The document provides an introduction to data structures and algorithms analysis. It discusses that a program consists of organizing data in a structure and a sequence of steps or algorithm to solve a problem. A data structure is how data is organized in memory and an algorithm is the step-by-step process. It describes abstraction as focusing on relevant problem properties to define entities called abstract data types that specify what can be stored and operations performed. Algorithms transform data structures from one state to another and are analyzed based on their time and space complexity.
The document discusses brute force and exhaustive search approaches to solving problems. It provides examples of how brute force can be applied to sorting, searching, and string matching problems. Specifically, it describes selection sort and bubble sort as brute force sorting algorithms. For searching, it explains sequential search and brute force string matching. It also discusses using brute force to solve the closest pair, convex hull, traveling salesman, knapsack, and assignment problems, noting that brute force leads to inefficient exponential time algorithms for TSP and knapsack.
This document provides an introduction to data structures. It defines data structures as a way of organizing data so that it can be used efficiently. The document then discusses basic terminology, why data structures are important, how they are studied, and how they are classified as simple or compound, and linear or non-linear. It proceeds to describe common data structures like arrays, stacks, queues, linked lists, trees, and graphs, and how they support basic operations. The document concludes by discussing how to select an appropriate data structure based on the problem constraints and required operations.
Normalization is a process of organizing data to reduce redundancy and improve data integrity. It involves decomposing relations with anomalies into smaller, well-structured relations by identifying functional dependencies and applying normal forms. The normal forms are first normal form (1NF), second normal form (2NF), third normal form (3NF) and Boyce-Codd normal form (BCNF). Each normal form adds additional rules to reduce redundancy through a multi-step process of identifying dependencies and extracting subsets of data into new relations.
The document discusses data structures and arrays. It begins by defining data, data structures, and how data structures affect program design. It then categorizes data structures as primitive and non-primitive. Linear and non-linear data structures are described as examples of non-primitive structures. The document focuses on arrays as a linear data structure, covering array declaration, representation in memory, calculating size, types of arrays, and basic operations like traversing, searching, inserting, deleting and sorting. Two-dimensional arrays are also introduced.
The document discusses different searching algorithms. It describes sequential search which compares the search key to each element in the list sequentially until a match is found. The best case is 1 comparison, average is N/2 comparisons, and worst case is N comparisons. It also describes binary search which divides the sorted list in half at each step, requiring log(N) comparisons in the average and worst cases. The document also covers indexing which structures data for efficient retrieval based on key values and includes clustered vs unclustered indexes.
Linked Lists: Introduction Linked lists
Representation of linked list
operations on linked list
Comparison of Linked Lists with Arrays and Dynamic Arrays
Types of Linked Lists and operations-Circular Single Linked List, Double Linked List, Circular Double Linked List
1. Linear search is a method for finding a particular value in a list that checks each element in sequence until the desired element is found or the list is exhausted.
2. The best case for linear search is O(1) when the target is found at the first location. The worst case is O(n) when the target is at the end or not present.
3. The average time complexity of linear search is O(n) as the target has an equal chance of being in any position, so on average half the list must be searched.
This document provides an overview of trees as a non-linear data structure. It begins by discussing how trees are used to represent hierarchical relationships and defines some key tree terminology like root, parent, child, leaf, and subtree. It then explains that a tree consists of nodes connected in a parent-child relationship, with one root node and nodes that may have any number of children. The document also covers tree traversal methods like preorder, inorder, and postorder traversal. It introduces binary trees and binary search trees, and discusses operations on BSTs like search, insert, and delete. Finally, it provides a brief overview of the Huffman algorithm for data compression.
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 (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.
Insertion sort is a sorting algorithm that works by building a sorted array (or list) one item at a time. It maintains two groups, a sorted group and an unsorted group. It removes one element from the unsorted group, finds the location it belongs within the sorted group, and inserts it there. This continues until the unsorted group is empty, leaving a fully sorted list. The worst-case running time is O(n^2) as each insertion may require traversing the entire sorted portion. However, the average case is O(n) for nearly sorted data. A lower bound analysis shows that any algorithm relying on adjacent swaps has a worst case lower bound of Ω(n^2).
Self-organizing lists reorder elements based on access frequency to improve search efficiency. Elements with higher access probabilities are moved towards the front using heuristics like move-to-front, transposition, and counting access frequencies. This reduces average access time compared to random ordering. The worst case is searching for an element at the end, while the best case is finding a frequently accessed element at the front.
This document provides an overview of linear search and binary search algorithms.
It explains that linear search sequentially searches through an array one element at a time to find a target value. It is simple to implement but has poor efficiency as the time scales linearly with the size of the input.
Binary search is more efficient by cutting the search space in half at each step. It works on a sorted array by comparing the target to the middle element and determining which half to search next. The time complexity of binary search is logarithmic rather than linear.
Introduction to Data Structures Sorting and searching
This document provides an overview of data structures and algorithms. It begins by defining a data structure as a way of storing and organizing data in a computer so that it can be used efficiently by algorithms. Data structures can be primitive, directly operated on by machine instructions, or non-primitive, developed from primitive structures. Linear structures maintain adjacency between elements while non-linear do not. Common operations on data structures include adding, deleting, traversing, sorting, searching, and updating elements. The document also defines algorithms and their properties, including finiteness, definiteness, inputs, outputs, and effectiveness. It discusses analyzing algorithms based on time and space complexity and provides examples of different complexities including constant, logarithmic, linear, quadratic,
Binary search is an algorithm that finds the position of a target value within a sorted array. It works by recursively dividing the array range in half and searching only within the appropriate half. The time complexity is O(log n) in the average and worst cases and O(1) in the best case, making it very efficient for searching sorted data. However, it requires the list to be sorted for it to work.
Data Structure and Algorithm chapter two, This material is for Data Structure...
The document discusses algorithm analysis and different searching and sorting algorithms. It introduces sequential search and binary search as simple searching algorithms. Sequential search, also called linear search, examines each element of a list sequentially until a match is found. It has average time complexity of O(n) as it may need to examine all n elements in the worst case.
The document provides an introduction to algorithms and their analysis. It defines an algorithm and lists its key criteria. It discusses different representations of algorithms including flowcharts and pseudocode. It also outlines the main areas of algorithm analysis: devising algorithms, validating them, analyzing performance, and testing programs. Finally, it provides examples of algorithms and their analysis including calculating time complexity based on counting operations.
Download Complete Material - https://www.instamojo.com/prashanth_ns/
This Data Structures and Algorithms contain 15 Units and each Unit contains 60 to 80 slides in it.
Contents…
• Introduction
• Algorithm Analysis
• Asymptotic Notation
• Foundational Data Structures
• Data Types and Abstraction
• Stacks, Queues and Deques
• Ordered Lists and Sorted Lists
• Hashing, Hash Tables and Scatter Tables
• Trees and Search Trees
• Heaps and Priority Queues
• Sets, Multi-sets and Partitions
• Dynamic Storage Allocation: The Other Kind of Heap
• Algorithmic Patterns and Problem Solvers
• Sorting Algorithms and Sorters
• Graphs and Graph Algorithms
• Class Hierarchy Diagrams
• Character Codes
The document discusses algorithms and data structures. It defines an algorithm as a step-by-step procedure for solving a problem using a computer in a finite number of steps. It categorizes common types of algorithms as search, sort, insert, update, and delete algorithms. The document also defines a data structure as a way to store and organize data for efficient use. It distinguishes between linear and non-linear as well as static and dynamic data structures. Finally, it discusses algorithm design strategies like divide and conquer, merge sort, and dynamic programming.
This slides contains assymptotic notations, recurrence relation like subtitution method, iteration method, master method and recursion tree method and sorting algorithms like merge sort, quick sort, heap sort, counting sort, radix sort and bucket sort.
The document discusses data structures and their importance in organizing data efficiently for computer programs. It defines what a data structure is and how choosing the right one can improve a program's performance. Several examples are provided to illustrate how analyzing a problem's specific needs guides the selection of an optimal data structure.
The document provides an overview of entity-relationship (ER) modeling concepts used in database design. It defines key terms like entities, attributes, relationships, and cardinalities. It explains how ER diagrams visually represent these concepts using symbols like rectangles, diamonds, and lines. The document also discusses entity types, relationship degrees, key attributes, weak entities, and how to model one-to-one, one-to-many, many-to-one, and many-to-many relationships. Overall, the document serves as a guide to basic ER modeling principles for conceptual database design.
The document describes splay trees, a type of self-adjusting binary search tree. Splay trees differ from other balanced binary search trees in that they do not explicitly rebalance after each insertion or deletion, but instead perform a process called "splaying" in which nodes are rotated to the root. This splaying process helps ensure search, insert, and delete operations take O(log n) amortized time. The document explains splaying operations like zig, zig-zig, and zig-zag that rotate nodes up the tree, and analyzes how these operations affect the tree's balance over time through a concept called the "rank" of the tree.
The document discusses brute force and exhaustive search approaches to solving problems. It provides examples of how brute force can be applied to sorting, searching, and string matching problems. Specifically, it describes selection sort and bubble sort as brute force sorting algorithms. For searching, it explains sequential search and brute force string matching. It also discusses using brute force to solve the closest pair, convex hull, traveling salesman, knapsack, and assignment problems, noting that brute force leads to inefficient exponential time algorithms for TSP and knapsack.
This document provides an introduction to data structures. It defines data structures as a way of organizing data so that it can be used efficiently. The document then discusses basic terminology, why data structures are important, how they are studied, and how they are classified as simple or compound, and linear or non-linear. It proceeds to describe common data structures like arrays, stacks, queues, linked lists, trees, and graphs, and how they support basic operations. The document concludes by discussing how to select an appropriate data structure based on the problem constraints and required operations.
Normalization is a process of organizing data to reduce redundancy and improve data integrity. It involves decomposing relations with anomalies into smaller, well-structured relations by identifying functional dependencies and applying normal forms. The normal forms are first normal form (1NF), second normal form (2NF), third normal form (3NF) and Boyce-Codd normal form (BCNF). Each normal form adds additional rules to reduce redundancy through a multi-step process of identifying dependencies and extracting subsets of data into new relations.
The document discusses data structures and arrays. It begins by defining data, data structures, and how data structures affect program design. It then categorizes data structures as primitive and non-primitive. Linear and non-linear data structures are described as examples of non-primitive structures. The document focuses on arrays as a linear data structure, covering array declaration, representation in memory, calculating size, types of arrays, and basic operations like traversing, searching, inserting, deleting and sorting. Two-dimensional arrays are also introduced.
The document discusses different searching algorithms. It describes sequential search which compares the search key to each element in the list sequentially until a match is found. The best case is 1 comparison, average is N/2 comparisons, and worst case is N comparisons. It also describes binary search which divides the sorted list in half at each step, requiring log(N) comparisons in the average and worst cases. The document also covers indexing which structures data for efficient retrieval based on key values and includes clustered vs unclustered indexes.
Linked Lists: Introduction Linked lists
Representation of linked list
operations on linked list
Comparison of Linked Lists with Arrays and Dynamic Arrays
Types of Linked Lists and operations-Circular Single Linked List, Double Linked List, Circular Double Linked List
1. Linear search is a method for finding a particular value in a list that checks each element in sequence until the desired element is found or the list is exhausted.
2. The best case for linear search is O(1) when the target is found at the first location. The worst case is O(n) when the target is at the end or not present.
3. The average time complexity of linear search is O(n) as the target has an equal chance of being in any position, so on average half the list must be searched.
This document provides an overview of trees as a non-linear data structure. It begins by discussing how trees are used to represent hierarchical relationships and defines some key tree terminology like root, parent, child, leaf, and subtree. It then explains that a tree consists of nodes connected in a parent-child relationship, with one root node and nodes that may have any number of children. The document also covers tree traversal methods like preorder, inorder, and postorder traversal. It introduces binary trees and binary search trees, and discusses operations on BSTs like search, insert, and delete. Finally, it provides a brief overview of the Huffman algorithm for data compression.
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 (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.
Insertion sort is a sorting algorithm that works by building a sorted array (or list) one item at a time. It maintains two groups, a sorted group and an unsorted group. It removes one element from the unsorted group, finds the location it belongs within the sorted group, and inserts it there. This continues until the unsorted group is empty, leaving a fully sorted list. The worst-case running time is O(n^2) as each insertion may require traversing the entire sorted portion. However, the average case is O(n) for nearly sorted data. A lower bound analysis shows that any algorithm relying on adjacent swaps has a worst case lower bound of Ω(n^2).
Self-organizing lists reorder elements based on access frequency to improve search efficiency. Elements with higher access probabilities are moved towards the front using heuristics like move-to-front, transposition, and counting access frequencies. This reduces average access time compared to random ordering. The worst case is searching for an element at the end, while the best case is finding a frequently accessed element at the front.
This document provides an overview of linear search and binary search algorithms.
It explains that linear search sequentially searches through an array one element at a time to find a target value. It is simple to implement but has poor efficiency as the time scales linearly with the size of the input.
Binary search is more efficient by cutting the search space in half at each step. It works on a sorted array by comparing the target to the middle element and determining which half to search next. The time complexity of binary search is logarithmic rather than linear.
Introduction to Data Structures Sorting and searchingMvenkatarao
This document provides an overview of data structures and algorithms. It begins by defining a data structure as a way of storing and organizing data in a computer so that it can be used efficiently by algorithms. Data structures can be primitive, directly operated on by machine instructions, or non-primitive, developed from primitive structures. Linear structures maintain adjacency between elements while non-linear do not. Common operations on data structures include adding, deleting, traversing, sorting, searching, and updating elements. The document also defines algorithms and their properties, including finiteness, definiteness, inputs, outputs, and effectiveness. It discusses analyzing algorithms based on time and space complexity and provides examples of different complexities including constant, logarithmic, linear, quadratic,
Binary search is an algorithm that finds the position of a target value within a sorted array. It works by recursively dividing the array range in half and searching only within the appropriate half. The time complexity is O(log n) in the average and worst cases and O(1) in the best case, making it very efficient for searching sorted data. However, it requires the list to be sorted for it to work.
Data Structure and Algorithm chapter two, This material is for Data Structure...bekidea
The document discusses algorithm analysis and different searching and sorting algorithms. It introduces sequential search and binary search as simple searching algorithms. Sequential search, also called linear search, examines each element of a list sequentially until a match is found. It has average time complexity of O(n) as it may need to examine all n elements in the worst case.
The document provides an introduction to algorithms and their analysis. It defines an algorithm and lists its key criteria. It discusses different representations of algorithms including flowcharts and pseudocode. It also outlines the main areas of algorithm analysis: devising algorithms, validating them, analyzing performance, and testing programs. Finally, it provides examples of algorithms and their analysis including calculating time complexity based on counting operations.
Download Complete Material - https://www.instamojo.com/prashanth_ns/
This Data Structures and Algorithms contain 15 Units and each Unit contains 60 to 80 slides in it.
Contents…
• Introduction
• Algorithm Analysis
• Asymptotic Notation
• Foundational Data Structures
• Data Types and Abstraction
• Stacks, Queues and Deques
• Ordered Lists and Sorted Lists
• Hashing, Hash Tables and Scatter Tables
• Trees and Search Trees
• Heaps and Priority Queues
• Sets, Multi-sets and Partitions
• Dynamic Storage Allocation: The Other Kind of Heap
• Algorithmic Patterns and Problem Solvers
• Sorting Algorithms and Sorters
• Graphs and Graph Algorithms
• Class Hierarchy Diagrams
• Character Codes
The document discusses algorithms and data structures. It defines an algorithm as a step-by-step procedure for solving a problem using a computer in a finite number of steps. It categorizes common types of algorithms as search, sort, insert, update, and delete algorithms. The document also defines a data structure as a way to store and organize data for efficient use. It distinguishes between linear and non-linear as well as static and dynamic data structures. Finally, it discusses algorithm design strategies like divide and conquer, merge sort, and dynamic programming.
This slides contains assymptotic notations, recurrence relation like subtitution method, iteration method, master method and recursion tree method and sorting algorithms like merge sort, quick sort, heap sort, counting sort, radix sort and bucket sort.
The document discusses data structures and their importance in organizing data efficiently for computer programs. It defines what a data structure is and how choosing the right one can improve a program's performance. Several examples are provided to illustrate how analyzing a problem's specific needs guides the selection of an optimal data structure.
The document discusses data structures and their importance in organizing data efficiently for computer programs. It defines what a data structure is and how choosing the right one can improve a program's performance. Several examples are provided to illustrate how analyzing a problem's specific needs guides the selection of an optimal data structure.
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.
This document discusses data structures and algorithms. It defines data structures as how data is organized in memory and algorithms as computational steps to solve problems. The first step to solve a problem is obtaining an abstract model by defining relevant entities and operations. Data structures model static data and algorithms model dynamic changes to data. Properties of good algorithms include being finite, definite, feasible, correct, and efficient. Analyzing algorithms involves determining their time and space complexity using theoretical and empirical methods. Complexity is classified based on how resource needs grow relative to problem size.
Fundamentals of the Analysis of Algorithm EfficiencySaranya Natarajan
This document discusses analyzing the efficiency of algorithms. It introduces the framework for analyzing algorithms in terms of time and space complexity. Time complexity indicates how fast an algorithm runs, while space complexity measures the memory required. The document outlines steps for analyzing algorithms, including measuring input size, determining the basic operations, calculating frequency counts of operations, and expressing efficiency in Big O notation order of growth. Worst-case, best-case, and average-case time complexities are also discussed.
SCHEDULING DIFFERENT CUSTOMER ACTIVITIES WITH SENSING DEVICEijait
Most periodic tasks are assigned to processors using partition scheduling policy after checking feasibility conditions. A new approach is proposed for scheduling different activities with one periodic task within the system. In this paper, control strategies are identified for allocating different types of tasks (activities) to
individual computing elements like Smartphone or microphones. In our simulation model, each periodic task generates an aperiodic tasks are taken into consideration. Different sets of periodic tasks and aperiodic tasks are scheduled together. This new approach proves that when all different activities are
scheduled with one periodic tasks leads to better performance.
Introduction to data structures and AlgorithmDhaval Kaneria
This document provides an introduction to data structures and algorithms. It discusses key concepts like algorithms, abstract data types (ADTs), data structures, time complexity, and space complexity. It describes common data structures like stacks, queues, linked lists, trees, and graphs. It also covers different ways to classify data structures, the process for selecting an appropriate data structure, and how abstract data types encapsulate both data and functions. The document aims to explain fundamental concepts related to organizing and manipulating data efficiently.
This document provides an introduction to data structures and algorithms. It discusses key concepts like abstract data types (ADTs), different types of data structures including linear and non-linear structures, analyzing algorithms to assess efficiency, and selecting appropriate data structures based on required operations and resource constraints. The document also covers topics like classifying data structures, properties of algorithms, analyzing time and space complexity, and examples of iterative and recursive algorithms and their complexity analysis.
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.
This document provides an overview of data structures and algorithms. It discusses key concepts like interfaces, implementations, time complexity, space complexity, asymptotic analysis, and common control structures. Some key points:
- A data structure organizes data to allow for efficient operations. It has an interface defining operations and an implementation defining internal representation.
- Algorithm analysis considers best, average, and worst case time complexities using asymptotic notations like Big O. Space complexity also measures memory usage.
- Common control structures include sequential, conditional (if/else), and repetitive (loops) structures that control program flow based on conditions.
This document discusses time and space complexity analysis of algorithms. It defines key concepts like computational problems, algorithms, inputs, outputs, and properties of good algorithms. It then explains space complexity and time complexity, and provides examples of typical time functions like constant, logarithmic, linear, quadratic, and exponential. An example C program for matrix multiplication is provided, with its time complexity analyzed as O(n^2) + O(n^3).
Data structures allow for the organization of data to enable efficient operations. They represent how data is stored in memory. Good data structures are designed to reduce complexity and improve efficiency. Common classifications of data structures include linear versus non-linear, homogeneous versus non-homogeneous, static versus dynamic based on whether size is fixed. Algorithms provide step-by-step instructions to solve problems and must have defined inputs, outputs, and steps. Time and space complexity analysis evaluates an algorithm's efficiency based on memory usage and speed.
This document provides an overview of algorithm analysis and asymptotic complexity. It discusses learning outcomes related to analyzing algorithm efficiency using Big O, Omega, and Theta notation. Key points covered include:
- Defining the problem size n and relating algorithm running time to n
- Distinguishing between best-case, worst-case, and average-case complexity
- Using asymptotic notation like Big O to give upper bounds on complexity rather than precise calculations
- Common asymptotic categories like O(n), O(n^2), O(n log n) that classify algorithm growth rates
1. The document outlines topics on SQL including data types, tables, queries, joins, and the semantics of SQL queries.
2. SQL is used to query and manipulate relational data and includes languages for data definition, data manipulation, and transactions. It allows selecting data from one or more tables and supports conditions, projections, ordering, and eliminating duplicates.
3. Joins are used to connect information from two or more tables by matching column values, and disambiguating names is needed when tables share attribute names. The meaning of SQL queries involves nested loops or parallel assignment to evaluate conditions and return selected columns.
This document provides an overview and introduction to Microsoft Access. It discusses what Access is and why one might choose to use Access over other database management systems or programs like Excel or SPSS. The document outlines some of Access' main features, including its ability to create and work with tables, queries, forms and reports. It also discusses more advanced Access concepts such as splitting databases, importing/linking data from external sources, and designing a graphical user interface using forms and reports. Overall, the document serves as an introductory primer and guide for getting started with the basic functions and capabilities of Microsoft Access.
This document discusses the importance of teaching mathematics through problem solving, noting that problem solving allows students to explore, develop, and apply their understanding of mathematical concepts. It emphasizes that problem solving should be the mainstay of mathematical teaching and describes the three-part problem-solving lesson structure of getting started, working on it, and reflecting and connecting.
This document describes the major internal and external components of a computer system. It explains that computers contain hardware components like the central processing unit (CPU) and memory chips, as well as input/output devices. The CPU interprets and executes program instructions. Other hardware includes the computer case, monitor, keyboard, mouse, disk drives, network cards, and printers. The document also discusses software components like operating systems, which connect hardware and allow users to interact with programs. Examples of operating systems are MS-DOS and Windows.
The document provides definitions and descriptions of basic computer parts and components. It discusses hardware components like the case, keyboard, monitor, mouse, as well as internal components like the power supply, hard drive, CD drive, motherboard, and memory. It also covers ports and connectors on the computer like video ports, parallel ports, serial ports, mouse and keyboard ports, and USB ports. Safety precautions are outlined when working with computer hardware.
The document discusses binary trees and binary search trees. It defines binary trees as trees where each node has at most two children. Binary search trees are binary trees where the left child of a node is less than the node and the right child is greater. The document covers traversing binary trees in preorder, inorder and postorder fashion. It also covers inserting nodes into and searching binary search trees.
IS230 - Chapter 4 - Keys and Relationship - Revised.pptwondmhunegn
This chapter discusses keys and relationships in database tables. It defines primary keys as fields that uniquely identify rows, and foreign keys as keys that link to primary keys in other tables to create relationships. There are three main relationship types: one-to-one, one-to-many, and many-to-many. The chapter demonstrates identifying primary keys, foreign keys, and relationships using examples from a sample database and emphasizes the importance of referential integrity between keys.
MS-Access Tables Forms Queries Reports.pptwondmhunegn
This document provides an introduction to Microsoft Access and its key components: tables, forms, queries, and reports. It explains that Access is a relational database application that allows users to create and maintain database tables with tools to define, construct, and manipulate data. The document outlines the basic functions of tables, forms, queries, and reports and how to design each component to structure, enter, display, and extract data from an Access database.
This document provides an overview of database fundamentals, including the key concepts of a database schema, tables, fields, records, primary keys, foreign keys, and relationships. It discusses different data types and normalization techniques to organize data into tables in first normal form, second normal form, and third normal form to avoid data duplication, insertion anomalies, deletion anomalies, and update anomalies. An example of normalizing an unnormalized sales orders table is provided.
Data types and field properties are used to format data in database tables. Data types define the type of data in a field (e.g. number, text) and field properties define how the data is formatted (e.g. size, mask). Setting the correct data types and field properties allows data to be sorted, searched, and used correctly. Common data types include text, number, date/time, and currency. Field properties like size, format, input mask and caption further control how data is entered and displayed.
The document summarizes a proposed campus notification system project at the University of Gondar. The current manual notice board system has several problems such as lack of organization, inability to easily search or edit notices, and not being accessible anywhere at any time. The proposed automated system would allow students and faculty to view course schedules, exam schedules, dormitory information and other notices online from any location. It would also allow notices to be more easily managed and organized through administrative accounts. The system design would include use cases, activity diagrams, sequence diagrams, class diagrams and database management.
How We Added Replication to QuestDB - JonTheBeachjavier ramirez
Building a database that can beat industry benchmarks is hard work, and we had to use every trick in the book to keep as close to the hardware as possible. In doing so, we initially decided QuestDB would scale only vertically, on a single instance.
A few years later, data replication —for horizontally scaling reads and for high availability— became one of the most demanded features, especially for enterprise and cloud environments. So, we rolled up our sleeves and made it happen.
Today, QuestDB supports an unbounded number of geographically distributed read-replicas without slowing down reads on the primary node, which can ingest data at over 4 million rows per second.
In this talk, I will tell you about the technical decisions we made, and their trade offs. You'll learn how we had to revamp the whole ingestion layer, and how we actually made the primary faster than before when we added multi-threaded Write Ahead Logs to deal with data replication. I'll also discuss how we are leveraging object storage as a central part of the process. And of course, I'll show you a live demo of high-performance multi-region replication in action.
Airline Satisfaction Project using Azure
This presentation is created as a foundation of understanding and comparing data science/machine learning solutions made in Python notebooks locally and on Azure cloud, as a part of Course DP-100 - Designing and Implementing a Data Science Solution on Azure.
University of Toronto degree offer diploma Transcript
Chapter 1 Data structure.pptx
2. 1.1. Introduction to Data Structures and Algorithms Analysis
A program is written in order to solve a problem. A solution to a problem
actually consists of two things:
I. A way to organize the data
II. Sequence of steps to solve the problem
The way data are organized in a computer’s memory is said to be data
structure and
The sequence of computational steps to solve a problem is said to be an
algorithm.
Therefore, a program is nothing but data structures plus algorithms.
A data structure is a systematic way of organizing and accessing data and
an algorithm is a step-by-step procedure for performing some task in a
finite amount of time.
3. Introduction to Data Structures
The first step to solve the problem is obtaining one’s own
abstract view, or model, of the problem.
This process of modeling is called abstraction.
The model defines an abstract view to the problem.
This implies that the model focuses only on problem related
stuff and
A programmer tries to define the properties of the problem.
3
4. Cont.
These properties Abstract data include
The data which are affected and
The operations that are involved in the problem.
With abstraction you create a well-defined entity that can be
properly handled.
These entities define the data structure of the program.
An entity with the properties just described is called an abstract
data type (ADT).
4
5. Abstract Data Types
An abstract data type (ADT) is a set of objects together with a set of
operations.
An ADT is a mathematical model of a data structure that specifies the
type of the data stored, the operations supported on them
Objects such as lists, sets, and graphs, along with their operations, can
be viewed as ADTs, just as integers, real’s, and booleans are data types.
The ADT specifies:
1. What can be stored in the Abstract Data Type?
2. What operations can be done on/by the Abstract Data Type?
5
6. Abstraction
Abstraction is a process of classifying characteristics as
relevant and irrelevant for the particular purpose at hand and
ignoring the irrelevant ones.
The abstraction is to distill a complicated system down to its
most fundamental parts and
describe these parts in a simple, precise language.
Typically, describing the parts of a system involves naming
them and explaining their functionality.
6
7. Algorithms
An algorithm is a well-defined computational procedure that
takes :
some value or a set of values as input and
produces some value or a set of values as output.
Data structures model the static part of the world.
They are unchanging while the world is changing.
In order to model the dynamic part of the world we need to
work with algorithms.
Algorithms are the dynamic part of a program’s world model.
An algorithm transforms data structures from one state to
another state in two ways:
An algorithm may change the value held by a data structure
An algorithm may change the data structure itself 7
8. Properties of an algorithm
What makes an algorithm good?
Finiteness: Algorithm must complete after a finite number of steps.
Definiteness: Each step must be clearly defined, having one and only
one interpretation. At each point in computation, one should be able
to tell exactly what happens next.
Sequence: Each step must have a unique defined preceding and
succeeding step. The first step (start step) and last step (halt step)
must be clearly noted.
Feasibility: It must be possible to perform each instruction.
Correctness: It must compute correct answer for all possible legal
inputs.
8
9. Cont.
Language Independence: It must not depend on any one
programming language.
Completeness: It must solve the problem completely.
Effectiveness: It must be possible to perform each step exactly and in
a finite amount of time.
Efficiency: It must solve with the least amount of computational
resources such as time and space.
Generality: Algorithm should be valid on all possible inputs.
Input/Output: There must be a specified number of input values, and
one or more result values.
9
10. Algorithm Analysis Concepts
Algorithm analysis refers to the process of determining the
amount of computing time and storage space required by
different algorithms.
In other words, it’s a process of predicting the resource
requirement of algorithms in a given environment.
It is the study of efficiency of programs.
Input size of the program, machine type used, implementation
quality, running time of algorithm and others affect the
efficiency of a program.
10
11. … Cont.
In order to solve a problem, there are many possible algorithms.
One has to be able to choose the best algorithm for the problem
at hand using some scientific method.
To classify some data structures and algorithms as good, we
need precise ways of analyzing them in terms of resource
requirement. The main resources are:
Running Time
Memory Usage
Communication Bandwidth
Algorithm analysis tries to estimate these resources required to
solve a problem at hand.
Running time is usually treated as the most important since
computational time is the most precious resource in most
problem domains.
11
12. --- Cont
There are two approaches to measure the efficiency of algorithms:
Empirical (Experimental) method: Programming competing
algorithms and trying them on different instances. This method is
used for absolute time measurement.
Analytical (Theoretical) Method: Determining the quantity of
resources required mathematically (like execution time, memory
space, etc.) needed by each algorithm.
However, it is difficult to use actual clock-time as a consistent
measure of an algorithm’s efficiency, because clock-time can vary
based on many things. For example,
Specific processor speed
Current processor load
Specific data for a particular run of the program
Input Size
Input Properties
Operating Environment
12
13. Complexity Analysis
Complexity Analysis is the systematic study of the cost of
computation, measured either in time units or in operations
performed, or in the amount of storage space required.
The goal is to have a meaningful measure that permits
comparison of algorithms independent of operating platform.
There are two things to consider:
Time Complexity: Determine the approximate number of
operations and time required to solve a problem of size n.
The running times of operations on the data structure should
be as small as possible.
Space Complexity: Determine the approximate memory
required to solve a problem of size n.
The data structure should use as little memory as possible.
13
14. Running time
The critical resource for a program is most often its running
time.
Running time is the amount of time that any algorithm takes to
run.
However, you cannot pay attention to running time alone.
You must also be concerned with other factors such as the space
required to run the program (main memory and disk space).
The primary analysis tool we use in this course involves
characterizing the running times of algorithms and data
structure operations.
Running time is a natural measure of “goodness,” since time is
a precious resource
- computer solutions should run as fast as possible.
14
15. 1.2.2. Complexity of Algorithms
There is no generally accepted set of rules for algorithm
analysis.
However, an exact count of operations is commonly used.
Arbitrary time unit is assumed for analyzing the algorithm,
and we have the following set of analysis rules.
Rule 1: Basic operations
The execution of the following operations takes one (1) time
unit.
Assignment Operation
Single Input/ Output Operation
Single Boolean Operations
Single Arithmetic Operations
Function Return 15
16. … Cont.
Rule 2: Selection statements
Running time of a selection statement (if, switch) is the time for the
condition evaluation + the maximum of the running times for the individual
clauses.
Rule 3: Loops
Running time for a loop is equal to the running time for the statements inside
the loop body multiplied (*) by number of iterations of the loop.
Rule 4: Nested Loops
The total running time of a statement inside a group of nested loops is the
running time of the statements multiplied by the product of the sizes of all
the loops.
Rule 5: Function call
Running time of a function call is 1 for setup + the time for any parameter
calculations + the time required for the execution of the function body.
Rule 6: Consecutive statements
For consecutive statements, the running time will be computed as the sum of
the running time of the separate blocks of code.
16
17. Example 1
The following examples show us how running time of the code fragments is computed.
Examples 1:
int count ( )
{
int k=0;
cout<< “Enter an integer”;
cin>>n;
for (i=0; i<n; i++)
k=k+1;
return 0;
}
Time Units to Compute
1 for the assignment statement: int k=0
1 for the output statement.
1 for the input statement.
For the loop (for):
1 assignment (i = 0), n+1 tests, and n increments.
n loops of 2 units for an assignment and addition.
1 for the return statement.
-------------------------------------------------------------------
T (n)= 1+1+1+(1+n+1+n)+2n+1 = 4n+6 = O(n)
17
18. Example 2:
int total(int n)
{
int sum=0;
for (int i=1;i<=n;i++)
sum=sum+1;
return sum;
}
Time Units to Compute
1 for the assignment statement: int sum=0
In the for loop:
1 assignment, n+1 tests, and n increments.
n loops of 2 units for an assignment and addition.
1 for the return statement.
-------------------------------------------------------------------
T (n)= 1+ (1+n+1+n)+2n+1 = 4n+4 = O(n)
18
19. Example 3:
void func( )
{ int x=0, i=0, j=1;
cout<< “Enter an Integer value”;
cin>>n;
while (i<n)
{ x++;
i++; }
while (j<n)
j++; }
Time Units to Compute
1 for the first assignment statement: x=0;
1 for the second assignment statement: i=0;
1 for the third assignment statement: j=1;
1 for the output statement.
1 for the input statement.
In the first while loop: n+1 tests
n loops of 2 units for the two increment (addition) operations
In the second while loop:
n tests
n-1 increments
-------------------------------------------------------------------
T (n)= 1+1+1+1+1+(n+1+2n)+(n+n-1) = 5n+5 = O(n) 19
20. Example 4:
int sum (int n)
{
int partial_sum = 0;
for (int i = 1; i <= n; i++)
partial_sum = partial_sum +(i * i * i);
return partial_sum;
}
Time Units to Compute
1 for the assignment.
1 assignment, n+1 tests, and n increments for the loop expression (for).
n loops of 4 units for an assignment, addition, and two multiplications.
1 for the return statement.
-------------------------------------------------------------------
T (n) = 1+(1+n+1+n)+4n+1 = 6n+4 = O(n)
20
21. Example 5:
void func ( )
{
int i =1, sum = 0;
while (i < = n)
{
for (int j =0;j<n; j++)
{ sum = i + j; }
i ++;
}}
Time Units to Compute
1 for the first assignment (i = 1).
1 for the second assignment (sum = 0).
In the while loop
n+1 tests
n loops of the following
For the for loop
1 assignment, n+1 tests, and n increments.
n loops of 2 units for an assignment and addition.
1 for the increment operation.
-------------------------------------------------------------------
T (n) = 1+1+(n+1)+n[(1+n+1+n+2n)+1] = 4n2+4n+3 = O(n2) 21
22. Example 6:
int k=0;
for (int i=1; i<n; i*=2)
for(int j=1;j<=n;j++)
k++;
Time Units to Compute
1 for the first assignment (k = 0).
For the first loop (for)
1 assignment, 1+ tests, and multiplication of i*=2.
iterations of the following
For the second loop (for)
1 assignment, n+1 tests, and n increments.
n loops of one unit (increment operation)
-------------------------------------------------------------------
T (n) = 1+1+1+ ++[(1+n+1+n)+n] = 3n+4+3= O(n)
22
23. 1.2.3. Formal Approach to Analysis
In the above examples we have seen that analysis is a bit
complex.
However, it can be simplified by using some formal approach in
which case we can ignore initializations, loop control, and book
keeping.
For Loops: Formally
In general, a for loop translates to a summation.
The index and bounds of the summation are the same as the
index and bounds of the for loop.
Suppose we count the number of additions that are done. There is 1
addition per iteration of the loop, hence N additions in total.
23
for (int i = 1; i <= N; i++) {
sum = sum+i;
}
N
N
i
1
1
24. Nested Loops: Formally
Nested for loops translate into multiple summations, one for each for loop.
Again, count the number of additions. The outer summation is for the outer for loop.
24
for (int i = 1; i <= N; i++) {
for (int j = 1; j <= M; j++) {
sum = sum+i+j;
}
}
MN
M
N
i
N
i
M
j
2
2
2
1
1 1
Consecutive Statements: Formally
Add the running times of the separate blocks of your code
for (int i = 1; i <= N; i++) {
sum = sum+i;
}
for (int i = 1; i <= N; i++) {
for (int j = 1; j <= N; j++) {
sum = sum+i+j;
}
}
2
1 1
1
2
2
1 N
N
N
i
N
j
N
i
25. Compute Running time with given input
Example:
Suppose we have hardware capable of executing 106
instructions per second. How long would it take to execute an
algorithm whose complexity function was T (n) = 2n2 on an
input size of n=108?
Solution
The total number of operations to be performed would be T
(108):
T(108) = 2*(108)2 =2*1016
The required number of seconds required would be given by
T(108)/106 so:
Running time =2*1016/106 = 2*1010
The number of seconds per day is 86,400 so this is about
231,480 days (634 years).
25
26. Exercises
Determine the run time equation and complexity of each of the following code segments.
1. for (i=0;i<n;i++)
for (j=0;j<n; j++)
sum=sum+i+j;
2. for(int i=1; i<=n; i++)
for (int j=1; j<=i; j++)
sum++;
What is the value of the sum if n=20?
3. int k=0;
for (int i=0; i<n; i++)
for (int j=i; j<n; j++)
k++;
What is the value of k when n is equal to 20?
4. int k=0;
for (int i=1; i<n; i*=2)
for(int j=1; j<n; j++)
k++;
What is the value of k when n is equal to 20?
26
27. Home Work
5. int x=0;
for(int i=1;i<n;i=i+5)
x++;
What is the value of x when n=25?
6. int x=0;
for(int k=n;k>=n/3;k=k-5)
x++;
What is the value of x when n=25?
7. int x=0;
for (int i=1; i<n;i=i+5)
for (int k=n;k>=n/3;k=k-5)
x++;
What is the value of x when n=25?
8. int x=0;
for(int i=1;i<n;i=i+5)
for(int j=0;j<i;j++)
for(int k=n;k>=n/2;k=k-3)
x++;
What is the correct big-Oh Notation for the above code segment?
27
28. 1.3. Measures of Times
The running time of an algorithm can be define into three
possible functions Tbest(n), Tavg(n) and Tworst(n)
Average Case (Tavg): The amount of time the algorithm takes
on an "average" set of inputs.
Worst Case (Tworst): The amount of time the algorithm takes on
the worst possible set of inputs.
Best Case (Tbest): The amount of time the algorithm takes on
the smallest possible set of inputs.
28
29. 1.4. Asymptotic Analysis
Asymptotic analysis is concerned with how the running time of an
algorithm increases with the size of the input in the limit, as the size of
the input increases without bound.
We will see the most important functions used in the analysis of
algorithms.
O(1) – Constant Time
Pronounced: "Order 1", "O of 1", "big O of 1"
The runtime is constant, i.e., independent of the number of input
elements n.
When evaluating overall running time, we typically ignore these
statements since they don’t factor into the complexity.
This is the function, f (n) = c.
29
30. O(n) – Linear Time
Pronounced: "Order n", "O of n", "big O of n"
The time grows linearly with the number of input elements n:
If n doubles, then the time approximately doubles, too.
O(n²) – Quadratic Time(square time)
Pronounced: "Order n squared", "O of n squared", "big O of n squared"
The time grows linearly to the square of the number of input elements:
If the number of input elements n doubles, then the time roughly
quadruples.
30
31. Cont.
O(n²) Examples
Examples of quadratic time are simple sorting
algorithms like Insertion Sort, Selection Sort,
and Bubble Sort.
O(log n) – Logarithmic Time
Pronounced: "Order log n", "O of log n", "big O of log
n"
The effort increases approximately by a constant
amount when the number of input elements doubles.
An example of logarithmic growth is the binary
search for a specific element in a sorted array of size n.
31
33. Cont .
There are five notations used to describe a running time
function. These are:
Big-Oh Notation (O)
Big-Omega Notation (W)
Theta Notation (Q)
Little-o Notation (o)
Little-Omega Notation (w)
33
34. The Big-Oh Notation
Big-Oh notation is a way of comparing algorithms and
It is used for computing the complexity of algorithms; i.e.,
the amount of time that it takes for computer program to run.
It’s only concerned with what happens for very a large value of n.
Amount of work the CPU has to do (time complexity)
as the input size grows (towards infinity).
Formal Definition: f (n)= O (g (n)) if there exist c, k ∊ ℛ+ such that for all n≥
k, f (n) ≤ c.g (n).
Examples: The following points are facts that you can use for Big-Oh
problems:
1<=n for all n>=1
n<=n2 for all n>=1
2n <=n! for all n>=4
log2n<=n for all n>=2
n<=nlog2n for all n>=2 34
35. Read The remaining notations of running time
35