This document provides an introduction to algorithms and their analysis. It discusses algorithm design techniques like insertion sort and asymptotic analysis using big O notation to describe an algorithm's running time. Insertion sort is analyzed as an example, with its best, average, and worst case times shown to be O(n), O(n^2), and O(n^2) respectively, where n is the input size. Common functions and standard asymptotic notations are also introduced.
Algorithm in Computer, Sorting and NotationsAbid Kohistani
The document discusses algorithms and their analysis. It begins by introducing algorithms and their importance in computer science. The problem of sorting is used as an example to introduce algorithms. Insertion sort is presented as a basic sorting algorithm, with examples of how it works. The analysis of algorithms is then discussed, including analyzing insertion sort's worst case running time, which grows quadratically as Θ(n^2). Asymptotic notation such as O, Ω, Θ is also introduced to analyze long term algorithm running times independent of machine details.
The document discusses insertion sort and its analysis. It begins by providing an overview of insertion sort, describing how it works to sort a sequence by iteratively inserting elements into their sorted position. It then gives pseudocode for insertion sort and works through an example. Next, it analyzes insertion sort's runtime, showing it is O(n^2) in the worst case and O(n) in the best case. The document concludes by introducing the divide and conquer approach for sorting, which will be covered in the next section on merge sort.
Analysis and design of algorithms part2Deepak John
Analysis of searching and sorting. Insertion sort, Quick sort, Merge sort and Heap sort. Binomial Heaps and Fibonacci Heaps, Lower bounds for sorting by comparison of keys. Comparison of sorting algorithms. Amortized Time Analysis. Red-Black Trees – Insertion & Deletion.
This document discusses algorithm analysis and complexity. It introduces algorithm analysis as a way to predict and compare algorithm performance. Different algorithms for computing factorials and finding the maximum subsequence sum are presented, along with their time complexities. The importance of efficient algorithms for problems involving large datasets is discussed.
Algorithm And analysis Lecture 03& 04-time complexity.Tariq Khan
This document discusses algorithm efficiency and complexity analysis. It defines key terms like algorithms, asymptotic complexity, Big O notation, and different complexity classes. It provides examples of analyzing time complexity for different algorithms like loops, nested loops, and recursive functions. The document explains that Big O notation allows analyzing algorithms independent of machine or input by focusing on the highest order term as the problem size increases. Overall, the document introduces methods for measuring an algorithm's efficiency and analyzing its time and space complexity asymptotically.
Algorithm in Computer, Sorting and NotationsAbid Kohistani
The document discusses algorithms and their analysis. It begins by introducing algorithms and their importance in computer science. The problem of sorting is used as an example to introduce algorithms. Insertion sort is presented as a basic sorting algorithm, with examples of how it works. The analysis of algorithms is then discussed, including analyzing insertion sort's worst case running time, which grows quadratically as Θ(n^2). Asymptotic notation such as O, Ω, Θ is also introduced to analyze long term algorithm running times independent of machine details.
The document discusses insertion sort and its analysis. It begins by providing an overview of insertion sort, describing how it works to sort a sequence by iteratively inserting elements into their sorted position. It then gives pseudocode for insertion sort and works through an example. Next, it analyzes insertion sort's runtime, showing it is O(n^2) in the worst case and O(n) in the best case. The document concludes by introducing the divide and conquer approach for sorting, which will be covered in the next section on merge sort.
Analysis and design of algorithms part2Deepak John
Analysis of searching and sorting. Insertion sort, Quick sort, Merge sort and Heap sort. Binomial Heaps and Fibonacci Heaps, Lower bounds for sorting by comparison of keys. Comparison of sorting algorithms. Amortized Time Analysis. Red-Black Trees – Insertion & Deletion.
This document discusses algorithm analysis and complexity. It introduces algorithm analysis as a way to predict and compare algorithm performance. Different algorithms for computing factorials and finding the maximum subsequence sum are presented, along with their time complexities. The importance of efficient algorithms for problems involving large datasets is discussed.
Algorithm And analysis Lecture 03& 04-time complexity.Tariq Khan
This document discusses algorithm efficiency and complexity analysis. It defines key terms like algorithms, asymptotic complexity, Big O notation, and different complexity classes. It provides examples of analyzing time complexity for different algorithms like loops, nested loops, and recursive functions. The document explains that Big O notation allows analyzing algorithms independent of machine or input by focusing on the highest order term as the problem size increases. Overall, the document introduces methods for measuring an algorithm's efficiency and analyzing its time and space complexity asymptotically.
Algorithms Lecture 2: Analysis of Algorithms IMohamed Loey
This document discusses analysis of algorithms and time complexity. It explains that analysis of algorithms determines the resources needed to execute algorithms. The time complexity of an algorithm quantifies how long it takes. There are three cases to analyze - worst case, average case, and best case. Common notations for time complexity include O(1), O(n), O(n^2), O(log n), and O(n!). The document provides examples of algorithms and determines their time complexity in different cases. It also discusses how to combine complexities of nested loops and loops in algorithms.
The document discusses the framework for analyzing the efficiency of algorithms by measuring how the running time and space requirements grow as the input size increases, focusing on determining the order of growth of the number of basic operations using asymptotic notation such as O(), Ω(), and Θ() to classify algorithms based on their worst-case, best-case, and average-case time complexities.
The document discusses algorithms and their complexity. It provides an example of a search algorithm and analyzes its time complexity. The dominating operations are comparisons, and the data size is the length of the array. The algorithm's worst-case time complexity is O(n), as it may require searching through the entire array of length n. The average time complexity depends on the probability distribution of the input data.
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.
The document summarizes a lecture on algorithms that covered insertion sort, analyzing its time complexity, and an introduction to the divide and conquer approach and merge sort. It included pseudocode for insertion sort algorithms and discussed how merge sort follows the divide and conquer paradigm by dividing the problem into subproblems, solving them recursively, and combining the solutions. Pseudocode was also provided for the merge sort algorithm.
This document provides an overview of a lecture on designing and analyzing computer algorithms. It discusses key concepts like what an algorithm and program are, common algorithm design techniques like divide-and-conquer and greedy methods, and how to analyze algorithms' time and space complexity. The goals of analyzing algorithms are to understand their behavior, improve efficiency, and determine whether problems can be solved within a reasonable time frame.
The document discusses the analysis of algorithms. It begins by defining an algorithm and describing different types. It then covers analyzing algorithms in terms of correctness, time efficiency, space efficiency, and optimality through theoretical and empirical analysis. The document discusses analyzing time efficiency by determining the number of repetitions of basic operations as a function of input size. It provides examples of input size, basic operations, and formulas for counting operations. It also covers analyzing best, worst, and average cases and establishes asymptotic efficiency classes. The document then analyzes several examples of non-recursive and recursive algorithms.
This document provides an introduction to analyzing algorithms. It discusses that algorithm analysis involves assessing correctness, time efficiency, space efficiency, and optimality. Theoretical analysis determines time efficiency by calculating the number of basic operations as a function of input size, while empirical analysis involves measuring actual runtimes. Algorithms can be analyzed in terms of their best-case, worst-case, and average-case time efficiencies. Asymptotic analysis compares algorithms' growth rates to determine asymptotic time complexity. Common complexity classes and examples of analyzing non-recursive algorithms are also presented.
This document provides an introduction to algorithms and algorithm analysis. It defines what an algorithm is, provides examples, and discusses analyzing algorithms to determine their efficiency. Insertion sort and merge sort are presented as examples and their time complexities are analyzed. Asymptotic notation is introduced to describe an algorithm's order of growth and provide bounds on its running time. Key points covered include analyzing best-case and worst-case time complexities, using recurrences to model algorithms, and the properties of asymptotic notation. Homework problems are assigned from the textbook chapters.
1) The document discusses complexity analysis of algorithms, which involves determining the time efficiency of algorithms by counting the number of basic operations performed based on input size.
2) It covers motivations for complexity analysis, machine independence, and analyzing best, average, and worst case complexities.
3) Simple rules are provided for determining the complexity of code structures like loops, nested loops, if/else statements, and switch cases based on the number of iterations and branching.
This document provides an overview of algorithm analysis. It discusses how to analyze the time efficiency of algorithms by counting the number of operations and expressing efficiency using growth functions. Different common growth rates like constant, linear, quadratic, and exponential are introduced. Examples are provided to demonstrate how to determine the growth rate of different algorithms, including recursive algorithms, by deriving their time complexity functions. The key aspects covered are estimating algorithm runtime, comparing growth rates of algorithms, and using Big O notation to classify algorithms by their asymptotic behavior.
This document discusses data structures and asymptotic analysis. It begins by defining key terminology related to data structures, such as abstract data types, algorithms, and implementations. It then covers asymptotic notations like Big-O, describing how they are used to analyze algorithms independently of implementation details. Examples are given of analyzing the runtime of linear search and binary search, showing that binary search has better asymptotic performance of O(log n) compared to linear search's O(n).
Introducción al Análisis y diseño de algoritmosluzenith_g
The document discusses algorithms and their analysis. It defines an algorithm as a well-defined computational procedure that takes inputs and produces outputs. It discusses analyzing algorithms to determine their time and space complexity, and how this involves determining how the resources required grow with the size of the problem. It provides examples of analyzing simple algorithms and determining whether they have linear, quadratic, or other complexity.
The document discusses algorithms and their analysis. It defines an algorithm as a well-defined computational procedure that takes inputs and produces outputs. It discusses analyzing algorithms based on their time complexity, space complexity, and correctness. It provides examples of analyzing simple algorithms and calculating their complexity based on the number of elementary operations.
This file contains the contents about dynamic programming, greedy approach, graph algorithm, spanning tree concepts, backtracking and branch and bound approach.
Hi:
This is the first slide of my class on analysis of algorithms based in Cormen's book.
In this slides, we define the following concepts:
1.- What is an algorithm?
2.- What problems are solved by algorithms?
3.- What subjects will be studied in this class?
4.- Cautionary tale about complexities
The document discusses analyzing the running time of algorithms using Big-O notation. It begins by introducing Big-O notation and how it is used to generalize the running time of algorithms as input size grows. It then provides examples of calculating the Big-O running time of simple programs and algorithms with loops but no subprogram calls or recursion. Key concepts covered include analyzing worst-case and average-case running times, and rules for analyzing the running time of programs with basic operations and loops.
Dr. James Mountstephens will be teaching the Algorithm Analysis course this semester. He outlines some rules for lectures, including being punctual and not talking during lectures. He describes the course as crucial and difficult, covering complex topics. Students will have quizzes, assignments, a midterm, and final exam. The textbook is recommended reading. The first two lectures may be the hardest, covering introductions to algorithms and their analysis.
Algorithm analysis insertion sort and asymptotic notationsAmit Kumar Rathi
This document discusses algorithms and their analysis. It begins by introducing algorithms and their importance in computer science. Sorting algorithms are used as an example to explain algorithm design. Insertion sort is presented as a specific sorting algorithm, including pseudocode for how it works and analysis of its best, average, and worst case time complexities, which are O(n), O(n^2) and O(n^2) respectively. Asymptotic notation is also introduced to describe an algorithm's growth rate regardless of lower order terms or constants.
Algorithms Lecture 2: Analysis of Algorithms IMohamed Loey
This document discusses analysis of algorithms and time complexity. It explains that analysis of algorithms determines the resources needed to execute algorithms. The time complexity of an algorithm quantifies how long it takes. There are three cases to analyze - worst case, average case, and best case. Common notations for time complexity include O(1), O(n), O(n^2), O(log n), and O(n!). The document provides examples of algorithms and determines their time complexity in different cases. It also discusses how to combine complexities of nested loops and loops in algorithms.
The document discusses the framework for analyzing the efficiency of algorithms by measuring how the running time and space requirements grow as the input size increases, focusing on determining the order of growth of the number of basic operations using asymptotic notation such as O(), Ω(), and Θ() to classify algorithms based on their worst-case, best-case, and average-case time complexities.
The document discusses algorithms and their complexity. It provides an example of a search algorithm and analyzes its time complexity. The dominating operations are comparisons, and the data size is the length of the array. The algorithm's worst-case time complexity is O(n), as it may require searching through the entire array of length n. The average time complexity depends on the probability distribution of the input data.
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.
The document summarizes a lecture on algorithms that covered insertion sort, analyzing its time complexity, and an introduction to the divide and conquer approach and merge sort. It included pseudocode for insertion sort algorithms and discussed how merge sort follows the divide and conquer paradigm by dividing the problem into subproblems, solving them recursively, and combining the solutions. Pseudocode was also provided for the merge sort algorithm.
This document provides an overview of a lecture on designing and analyzing computer algorithms. It discusses key concepts like what an algorithm and program are, common algorithm design techniques like divide-and-conquer and greedy methods, and how to analyze algorithms' time and space complexity. The goals of analyzing algorithms are to understand their behavior, improve efficiency, and determine whether problems can be solved within a reasonable time frame.
The document discusses the analysis of algorithms. It begins by defining an algorithm and describing different types. It then covers analyzing algorithms in terms of correctness, time efficiency, space efficiency, and optimality through theoretical and empirical analysis. The document discusses analyzing time efficiency by determining the number of repetitions of basic operations as a function of input size. It provides examples of input size, basic operations, and formulas for counting operations. It also covers analyzing best, worst, and average cases and establishes asymptotic efficiency classes. The document then analyzes several examples of non-recursive and recursive algorithms.
This document provides an introduction to analyzing algorithms. It discusses that algorithm analysis involves assessing correctness, time efficiency, space efficiency, and optimality. Theoretical analysis determines time efficiency by calculating the number of basic operations as a function of input size, while empirical analysis involves measuring actual runtimes. Algorithms can be analyzed in terms of their best-case, worst-case, and average-case time efficiencies. Asymptotic analysis compares algorithms' growth rates to determine asymptotic time complexity. Common complexity classes and examples of analyzing non-recursive algorithms are also presented.
This document provides an introduction to algorithms and algorithm analysis. It defines what an algorithm is, provides examples, and discusses analyzing algorithms to determine their efficiency. Insertion sort and merge sort are presented as examples and their time complexities are analyzed. Asymptotic notation is introduced to describe an algorithm's order of growth and provide bounds on its running time. Key points covered include analyzing best-case and worst-case time complexities, using recurrences to model algorithms, and the properties of asymptotic notation. Homework problems are assigned from the textbook chapters.
1) The document discusses complexity analysis of algorithms, which involves determining the time efficiency of algorithms by counting the number of basic operations performed based on input size.
2) It covers motivations for complexity analysis, machine independence, and analyzing best, average, and worst case complexities.
3) Simple rules are provided for determining the complexity of code structures like loops, nested loops, if/else statements, and switch cases based on the number of iterations and branching.
This document provides an overview of algorithm analysis. It discusses how to analyze the time efficiency of algorithms by counting the number of operations and expressing efficiency using growth functions. Different common growth rates like constant, linear, quadratic, and exponential are introduced. Examples are provided to demonstrate how to determine the growth rate of different algorithms, including recursive algorithms, by deriving their time complexity functions. The key aspects covered are estimating algorithm runtime, comparing growth rates of algorithms, and using Big O notation to classify algorithms by their asymptotic behavior.
This document discusses data structures and asymptotic analysis. It begins by defining key terminology related to data structures, such as abstract data types, algorithms, and implementations. It then covers asymptotic notations like Big-O, describing how they are used to analyze algorithms independently of implementation details. Examples are given of analyzing the runtime of linear search and binary search, showing that binary search has better asymptotic performance of O(log n) compared to linear search's O(n).
Introducción al Análisis y diseño de algoritmosluzenith_g
The document discusses algorithms and their analysis. It defines an algorithm as a well-defined computational procedure that takes inputs and produces outputs. It discusses analyzing algorithms to determine their time and space complexity, and how this involves determining how the resources required grow with the size of the problem. It provides examples of analyzing simple algorithms and determining whether they have linear, quadratic, or other complexity.
The document discusses algorithms and their analysis. It defines an algorithm as a well-defined computational procedure that takes inputs and produces outputs. It discusses analyzing algorithms based on their time complexity, space complexity, and correctness. It provides examples of analyzing simple algorithms and calculating their complexity based on the number of elementary operations.
This file contains the contents about dynamic programming, greedy approach, graph algorithm, spanning tree concepts, backtracking and branch and bound approach.
Hi:
This is the first slide of my class on analysis of algorithms based in Cormen's book.
In this slides, we define the following concepts:
1.- What is an algorithm?
2.- What problems are solved by algorithms?
3.- What subjects will be studied in this class?
4.- Cautionary tale about complexities
The document discusses analyzing the running time of algorithms using Big-O notation. It begins by introducing Big-O notation and how it is used to generalize the running time of algorithms as input size grows. It then provides examples of calculating the Big-O running time of simple programs and algorithms with loops but no subprogram calls or recursion. Key concepts covered include analyzing worst-case and average-case running times, and rules for analyzing the running time of programs with basic operations and loops.
Dr. James Mountstephens will be teaching the Algorithm Analysis course this semester. He outlines some rules for lectures, including being punctual and not talking during lectures. He describes the course as crucial and difficult, covering complex topics. Students will have quizzes, assignments, a midterm, and final exam. The textbook is recommended reading. The first two lectures may be the hardest, covering introductions to algorithms and their analysis.
Algorithm analysis insertion sort and asymptotic notationsAmit Kumar Rathi
This document discusses algorithms and their analysis. It begins by introducing algorithms and their importance in computer science. Sorting algorithms are used as an example to explain algorithm design. Insertion sort is presented as a specific sorting algorithm, including pseudocode for how it works and analysis of its best, average, and worst case time complexities, which are O(n), O(n^2) and O(n^2) respectively. Asymptotic notation is also introduced to describe an algorithm's growth rate regardless of lower order terms or constants.
The document defines algorithms and describes their characteristics and design techniques. It states that an algorithm is a step-by-step procedure to solve a problem and get the desired output. It discusses algorithm development using pseudocode and flowcharts. Various algorithm design techniques like top-down, bottom-up, incremental, divide and conquer are explained. The document also covers algorithm analysis in terms of time and space complexity and asymptotic notations like Big-O, Omega and Theta to analyze best, average and worst case running times. Common time complexities like constant, linear, quadratic, and exponential are provided with examples.
Data Structure & Algorithms - Introductionbabuk110
This document introduces key concepts in data structures and algorithms including algorithms, programs, data structures, objects, and relations between data structures and objects. It discusses analyzing algorithms through measuring running time experimentally and theoretically using asymptotic analysis. Examples are provided of insertion sort and prefix averages algorithms, analyzing their best, worst, and average cases, and calculating their asymptotic running times as O(n) and O(n^2) respectively. The document outlines criteria for good algorithms and techniques for asymptotic analysis including Big-O notation.
Analysis and Algorithms: basic Introductionssuseraf8b2f
This document discusses analyzing algorithms and their time and space complexity. It introduces various metrics for analyzing algorithms such as correctness, time complexity, space complexity, and optimality. Time complexity, which is the main focus, refers to the amount of time an algorithm takes to complete as a function of the input size. Various algorithm examples are provided and different approaches for calculating time complexity like worst-case, best-case, average-case and asymptotic analysis are explained. Asymptotic notations like Big-O, Big-Omega and Theta notation are introduced to describe the asymptotic behavior of algorithms.
Linear search examines each element of a list sequentially, one by one, and checks if it is the target value. It has a time complexity of O(n) as it requires searching through each element in the worst case. While simple to implement, linear search is inefficient for large lists as other algorithms like binary search require fewer comparisons.
This document introduces algorithms and asymptotic notation used to analyze algorithm performance. It defines common asymptotic notations like O, Ω, and Θ notation, and gives examples of standard functions like logarithms and factorials. It notes that accurately measuring algorithm performance requires specifying the programming language, working program, computer used, and compiler options.
This document discusses data structures and algorithms. It provides course objectives which include imparting concepts of data structures and algorithms, introducing searching and sorting techniques, and developing applications using suitable data structures. Course outcomes include understanding algorithm performance analysis, concepts of data structures, linear data structures, and identifying efficient data structure implementations. The document also covers algorithm basics, specifications, expressions, analysis techniques and asymptotic notations for analyzing algorithms.
The document discusses algorithms and their analysis. It defines an algorithm as a sequence of unambiguous steps to solve a problem within a finite time. Characteristics of algorithms include being unambiguous, having inputs/outputs, and terminating in finite time. Algorithm analysis involves determining theoretical and empirical time and space complexity as input size increases. Time complexity is analyzed by counting basic operations, while space complexity considers fixed and variable memory usage. Worst, best, and average cases analyze how efficiency varies with different inputs. Asymptotic analysis focuses on long-term growth rates to compare algorithms.
Advanced Datastructures and algorithms CP4151unit1b.pdfSheba41
Insertion sort has a running time of O(n^2) in the worst case. It works by iterating through the array (n times) and inserting each element into its sorted position (taking up to n steps). This results in a total worst case time of n(n) = O(n^2) operations.
The document provides an introduction and overview of the Design and Analysis of Algorithms course. It covers key topics like asymptotic notations and their properties, analyzing recursive and non-recursive algorithms, divide-and-conquer algorithms like quicksort and mergesort, and sorting algorithms like heap sort. Examples of insertion sort and analysis of its worst-case running time of O(n2) are provided. Asymptotic notation like Big-O, Ω, and Θ are introduced to analyze algorithms' time complexities as the problem size n approaches infinity.
asymptotic analysis and insertion sort analysisAnindita Kundu
This document discusses asymptotic analysis of algorithms. It introduces key concepts like algorithms, data structures, best/average/worst case running times, and asymptotic notations like Big-O, Big-Omega, and Big-Theta. These notations are used to describe the long-term growth rates of functions and provide upper/lower/tight bounds on the running time of algorithms as the input size increases. Examples show how to analyze the asymptotic running time of algorithms like insertion sort, which is O(n^2) in the worst case but O(n) in the best case.
Design Analysis of Alogorithm 1 ppt 2024.pptxrajesshs31r
This document discusses algorithms and their analysis. It begins by defining an algorithm as a sequence of unambiguous instructions to solve a problem in a finite amount of time. It then provides examples of Euclid's algorithm for computing the greatest common divisor. The document goes on to discuss the fundamentals of algorithmic problem solving, including understanding the problem, choosing exact or approximate solutions, and algorithm design techniques. It also covers analyzing algorithms by measuring time and space complexity using asymptotic notations.
Analysis of Algorithm full version 2024.pptxrajesshs31r
This document discusses algorithms and their analysis. It begins by defining an algorithm as a sequence of unambiguous instructions to solve a problem in a finite amount of time. Euclid's algorithm for computing the greatest common divisor is provided as an example. The document then covers fundamentals of algorithmic problem solving, including understanding the problem, choosing exact or approximate solutions, and algorithm design techniques. It also discusses analyzing algorithms based on time and space complexity, as well as worst-case, best-case, and average-case efficiencies. Common problem types like sorting, searching, and graph problems are briefly outlined.
This document introduces algorithms and their basics. It defines an algorithm as a step-by-step procedure to solve a problem and get the desired output. Algorithms can be implemented in different programming languages. Common algorithm categories include search, sort, insert, update, and delete operations on data structures. An algorithm must be unambiguous, have well-defined inputs and outputs, terminate in a finite number of steps, and be feasible with available resources. The document also discusses how to write algorithms, analyze their complexity, and commonly used asymptotic notations like Big-O, Omega, and Theta.
The document discusses data structures and algorithms. It defines key concepts like algorithms, programs, data structures, and asymptotic analysis. It explains how to analyze algorithms to determine their efficiency, including analyzing best, worst, and average cases. Common notations for describing asymptotic running time like Big-O, Big-Omega, and Big-Theta are introduced. The document provides examples of analyzing sorting algorithms like insertion sort and calculating running times. It also discusses techniques for proving an algorithm's correctness like assertions and loop invariants.
This document discusses algorithms and their analysis. It begins with definitions of algorithms and their characteristics. Different methods for specifying algorithms are described, including pseudocode. The goal of algorithm analysis is introduced as comparing algorithms based on running time and other factors. Common algorithm analysis methods like worst-case, best-case, and average-case are defined. Big-O notation and time/space complexity are explained. Common algorithm design strategies like divide-and-conquer and randomized algorithms are summarized. Specific algorithms like repeated element detection and primality testing are mentioned.
Data structures and algorithms involve organizing data to solve problems efficiently. An algorithm describes computational steps, while a program implements an algorithm. Key aspects of algorithms include efficiency as input size increases. Experimental studies measure running time but have limitations. Pseudocode describes algorithms at a high level. Analysis counts primitive operations to determine asymptotic running time, ignoring constant factors. The best, worst, and average cases analyze efficiency. Asymptotic notation like Big-O simplifies analysis by focusing on how time increases with input size.
Time complexity analysis specifies how the running time of an algorithm depends on the size of its input. It is determined by identifying the basic operation of the algorithm and counting how many times it is executed as the input size increases. The time complexity of an algorithm can be expressed as a function T(n) relating the input size n to the running time. Common time complexities include constant O(1), linear O(n), logarithmic O(log n), and quadratic O(n^2). The order of growth indicates how fast the running time grows as n increases and is used to compare the efficiency of algorithms.
This document provides an overview of algorithms including definitions, characteristics, design, and analysis. It defines an algorithm as a finite step-by-step procedure to solve a problem and discusses their key characteristics like input, definiteness, effectiveness, finiteness, and output. The document outlines the design of algorithms using pseudo-code and their analysis in terms of time and space complexity using asymptotic notations like Big O, Big Omega, and Big Theta. Examples are provided to illustrate linear search time complexity and the use of different notations to determine algorithm efficiency.
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...shadow0702a
This document serves as a comprehensive step-by-step guide on how to effectively use PyCharm for remote debugging of the Windows Subsystem for Linux (WSL) on a local Windows machine. It meticulously outlines several critical steps in the process, starting with the crucial task of enabling permissions, followed by the installation and configuration of WSL.
The guide then proceeds to explain how to set up the SSH service within the WSL environment, an integral part of the process. Alongside this, it also provides detailed instructions on how to modify the inbound rules of the Windows firewall to facilitate the process, ensuring that there are no connectivity issues that could potentially hinder the debugging process.
The document further emphasizes on the importance of checking the connection between the Windows and WSL environments, providing instructions on how to ensure that the connection is optimal and ready for remote debugging.
It also offers an in-depth guide on how to configure the WSL interpreter and files within the PyCharm environment. This is essential for ensuring that the debugging process is set up correctly and that the program can be run effectively within the WSL terminal.
Additionally, the document provides guidance on how to set up breakpoints for debugging, a fundamental aspect of the debugging process which allows the developer to stop the execution of their code at certain points and inspect their program at those stages.
Finally, the document concludes by providing a link to a reference blog. This blog offers additional information and guidance on configuring the remote Python interpreter in PyCharm, providing the reader with a well-rounded understanding of the process.
Embedded machine learning-based road conditions and driving behavior monitoringIJECEIAES
Car accident rates have increased in recent years, resulting in losses in human lives, properties, and other financial costs. An embedded machine learning-based system is developed to address this critical issue. The system can monitor road conditions, detect driving patterns, and identify aggressive driving behaviors. The system is based on neural networks trained on a comprehensive dataset of driving events, driving styles, and road conditions. The system effectively detects potential risks and helps mitigate the frequency and impact of accidents. The primary goal is to ensure the safety of drivers and vehicles. Collecting data involved gathering information on three key road events: normal street and normal drive, speed bumps, circular yellow speed bumps, and three aggressive driving actions: sudden start, sudden stop, and sudden entry. The gathered data is processed and analyzed using a machine learning system designed for limited power and memory devices. The developed system resulted in 91.9% accuracy, 93.6% precision, and 92% recall. The achieved inference time on an Arduino Nano 33 BLE Sense with a 32-bit CPU running at 64 MHz is 34 ms and requires 2.6 kB peak RAM and 139.9 kB program flash memory, making it suitable for resource-constrained embedded systems.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
The CBC machine is a common diagnostic tool used by doctors to measure a patient's red blood cell count, white blood cell count and platelet count. The machine uses a small sample of the patient's blood, which is then placed into special tubes and analyzed. The results of the analysis are then displayed on a screen for the doctor to review. The CBC machine is an important tool for diagnosing various conditions, such as anemia, infection and leukemia. It can also help to monitor a patient's response to treatment.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...IJECEIAES
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Redefining brain tumor segmentation: a cutting-edge convolutional neural netw...IJECEIAES
Medical image analysis has witnessed significant advancements with deep learning techniques. In the domain of brain tumor segmentation, the ability to
precisely delineate tumor boundaries from magnetic resonance imaging (MRI)
scans holds profound implications for diagnosis. This study presents an ensemble convolutional neural network (CNN) with transfer learning, integrating
the state-of-the-art Deeplabv3+ architecture with the ResNet18 backbone. The
model is rigorously trained and evaluated, exhibiting remarkable performance
metrics, including an impressive global accuracy of 99.286%, a high-class accuracy of 82.191%, a mean intersection over union (IoU) of 79.900%, a weighted
IoU of 98.620%, and a Boundary F1 (BF) score of 83.303%. Notably, a detailed comparative analysis with existing methods showcases the superiority of
our proposed model. These findings underscore the model’s competence in precise brain tumor localization, underscoring its potential to revolutionize medical
image analysis and enhance healthcare outcomes. This research paves the way
for future exploration and optimization of advanced CNN models in medical
imaging, emphasizing addressing false positives and resource efficiency.
2. IntroductionIntroduction
• The methods of algorithm design form one of the core
practical technologies of computer science.
• The main aim of this lecture is to familiarize the student
with the framework we shall use through the course
about the design and analysis of algorithms.
• We start with a discussion of the algorithms needed to
solve computational problems. The problem of sorting is
used as a running example.
• We introduce a pseudocode to show how we shall
specify the algorithms.
3. AlgorithmsAlgorithms
• The word algorithm comes from the name of a Persian
mathematician Abu Ja’far Mohammed ibn-i Musa al
Khowarizmi.
• In computer science, this word refers to a special
method useable by a computer for solution of a problem.
The statement of the problem specifies in general terms
the desired input/output relationship.
• For example, sorting a given sequence of numbers into
nondecreasing order provides fertile ground for
introducing many standard design techniques and
analysis tools.
17. Analysis of algorithmsAnalysis of algorithms
The theoretical study of computer-program
performance and resource usage.
What’s more important than performance?
• modularity
• correctness
• maintainability
• functionality
• robustness
• user-friendliness
• programmer time
• simplicity
• extensibility
• reliability
18. Analysis of algorithmsAnalysis of algorithms
Why study algorithms and performance?
• Algorithms help us to understand scalability.
• Performance often draws the line between what is feasible
and what is impossible.
• Algorithmic mathematics provides a language for talking
about program behavior.
• The lessons of program performance generalize to other
computing resources.
• Speed is fun!
19. Running TimeRunning Time
• The running time depends on the input: an already
sorted sequence is easier to sort.
• Parameterize the running time by the size of the
input, since short sequences are easier to sort than
long ones.
• Generally, we seek upper bounds on the running
time, because everybody likes a guarantee.
20. Kinds of analysesKinds of analyses
Worst-case: (usually)
• T(n) = maximum time of algorithm on any input of
size n.
Average-case: (sometimes)
• T(n) = expected time of algorithm over all inputs of
size n.
• Need assumption of statistical distribution of inputs.
Best-case:
• Cheat with a slow algorithm that works fast on some
input.
21. Machine-Machine-IIndependent timendependent time
The RAM Model
Machine independent algorithm design depends on a
hypothetical computer called Random Acces Machine (RAM).
Assumptions:
• Each simple operation such as +, -, if ...etc takes exactly
one time step.
• Loops and subroutines are not considered simple
operations.
• Each memory acces takes exactly one time step.
22. Machine-independent timeMachine-independent time
What is insertion sort’s worst-case time?
• It depends on the speed of our computer,
• relative speed (on the same machine),
• absolute speed (on different machines).
BIG IDEA:
• Ignore machine-dependent constants.
• Look at growth of
“Asymptotic Analysis”
∞→nnT as)(
23. Machine-independent time: An exampleMachine-independent time: An example
A pseudocode for insertion sort ( INSERTION SORT ).
INSERTION-SORT(A)
1 for j ← 2 to length [A]
2 do key ← A[ j]
3 ∇ Insert A[j] into the sortted sequence A[1,..., j-1].
4 i ← j – 1
5 while i > 0 and A[i] > key
6 do A[i+1] ← A[i]
7 i ← i – 1
8 A[i +1] ← key
24. Analysis of INSERTION-SORT(contd.)Analysis of INSERTION-SORT(contd.)
1]1[8
)1(17
)1(][]1[6
][05
114
10]11[sequence
sortedtheinto][Insert3
1][2
][21
timescostSORT(A)-INSERTION
8
27
26
25
4
2
1
−←+
−−←
−←+
>>
−−←
−−⋅⋅
∇
−←
←
∑
∑
∑
=
=
=
nckeyiA
tcii
tciAiA
tckeyiAandi
ncji
njA
jA
ncjAkey
ncAlengthj
n
j j
n
j j
n
j j
do
while
do
tofor
25. Analysis of INSERTION-SORT(contd.)Analysis of INSERTION-SORT(contd.)
)1()1()1()(
2
6
2
5421 −++−+−+= ∑∑
==
n
j
j
n
j
j tctcncnccnT
).1()1( 8
2
7 −+−+ ∑
=
nctc
n
j
j
The total running time is
26. Analysis of INSERTION-SORT(contd.)Analysis of INSERTION-SORT(contd.)
The best case: The array is already sorted.
(tj =1 for j=2,3, ...,n)
)1()1()1()1()( 85421 −+−+−+−+= ncncncncncnT
).()( 854285421 ccccnccccc +++−++++=
27. Analysis of INSERTION-SORT(contd.)Analysis of INSERTION-SORT(contd.)
•The worst case: The array is reverse sorted
(tj =j for j=2,3, ...,n).
)12/)1(()1()( 521 −++−+= nncncncnT
)1()2/)1(()2/)1(( 876 −+−+−+ ncnncnnc
ncccccccnccc )2/2/2/()2/2/2/( 8765421
2
765 +−−++++++=
2
)1(
1
+
=∑
=
nn
j
n
j
cbnannT ++= 2
)(
28. Growth of FunctionsGrowth of Functions
Although we can sometimes determine the exact
running time of an algorithm, the extra precision is not
usually worth the effort of computing it.
For large inputs, the multiplicative constants and lower
order terms of an exact running time are dominated by
the effects of the input size itself.
29. Asymptotic NotationAsymptotic Notation
The notation we use to describe the asymptotic running
time of an algorithm are defined in terms of functions
whose domains are the set of natural numbers
{ }...,2,1,0=N
30. O-notationO-notation
• For a given function , we denote by the
set of functions
• We use O-notation to give an asymptotic upper bound of
a function, to within a constant factor.
• means that there existes some constant c
s.t. is always for large enough n.
)(ng ))(( ngO
≥≤≤
=
0
0
allfor)()(0
s.t.andconstantspositiveexistthere:)(
))((
nnncgnf
ncnf
ngO
))(()( ngOnf =
)(ncg≤)(nf
31. ΩΩ--OmegaOmega notationnotation
• For a given function , we denote by the
set of functions
• We use Ω-notation to give an asymptotic lower bound on
a function, to within a constant factor.
• means that there exists some constant c s.t.
is always for large enough n.
)(ng ))(( ngΩ
≥≤≤
=Ω
0
0
allfor)()(0
s.t.andconstantspositiveexistthere:)(
))((
nnnfncg
ncnf
ng
))(()( ngnf Ω=
)(nf )(ncg≥
32. --ThetaTheta notationnotation
• For a given function , we denote by the
set of functions
• A function belongs to the set if there
exist positive constants and such that it can be
“sand- wiched” between and or sufficienly
large n.
• means that there exists some constant c1
and c2 s.t. for large enough n.
)(ng ))(( ngΘ
≥≤≤≤
=Θ
021
021
allfor)()()(c0
s.t.and,,constantspositiveexistthere:)(
))((
nnngcnfng
nccnf
ng
)(nf ))(( ngΘ
1c 2c
)(1 ngc )(2 ngc
Θ
))(()( ngnf Θ=
)()()( 21 ngcnfngc ≤≤
34. 2
2
22
1 3
2
1
ncnnnc ≤−≤
21
3
2
1
c
n
c ≤−≤
Example 1.Example 1.
Show that
We must find c1 and c2 such that
Dividing bothsides by n2 yields
For
)(3
2
1
)( 22
nnnnf Θ=−=
)(3
2
1
,7 22
0 nnnn Θ=−≥
35. TheoremTheorem
• For any two functions and , we have
if and only if
)(ng
))(()( ngnf Θ=
)(nf
)).(()(and))(()( ngnfngOnf Ω==
36. Because :
)2(5223 nnn Ω=+−
Example 2.Example 2.
)2(5223)( nnnnf Θ=+−=
)2(5223 nOnn =+−
46. Standard notations and common functionsStandard notations and common functions
• Floors and ceilings
11 +<≤≤<− xxxxx
47. Standard notations and common functionsStandard notations and common functions
• Logarithms:
)lg(lglglg
)(loglog
logln
loglg 2
nn
nn
nn
nn
kk
e
=
=
=
=
48. Standard notations and common functionsStandard notations and common functions
• Logarithms:
For all real a>0, b>0, c>0, and n
b
a
a
ana
baab
ba
c
c
b
b
n
b
ccc
ab
log
log
log
loglog
loglog)(log
log
=
=
+=
=
49. Standard notations and common functionsStandard notations and common functions
• Logarithms:
b
a
ca
aa
a
b
ac
bb
bb
log
1
log
log)/1(log
loglog
=
=
−=
50. Standard notations and common functionsStandard notations and common functions
• Factorials
For the Stirling approximation:
Θ+
π=
ne
n
nn
n
1
12!
0≥n
)lg()!lg(
)2(!
)(!
nnn
n
non
n
n
Θ=
ω=
=