree during a union operation, keeping tree heights small. Path compression further optimizes find operations by updating the parent pointers along the search path. Together these optimizations allow union-find algorithms to run in almost linear time for practical purposes.
computer notes - Data Structures - 20
The document discusses AVL trees and balanced binary search trees. It provides the following key points:
1) An AVL tree is a self-balancing binary search tree where the height of the two child subtrees of every node differ by at most one.
2) A balanced binary search tree is one where the height of the left and right subtrees of each node differ by no more than one.
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computer notes - Data Structures - 4
The document discusses different types of linked lists, including singly linked lists, doubly linked lists, and circularly linked lists. It provides code examples for implementing linked lists in C++ and compares the time complexity of different linked list operations. It also describes how a circularly linked list can be used to solve the Josephus problem of eliminating people seated in a circle.
computer notes - Data Structures - 16
The document discusses deleting nodes from a binary search tree (BST). There are three cases to consider when deleting a node: 1) if the node is a leaf, it can be deleted immediately, 2) if the node has one child, its parent pointer is redirected to the child node, 3) if the node has two children, it is replaced with its inorder successor. The algorithm and C++ code for deleting nodes from a BST is presented.
computer notes - Data Structures - 22
The document discusses deletion in AVL trees and outlines 5 cases to consider when deleting nodes from an AVL tree. It also discusses expression trees and parse trees, providing examples of an expression tree for a mathematical expression and a parse tree for an SQL query. Other uses of binary trees mentioned include their use in compilers for expression trees, parse trees, and abstract syntax trees.
computer notes - Data Structures - 36
The document discusses different methods for handling collisions in hash tables, which occur when two keys hash to the same slot. It describes linear probing, where the next empty slot is used to store the colliding key; quadratic probing which uses a quadratic function to determine subsequent slots; and chaining, where each slot contains a linked list of colliding keys. It notes the advantages and disadvantages of each approach.
computer notes - Data Structures - 14
The document discusses recursion and different traversal methods for binary trees. It explains how the call stack is used during recursive function calls and shows examples of preorder and inorder recursive tree traversals. It then describes how to perform non-recursive inorder traversal using an explicit stack. Finally, it introduces level-order traversal, which visits all nodes at each level from left to right before proceeding to the next level.
computer notes - Data Structures - 29
The document discusses using trees and parent pointers to represent sets and solve the dynamic equivalence problem. Each element begins in its own set, represented as a tree with that element as the root. The union operation merges two trees by making one root point to the other. Find returns the root of the tree an element belongs to by traversing parent pointers up the tree. This can be optimized using a technique called union by rank to keep tree heights small.
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