Merge sort is a divide and conquer algorithm that works as follows:
1) Divide the array to be sorted into two halves recursively until single element subarrays are reached.
2) Merge the subarrays in a way that combines them in a sorted order.
3) The merging process involves taking the first element of each subarray and comparing them to place the smaller element in the final array until all elements are merged.
Merge sort runs in O(n log n) time in all cases making it one of the most efficient sorting algorithms.
Merge sort is a sorting technique based on divide and conquer technique. With worst-case time complexity being Ο(n log n), it is one of the most respected algorithms.
Merge sort first divides the array into equal halves and then combines them in a sorted manner.
Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
It is related to Analysis and Design Of Algorithms Subject.Basically it describe basic of topological sorting, it's algorithm and step by step process to solve the example of topological sort.
presentation about bubble sort
presented by: Ahmed al-butty
Arab Open University - Riyadh , Saudi Arabia
the content
Introduction to Sorting Algorithms
What is Bubble Sort
Bubble Sort Algorithm
Example of Bubble Sort
Complexity Analysis
When to Choose Bubble Sort
Merge sort is a sorting technique based on divide and conquer technique. With worst-case time complexity being Ο(n log n), it is one of the most respected algorithms.
Merge sort first divides the array into equal halves and then combines them in a sorted manner.
Divide and Conquer Algorithms - D&C forms a distinct algorithm design technique in computer science, wherein a problem is solved by repeatedly invoking the algorithm on smaller occurrences of the same problem. Binary search, merge sort, Euclid's algorithm can all be formulated as examples of divide and conquer algorithms. Strassen's algorithm and Nearest Neighbor algorithm are two other examples.
It is related to Analysis and Design Of Algorithms Subject.Basically it describe basic of topological sorting, it's algorithm and step by step process to solve the example of topological sort.
presentation about bubble sort
presented by: Ahmed al-butty
Arab Open University - Riyadh , Saudi Arabia
the content
Introduction to Sorting Algorithms
What is Bubble Sort
Bubble Sort Algorithm
Example of Bubble Sort
Complexity Analysis
When to Choose Bubble Sort
In computer science, divide and conquer (D&C) is an algorithm design paradigm based on multi-branched recursion. A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same (or related) type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.
In computer science, merge sort (also commonly spelled mergesort) is an O(n log n) comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Mergesort is a divide and conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up mergesort appeared in a report by Goldstine and Neumann as early as 1948.
A Comprehensive Look at Generative AI in Retail App Testing.pdfkalichargn70th171
Traditional software testing methods are being challenged in retail, where customer expectations and technological advancements continually shape the landscape. Enter generative AI—a transformative subset of artificial intelligence technologies poised to revolutionize software testing.
Modern design is crucial in today's digital environment, and this is especially true for SharePoint intranets. The design of these digital hubs is critical to user engagement and productivity enhancement. They are the cornerstone of internal collaboration and interaction within enterprises.
Into the Box Keynote Day 2: Unveiling amazing updates and announcements for modern CFML developers! Get ready for exciting releases and updates on Ortus tools and products. Stay tuned for cutting-edge innovations designed to boost your productivity.
In 2015, I used to write extensions for Joomla, WordPress, phpBB3, etc and I ...Juraj Vysvader
In 2015, I used to write extensions for Joomla, WordPress, phpBB3, etc and I didn't get rich from it but it did have 63K downloads (powered possible tens of thousands of websites).
Field Employee Tracking System| MiTrack App| Best Employee Tracking Solution|...informapgpstrackings
Keep tabs on your field staff effortlessly with Informap Technology Centre LLC. Real-time tracking, task assignment, and smart features for efficient management. Request a live demo today!
For more details, visit us : https://informapuae.com/field-staff-tracking/
Globus Connect Server Deep Dive - GlobusWorld 2024Globus
We explore the Globus Connect Server (GCS) architecture and experiment with advanced configuration options and use cases. This content is targeted at system administrators who are familiar with GCS and currently operate—or are planning to operate—broader deployments at their institution.
How Recreation Management Software Can Streamline Your Operations.pptxwottaspaceseo
Recreation management software streamlines operations by automating key tasks such as scheduling, registration, and payment processing, reducing manual workload and errors. It provides centralized management of facilities, classes, and events, ensuring efficient resource allocation and facility usage. The software offers user-friendly online portals for easy access to bookings and program information, enhancing customer experience. Real-time reporting and data analytics deliver insights into attendance and preferences, aiding in strategic decision-making. Additionally, effective communication tools keep participants and staff informed with timely updates. Overall, recreation management software enhances efficiency, improves service delivery, and boosts customer satisfaction.
Advanced Flow Concepts Every Developer Should KnowPeter Caitens
Tim Combridge from Sensible Giraffe and Salesforce Ben presents some important tips that all developers should know when dealing with Flows in Salesforce.
Designing for Privacy in Amazon Web ServicesKrzysztofKkol1
Data privacy is one of the most critical issues that businesses face. This presentation shares insights on the principles and best practices for ensuring the resilience and security of your workload.
Drawing on a real-life project from the HR industry, the various challenges will be demonstrated: data protection, self-healing, business continuity, security, and transparency of data processing. This systematized approach allowed to create a secure AWS cloud infrastructure that not only met strict compliance rules but also exceeded the client's expectations.
TROUBLESHOOTING 9 TYPES OF OUTOFMEMORYERRORTier1 app
Even though at surface level ‘java.lang.OutOfMemoryError’ appears as one single error; underlyingly there are 9 types of OutOfMemoryError. Each type of OutOfMemoryError has different causes, diagnosis approaches and solutions. This session equips you with the knowledge, tools, and techniques needed to troubleshoot and conquer OutOfMemoryError in all its forms, ensuring smoother, more efficient Java applications.
Enhancing Research Orchestration Capabilities at ORNL.pdfGlobus
Cross-facility research orchestration comes with ever-changing constraints regarding the availability and suitability of various compute and data resources. In short, a flexible data and processing fabric is needed to enable the dynamic redirection of data and compute tasks throughout the lifecycle of an experiment. In this talk, we illustrate how we easily leveraged Globus services to instrument the ACE research testbed at the Oak Ridge Leadership Computing Facility with flexible data and task orchestration capabilities.
Why React Native as a Strategic Advantage for Startup Innovation.pdfayushiqss
Do you know that React Native is being increasingly adopted by startups as well as big companies in the mobile app development industry? Big names like Facebook, Instagram, and Pinterest have already integrated this robust open-source framework.
In fact, according to a report by Statista, the number of React Native developers has been steadily increasing over the years, reaching an estimated 1.9 million by the end of 2024. This means that the demand for this framework in the job market has been growing making it a valuable skill.
But what makes React Native so popular for mobile application development? It offers excellent cross-platform capabilities among other benefits. This way, with React Native, developers can write code once and run it on both iOS and Android devices thus saving time and resources leading to shorter development cycles hence faster time-to-market for your app.
Let’s take the example of a startup, which wanted to release their app on both iOS and Android at once. Through the use of React Native they managed to create an app and bring it into the market within a very short period. This helped them gain an advantage over their competitors because they had access to a large user base who were able to generate revenue quickly for them.
SOCRadar Research Team: Latest Activities of IntelBrokerSOCRadar
The European Union Agency for Law Enforcement Cooperation (Europol) has suffered an alleged data breach after a notorious threat actor claimed to have exfiltrated data from its systems. Infamous data leaker IntelBroker posted on the even more infamous BreachForums hacking forum, saying that Europol suffered a data breach this month.
The alleged breach affected Europol agencies CCSE, EC3, Europol Platform for Experts, Law Enforcement Forum, and SIRIUS. Infiltration of these entities can disrupt ongoing investigations and compromise sensitive intelligence shared among international law enforcement agencies.
However, this is neither the first nor the last activity of IntekBroker. We have compiled for you what happened in the last few days. To track such hacker activities on dark web sources like hacker forums, private Telegram channels, and other hidden platforms where cyber threats often originate, you can check SOCRadar’s Dark Web News.
Stay Informed on Threat Actors’ Activity on the Dark Web with SOCRadar!
How to Position Your Globus Data Portal for Success Ten Good PracticesGlobus
Science gateways allow science and engineering communities to access shared data, software, computing services, and instruments. Science gateways have gained a lot of traction in the last twenty years, as evidenced by projects such as the Science Gateways Community Institute (SGCI) and the Center of Excellence on Science Gateways (SGX3) in the US, The Australian Research Data Commons (ARDC) and its platforms in Australia, and the projects around Virtual Research Environments in Europe. A few mature frameworks have evolved with their different strengths and foci and have been taken up by a larger community such as the Globus Data Portal, Hubzero, Tapis, and Galaxy. However, even when gateways are built on successful frameworks, they continue to face the challenges of ongoing maintenance costs and how to meet the ever-expanding needs of the community they serve with enhanced features. It is not uncommon that gateways with compelling use cases are nonetheless unable to get past the prototype phase and become a full production service, or if they do, they don't survive more than a couple of years. While there is no guaranteed pathway to success, it seems likely that for any gateway there is a need for a strong community and/or solid funding streams to create and sustain its success. With over twenty years of examples to draw from, this presentation goes into detail for ten factors common to successful and enduring gateways that effectively serve as best practices for any new or developing gateway.
Paketo Buildpacks : la meilleure façon de construire des images OCI? DevopsDa...Anthony Dahanne
Les Buildpacks existent depuis plus de 10 ans ! D’abord, ils étaient utilisés pour détecter et construire une application avant de la déployer sur certains PaaS. Ensuite, nous avons pu créer des images Docker (OCI) avec leur dernière génération, les Cloud Native Buildpacks (CNCF en incubation). Sont-ils une bonne alternative au Dockerfile ? Que sont les buildpacks Paketo ? Quelles communautés les soutiennent et comment ?
Venez le découvrir lors de cette session ignite
Exploring Innovations in Data Repository Solutions - Insights from the U.S. G...Globus
The U.S. Geological Survey (USGS) has made substantial investments in meeting evolving scientific, technical, and policy driven demands on storing, managing, and delivering data. As these demands continue to grow in complexity and scale, the USGS must continue to explore innovative solutions to improve its management, curation, sharing, delivering, and preservation approaches for large-scale research data. Supporting these needs, the USGS has partnered with the University of Chicago-Globus to research and develop advanced repository components and workflows leveraging its current investment in Globus. The primary outcome of this partnership includes the development of a prototype enterprise repository, driven by USGS Data Release requirements, through exploration and implementation of the entire suite of the Globus platform offerings, including Globus Flow, Globus Auth, Globus Transfer, and Globus Search. This presentation will provide insights into this research partnership, introduce the unique requirements and challenges being addressed and provide relevant project progress.
Gamify Your Mind; The Secret Sauce to Delivering Success, Continuously Improv...Shahin Sheidaei
Games are powerful teaching tools, fostering hands-on engagement and fun. But they require careful consideration to succeed. Join me to explore factors in running and selecting games, ensuring they serve as effective teaching tools. Learn to maintain focus on learning objectives while playing, and how to measure the ROI of gaming in education. Discover strategies for pitching gaming to leadership. This session offers insights, tips, and examples for coaches, team leads, and enterprise leaders seeking to teach from simple to complex concepts.
2. Merge Sort
Divide and Conquer
Recursive in structure
Divide the problem into sub-problems that are similar
to the original but smaller in size
Conquer the sub-problems by solving them recursively.
If they are small enough, just solve them in a
straightforward manner.
Combine the solutions to create a solution to the
original problem
3. An Example: Merge Sort
Sorting Problem: Sort a sequence of n elements into
non-decreasing order.
Divide: Divide the n-element sequence to be
sorted into two subsequences of n/2 elements each
Conquer: Sort the two subsequences recursively
using merge sort.
Combine: Merge the two sorted subsequences to
produce the sorted answer.
5. Merge-Sort (A, p, r)
INPUT: a sequence of n numbers stored in array A
OUTPUT: an ordered sequence of n numbers
MergeSort (A, p, r) // sort A[p..r] by divide & conquer
1 if p < r
2 then q (p+r)/2
3 MergeSort (A, p, q)
4 MergeSort (A, q+1, r)
5 Merge (A, p, q, r) // merges A[p..q] with A[q+1..r]
Initial Call: MergeSort(A, 1, n)
6. Procedure Merge
Merge(A, p, q, r)
1 n1 q – p + 1
2 n2 r – q
3 for i 1 to n1
4 do L[i] A[p + i – 1]
5 for j 1 to n2
6 do R[j] A[q + j]
7 L[n1+1]
8 R[n2+1]
9 i 1
10 j 1
11 for k p to r
12 do if L[i] R[j]
13 then A[k] L[i]
14 i i + 1
15 else A[k] R[j]
16 j j + 1
Input: Array containing sorted subarrays
A[p..q] and A[q+1..r].
Output: Merged sorted subarray in A[p..r].
7. j
Merge – Example
6 8 26 32 1 9 42 43… …A
k
6 8 26 32 1 9 42 43
k k k k k k k
i i i i
i j j j j
6 8 26 32 1 9 42 43
1 6 8 9 26 32 42 43
k
L R
8. Analysis of Merge Sort
Running time T(n) of Merge Sort:
Divide: computing the middle takes (1)
Conquer: solving 2 sub-problems takes 2T(n/2)
Combine: merging n elements takes (n)
Total:
T(n) = (1) if n = 1
T(n) = 2T(n/2) + (n) if n > 1
T(n) = 2 T(n/2) + n
= 2 ((n/2)log(n/2) + (n/2)) + n
= n (log(n/2)) + 2n
= n log n – n + 2n
= n log n + n
= O(n log n )
9. Comparing the Algorithms
Best Average Worst
Case Case Case
Bubble Sort O(n) O(n2) O(n2)
Insertion Sort O(n) O(n2) O(n2)
Selection Sort O(n2) O(n2) O(n2)
Merge Sort O(n log n) O(n log n) O(n log n)
Quick Sort O(n log n) O(n log n) O(n2)
Heap Sort O(n log n) O(n log n) O(n log n)