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• Cursor-Killing: Retrieving Recently Modified Data

  Cursors are considered by many to be the bane of good T-SQL. What are the best ways to avoid iterative T-SQL and to write queries that look and perform beautifully? In the next part of an ongoing series, we look at ways to efficiently retrieve recently modified data. FREE eBook – "45 Database Performance Tips for Developers"Improve your database performance with 45 tips from SQL Server MVPs and industry experts. Get the eBook here.

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• Physics Engine [Collision Response, 2-dimensional] experts, help!! My stack is unstable!

  - by Register Sole

  Previously, I struggle with the sequential impulse-based method I developed. Thanks to jedediah referring me to this paper, I managed to rebuild the codes and implement the simultaneous impulse based method with Projected-Gauss-Seidel (PGS) iterative solver as described by Erin Catto (mentioned in the reference of the paper as [Catt05]). So here's how it currently is: The simulation handles 2-dimensional rotating convex polygons. Detection is using separating-axis test, with a SKIN, meaning closest points between two polygons is detected and determined if their distance is less than SKIN. To resolve collision, simultaneous impulse-based method is used. It is solved using iterative solver (PGS-solver) as in Erin Catto's paper. Error-correction is implemented using Baumgarte's stabilization (you can refer to either paper for this) using J V = beta/dt*overlap, J is the Jacobian for the constraints, V the matrix containing the velocities of the bodies, beta an error-correction parameter that is better be < 1, dt the time-step taken by the engine, and overlap, the overlap between the bodies (true overlap, so SKIN is ignored). However, it is still less stable than I expected :s I tried to stack hexagons (or squares, doesn't really matter), and even with only 4 to 5 of them, they hardly stand still! Also note that I am not looking for a sleeping scheme. But I would settle if you have any explicit scheme to handle resting contacts. That said, I would be more than happy if you have a way of treating it generally (as continuous collision, instead of explicitly as a special state). Ideas I have: I would try adding a damping term (proportional to velocity) to the Baumgarte. Is this a good idea in general? If not I would not want to waste my time trying to tune the parameter hoping it magically works. Ideas I have tried: Using simultaneous position based error correction as described in the paper in section 5.3.2, turned out to be worse than the current scheme. If you want to know the parameters I used: Hexagons, side 50 (pixels) gravity 2400 (pixels/sec^2) time-step 1/60 (sec) beta 0.1 restitution 0 to 0.2 coeff. of friction 0.2 PGS iteration 10 initial separation 10 (pixels) mass 1 (unit is irrelevant for now, i modified velocity directly<-impulse method) inertia 1/1000 Thanks in advance! I really appreciate any help from you guys!! :)

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• Organizational characteristics that impact the selection of Development Methodology concepts applied to a project

  Based on my experience, no one really follows a specific methodology exactly as it is formally designed. In fact, the key concepts of a few methodologies are usually combined to form a hybrid methodology for each project based on the current organizational makeup and the project need/requirements to be accomplished. Organizational characteristics that impact the selection of methodology concepts applied to a project. Prior subject knowledge pertaining to a project can be critical when deciding on what methodology or combination of methodologies to apply to a project. For example, if a project is very straight forward, and the development staff has experience in developing  that are similar, then the waterfall method could possibly be the best choice because little to no research is needed  in order to complete the project tasks and there is very little need for changes to occur.  On the other hand, if the development staff has limited subject knowledge or the requirements/specification of the project could possibly change as the project progresses then the use of spiral, iterative, incremental, agile, or any combination would be preferred. The previous methodologies used by an organization typically do not change much from project to project unless the needs of a project dictate differently. For example, if the waterfall method is the preferred development methodology then most projects will be developed by the waterfall method. Depending on the time allotted to a project each day can impact the selection of a development methodology. In one example, if the staff can only devote a few hours a day to a project then the incremental methodology might be ideal because modules can be added to the final project as they are developed. On the other hand, if daily time allocation is not an issue, then a multitude of methodologies could work well for a project. Project characteristics that impact the selection of methodology concepts applied to a project. The type of project being developed can often dictate the type of methodology used for the project. Based on my experience, projects that tend to have a lot of user interaction, follow a more iterative, incremental, or agile approach typically using a prototype that develops into a final project. These methodologies desire back and forth communication between users, clients, and developers to allow for requirements to change and functionality to be enhanced. Conversely, limited interaction applications or automated services can still sometimes get away with using the waterfall or transactional approach. The timeline of a project can also force an organization to prefer a particular methodology over the rest. For instance, if the project must be completed within 24 hours, then there is very little time for discussions back and forth between clients, users and the development team. In this scenario, the waterfall method would be perfect because the only interaction with the client occurs prior to a development project to outline the system requirements, and the development team can quickly move through the software development stages in order to complete the project within the deadline. If the team had more time, then the other methodologies could also be considered because there is more time for client and users to review the project and make changes as they see fit, and/or allow for more time to review the project in order to enhance the business performance and functionality. Sometimes the client and or user involvement can dictate the selection of methodologies applied to a project. One example of this is if a client is highly motivated to get a project completed and desires to play an active part in the development process then the agile development approach would work perfectly with this client because it allows for frequent interaction between clients, users and the development team. The inverse of this situation is a client that just wants to provide the project requirements and only wants to get involved when the project is to be delivered. In this case the waterfall method would work well because there is no room for changes and no back and forth between the users, clients or the development team.

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• Updated SOA Documents now available in ITSO Reference Library

  - by Bob Rhubart

  Nine documents within the IT Strategies from Oracle (ITSO) reference library have recently been updated. (Access to the ITSO collection is free to registered Oracle.com members -- and that membership is free.) All nine documents fall within the Service Oriented Architecture section of the ITSO collection, and cover the following topics: SOA Practitioner Guides Creating an SOA Roadmap (PDF, 54 pages, published: February 2012) The secret to successful SOA is to build a roadmap that can be successfully executed. SOA offers an opportunity to adopt an iterative technique to deliver solutions incrementally. This document offers a structured, iterative methodology to help you stay focused on business results, mitigate technology and organizational risk, and deliver successful SOA projects. A Framework for SOA Governance (PDF, 58 pages, published: February 2012) Successful SOA requires a strong governance strategy that designs-in measurement, management, and enforcement procedures. Enterprise SOA adoption introduces new assets, processes, technologies, standards, roles, etc. which require application of appropriate governance policies and procedures. This document offers a framework for defining and building a proper SOA governance model. Determining ROI of SOA through Reuse (PDF, 28 pages, published: February 2012) SOA offers the opportunity to save millions of dollars annually through reuse. Sharing common services intuitively reduces workload, increases developer productivity, and decreases maintenance costs. This document provides an approach for estimating the reuse value of the various software assets contained in a typical portfolio. Identifying and Discovering Services (PDF, 64 pages, published: March 2012) What services should we build? How can we promote the reuse of existing services? A sound approach to answer these questions is a primary measure for the success of a SOA initiative. This document describes a pragmatic approach for collecting the necessary information for identifying proper services and facilitating service reuse. Software Engineering in an SOA Environment (PDF, 66 pages, published: March 2012) Traditional software delivery methods are too narrowly focused and need to be adjusted to enable SOA. This document describes an engineering approach for delivering projects within an SOA environment. It identifies the unique software engineering challenges faced by enterprises adopting SOA and provides a framework to remove the hurdles and improve the efficiency of the SOA initiative. SOA Reference Architectures SOA Foundation (PDF, 70 pages, published: February 2012) This document describes they key tenets for SOA design, development, and execution environments. Topics include: service definition, service layering, service types, the service model, composite applications, invocation patterns, and standards. SOA Infrastructure (PDF, 86 pages, published: February 2012) Properly architected, SOA provides a robust and manageable infrastructure that enables faster solution delivery. This document describes the role of infrastructure and its capabilities. Topics include: logical architecture, deployment views, and Oracle product mapping. SOA White Papers and Data Sheets Oracle's Approach to SOA (white paper) (PDF, 14 pages, published: February 2012) Oracle has developed a pragmatic, holistic approach, based on years of experience with numerous companies to help customers successfully adopt SOA and realize measureable business benefits. This executive datasheet and whitepaper describe Oracle's proven approach to SOA. Oracle's Approach to SOA (data sheet) (PDF, 3 pages, published: March 2012) SOA adoption is complex and success is far from assured. This is why Oracle has developed a pragmatic, holistic approach, based on years of experience with numerous companies, to help customers successfully adopt SOA and realize measurable business benefits. This data sheet provides an executive overview of Oracle's proven approach to SOA.

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• How to make a stack stable? Need help for an explicit resting contact scheme (2-dimensional)

  - by Register Sole

  Previously, I struggle with the sequential impulse-based method I developed. Thanks to jedediah referring me to this paper, I managed to rebuild the codes and implement the simultaneous impulse based method with Projected-Gauss-Seidel (PGS) iterative solver as described by Erin Catto (mentioned in the reference of the paper as [Catt05]). So here's how it currently is: The simulation handles 2-dimensional rotating convex polygons. Detection is using separating-axis test, with a SKIN, meaning closest points between two polygons is detected and determined if their distance is less than SKIN. To resolve collision, simultaneous impulse-based method is used. It is solved using iterative solver (PGS-solver) as in Erin Catto's paper. Error-correction is implemented using Baumgarte's stabilization (you can refer to either paper for this) using J V = beta/dt*overlap, J is the Jacobian for the constraints, V the matrix containing the velocities of the bodies, beta an error-correction parameter that is better be < 1, dt the time-step taken by the engine, and overlap, the overlap between the bodies (true overlap, so SKIN is ignored). However, it is still less stable than I expected :s I tried to stack hexagons (or squares, doesn't really matter), and even with only 4 to 5 of them, they would swing! Also note that I am not looking for a sleeping scheme. But I would settle if you have any explicit scheme to handle resting contacts. That said, I would be more than happy if you have a way of treating it generally (as continuous collision, instead of explicitly as a special state). Ideas I have tried: Using simultaneous position based error correction as described in the paper in section 5.3.2, turned out to be worse than the current scheme. If you want to know the parameters I used: Hexagons, side 50 (pixels) gravity 2400 (pixels/sec^2) time-step 1/60 (sec) beta 0.1 restitution 0 to 0.2 coeff. of friction 0.2 PGS iteration 10 initial separation 10 (pixels) mass 1 (unit is irrelevant for now, i modified velocity directly<-impulse method) inertia 1/1000 Thanks in advance! I really appreciate any help from you guys!! :) EDIT In response to Cholesky's comment about warm starting the solver and Baumgarte: Oh right, I forgot to mention! I do save the contact history and the impulse determined in this time step to be used as initial guess in the next time step. As for the Baumgarte, here's what actually happens in the code. Collision is detected when the bodies' closest distance is less than SKIN, meaning they are actually still separated. If at this moment, I used the PGS solver without Baumgarte, restitution of 0 alone would be able to stop the bodies, separated by a distance of ~SKIN, in mid-air! So this isn't right, I want to have the bodies touching each other. So I turn on the Baumgarte, where its role is actually to pull the bodies together! Weird I know, a scheme intended to push the body apart becomes useful for the reverse. Also, I found that if I increase the number of iteration to 100, stacks become much more stable, though the program becomes so slow. UPDATE Since the stack swings left and right, could it be something is wrong with my friction model? Current friction constraint: relative_tangential_velocity = 0

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• Help with copy and deepcopy in Python

  - by Az

  Hi there, I think I tried to ask for far too much in my previous question so apologies for that. Let me lay out my situation in as simple a manner as I can this time. Basically, I've got a bunch of dictionaries that reference my objects, which are in turn mapped using SQLAlchemy. All fine with me. However, I want to make iterative changes to the contents of those dictionaries. The problem is that doing so will change the objects they reference---and using copy.copy() does no good since it only copies the references contained within the dictionary. Thus even if copied something, when I try to, say print the contents of the dictionary, I'll only get the latest updated values for the object. This is why I wanted to use copy.deepcopy() but that does not work with SQLAlchemy. Now I'm in a dilemma since I need to copy certain attributes of my object before making said iterative changes. In summary, I need to use SQLAlchemy and at the same time make sure I can have a copy of my object attributes when making changes so I don't change the referenced object itself. Any advice, help, suggestions, etc.?

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• C# Recursion SumOfOnlyNeg Elements

  - by Chris

  Hello, A array gets filled up with random elements (negative and positive). Now i want to calculate the sum of ONLY the postive elements. Iterative there is no problem, but in the recursion version i can only get the sum of both negative and postive. How can i "check" in the recursive version that it only sums up the Postive elements? Best Regards. Iterative version: public int IterSomPosElem(int[] tabel, int n) { n = 0; for (int i = 0; i < tabel.Length; i++) { if (tabel[i] >= 0) { n += tabel[i]; } } return n; } Recursive version atm (sums up all the elements insteed, of only the positive) public int RecuSomPosElem(int[] tabel, int n) { if(n == 1) return tabel[0]; //stopCriterium else { return (tabel[n - 1] + RecuSomPosElem(tabel, n - 1)); // how to check, so it only sums up the postive elements and "ignores" the negative elements. } }

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• Accessing appropriate array of double arrays in order of last created.

  - by Zach

  I have an array of double arrays, they are within a specified time window (8am-5pm), and are in order of last created over a period of several days. They are all timestamped and as such I have access to all C# DateTime methods. I then have a different iterative function that goes in the same order of the array of double arrays, however it isn't within a specified time window, it's 24/7. I want to access from this iterative function, the appropriate double array from the one within the window. Let's say that it's 4:30PM on DayOfYear 52, I'd like to access the last double array less than or equal to 4:30PM on DayOfYear 52. I'd expect the same double array if the time were 12:30AM on DayOfYear 53. However, if it were 9:00 AM of DayOfYear 53, well then I'd expect it to return something from the DayOfYear 53, less than or equal to 9:00AM. I think you get the idea. So I'm a having a bit of trouble grokking how to do this. Is anyone willing to offer a starting point or how they'd approach it? Edit: It is not a literal double[][], it is exactly as Anthony Pegram says: Dictionary<DateTime, double[]>

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• TDD with limited resources

  - by bunglestink

  I work in a large company, but on a just two man team developing desktop LOB applications. I have been researching TDD for quite a while now, and although it is easy to realize its benefits for larger applications, I am having a hard time trying to justify the time to begin using TDD on the scale of our applications. I understand its advantages in automating testing, improving maintainability, etc., but on our scale, writing even basic unit tests for all of our components could easily double development time. Since we are already undermanned with extreme deadlines, I am not sure what direction to take. While other practices such as agile iterative development make perfect since, I am kind of torn over the productivity trade-offs of TDD on a small team. Are the advantages of TDD worth the extra development time on small teams with very tight schedules?

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• Books or help on OO Analysis

  - by Pat

  I have this course where we learn about the domain model, use cases, contracts and eventually leap into class diagrams and sequence diagrams to define good software classes. I just had an exam and I got trashed, but part of the reason is we barely have any practical material, I spent at least two good months without drawing a single class diagram by myself from a case study. I'm not here to blame the system or the class I'm in, I'm just wondering if people have some exercise-style books that either provide domain models with glossaries, system sequence diagrams and ask you to use GRASP to make software classes? I could really use some alone-time practicing going from analysis to conception of software entities. I'm almost done with Larman's book called "Applying UML and Patterns An Introduction to Object-Oriented Analysis and Design and Iterative Development, Third Edition". It's a good book, but I'm not doing anything by myself since it doesn't come with exercises. Thanks.

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• Loops, Recursion and Memoization in JavaScript

  - by Ken Dason

  Originally posted on: http://geekswithblogs.net/kdason/archive/2013/07/25/loops-recursion-and-memoization-in-javascript.aspxAccording to Wikipedia, the factorial of a positive integer n (denoted by n!) is the product of all positive integers less than or equal to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. The value of 0! is 1. We can use factorials to demonstrate iterative loops and recursive functions in JavaScript.  Here is a function that computes the factorial using a for loop: Output: Time Taken: 51 ms Here is the factorial function coded to be called recursively: Output: Time Taken: 165 ms We can speed up the recursive function with the use of memoization.  Hence,  if the value has previously been computed, it is simply returned and the recursive call ends. Output: Time Taken: 17 ms

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• Separating text strings into a table of individual words in SQL via XML.

  - by Phil Factor

  p.MsoNormal {margin-top:0cm; margin-right:0cm; margin-bottom:10.0pt; margin-left:0cm; line-height:115%; font-size:11.0pt; font-family:"Calibri","sans-serif"; } Nearly nine years ago, Mike Rorke of the SQL Server 2005 XML team blogged ‘Querying Over Constructed XML Using Sub-queries’. I remember reading it at the time without being able to think of a use for what he was demonstrating. Just a few weeks ago, whilst preparing my article on searching strings, I got out my trusty function for splitting strings into words and something reminded me of the old blog. I’d been trying to think of a way of using XML to split strings reliably into words. The routine I devised turned out to be slightly slower than the iterative word chop I’ve always used in the past, so I didn’t publish it. It was then I suddenly remembered the old routine. Here is my version of it. I’ve unwrapped it from its obvious home in a function or procedure just so it is easy to appreciate. What it does is to chop a text string into individual words using XQuery and the good old nodes() method. I’ve benchmarked it and it is quicker than any of the SQL ways of doing it that I know about. Obviously, you can’t use the trick I described here to do it, because it is awkward to use REPLACE() on 1…n characters of whitespace. I’ll carry on using my iterative function since it is able to tell me the location of each word as a character-offset from the start, and also because this method leaves punctuation in (removing it takes time!). However, I can see other uses for this in passing lists as input or output parameters, or as return values.   if exists (Select * from sys.xml_schema_collections where name like 'WordList')   drop XML SCHEMA COLLECTION WordList go create xml schema collection WordList as ' <xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema"> <xs:element name="words">        <xs:simpleType>               <xs:list itemType="xs:string" />        </xs:simpleType> </xs:element> </xs:schema>'   go   DECLARE @string VARCHAR(MAX) –we'll get some sample data from the great Ogden Nash Select @String='This is a song to celebrate banks, Because they are full of money and you go into them and all you hear is clinks and clanks, Or maybe a sound like the wind in the trees on the hills, Which is the rustling of the thousand dollar bills. Most bankers dwell in marble halls, Which they get to dwell in because they encourage deposits and discourage withdrawals, And particularly because they all observe one rule which woe betides the banker who fails to heed it, Which is you must never lend any money to anybody unless they don''t need it. I know you, you cautious conservative banks! If people are worried about their rent it is your duty to deny them the loan of one nickel, yes, even one copper engraving of the martyred son of the late Nancy Hanks; Yes, if they request fifty dollars to pay for a baby you must look at them like Tarzan looking at an uppity ape in the jungle, And tell them what do they think a bank is, anyhow, they had better go get the money from their wife''s aunt or ungle. But suppose people come in and they have a million and they want another million to pile on top of it, Why, you brim with the milk of human kindness and you urge them to accept every drop of it, And you lend them the million so then they have two million and this gives them the idea that they would be better off with four, So they already have two million as security so you have no hesitation in lending them two more, And all the vice-presidents nod their heads in rhythm, And the only question asked is do the borrowers want the money sent or do they want to take it withm. Because I think they deserve our appreciation and thanks, the jackasses who go around saying that health and happi- ness are everything and money isn''t essential, Because as soon as they have to borrow some unimportant money to maintain their health and happiness they starve to death so they can''t go around any more sneering at good old money, which is nothing short of providential. '   –we now turn it into XML declare @xml_data xml(WordList)  set @xml_data='<words>'+ replace(@string,'&', '&amp;')+'</words>'    select T.ref.value('.', 'nvarchar(100)')  from (Select @xml_data.query('                      for $i in data(/words) return                      element li { $i }               '))  A(list) cross apply A.List.nodes('/li') T(ref)     …which gives (truncated, of course)…

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• S&OP best practices that can help your organization be more responsive and effective

  - by user717691

  If you want to increase revenue by quickly responding to market changes or want to ensure that your operating plans drive towards corporate financial goals, you need real-time sales and operations planning.Watch the replay of our recent Webcast to hear Christopher Neff from NCR Corporation discuss how NCR Corporation is leveraging Oracle's Real-Time Sales and Operations Planning solutions. Learn best practices that can help your organization be more responsive and effective. Discover how Oracle's comprehensive suite of best-in-class capabilities can: Synchronize plans and actions across the extended enterprise Maximize profits with the ability to sense, influence, and fulfill demand with industry leading demand management and real-time sales & operations Drive tactical decisions into operational planning and execution, while monitoring performance Profitably balance supply, demand, and budgets Move planning processes from periodic and reactive to real-time, iterative and proactive Register now for the on demand Webcast! http://www.oracle.com/webapps/dialogue/ns/dlgwelcome.jsp?p_ext=Y&p_dlg_id=8664804&src=6811174&Act=99NCR Corporation is a leader in Self Service Solution such as POS Solutions, Payment and Imaging Systems.

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• New Oracle Cloud support in OEPE

  - by gstachni

  Oracle Enterprise Pack for Eclipse 12c (12.1.1.1.1) includes updated support for development with the Java Cloud Service. Users can now do iterative development against their Java Cloud Service instance in addition to testing against local and remote WebLogic Server installations. Some details of the cloud tools are below: Templates and wizards to create projects and server configurations for Oracle Java Cloud Service Develop applications to run and deploy to the cloud, including Oracle ADF. Check cloud server runtime and deployment logs in new log analyzers Test applications before deployment with integrated whitelist scans. Whitelist tools support as-you-type validation, project build validation, and on demand scans to highlight coding violations. Errors are reported in application source, the Problems view, and a new Whitelist violations view. Access the Oracle Public Cloud administrative consoles directly from within Eclipse.

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• Improve Bad testing

  - by SetiSeeker

  We have a large team of developers and testers. The ratio is one tester for every one developer. We have full bug tracking and reporting systems in place. We have test plans in place. Every change to the product, the testing team is involved in the design of the feature and are included in the development process as much as possible. We build in small iterative blocks, using scrum methodology and every scrum they are included in, including the grooming sessions etc. But every release of the product, they miss even the most simple and obvious defects. How can we improve this?

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• Cursor-Killing: Accessing Data in the Next Row

  Cursors are considered by many to be the bane of good T-SQL. What are the best ways to avoid iterative T-SQL and to write queries that look and perform beautifully? This first part in an ongoing series of cursor-killing handles inter-row analysis. 24% of devs don’t use database source control – make sure you aren’t one of themVersion control is standard for application code, but databases haven’t caught up. So what steps can you take to put your SQL databases under version control? Why should you start doing it? Read more to find out…

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• diophantine equation

  - by krishna chaitanya

  Write an iterative program that finds the largest number of McNuggets that cannot be bought in exact quantity. Your program should print the answer in the following format (where the correct number is provided in place of n): "Largest number of McNuggets that cannot be bought in exact quantity: n" in python

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• Stack overflow code golf

  - by Chris Jester-Young

  To commemorate the public launch of Stack Overflow, what's the shortest code to cause a stack overflow? Any language welcome. ETA: Just to be clear on this question, seeing as I'm an occasional Scheme user: tail-call "recursion" is really iteration, and any solution which can be converted to an iterative solution relatively trivially by a decent compiler won't be counted. :-P ETA2: I've now selected a “best answer”; see this post for rationale. Thanks to everyone who contributed! :-)

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• I'm new to OOP/PHP. What's the practicality of visibility and extensibility in classes?

  - by marcdev

  I'm obviously brand new to these concepts. I just don't understand why you would limit access to properties or methods. It seems that you would just write the code according to intended results. Why would you create a private method instead of simply not calling that method? Is it for iterative object creation (if I'm stating that correctly), a multiple developer situation (don't mess up other people's work), or just so you don't mess up your own work accidentally?

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• Dedicating all processor power to a task

  - by Yktula

  Let's say we have a very processor-intensive task at hand which could be effectively parallelized. How can we dedicate all or almost all available processor power to performing that task? The task could be a variety of things, and iterative Fibonacci number generation that saves recorded numbers would be just one example.

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• Align 2 sets of 2D point clouds

  - by user108088

  From what I gather, there are two major methods to perform alignment on point clouds, Iterative Closest Point (ICP) and Particle Filtering. What are the advantages of each method? And can someone point me some good tutorials. For what I am currently doing, I think ICP would be easier, I can't seem to find any simple reference implementations online for 2d point sets. Has anyone seen (psuedo)code for ICP with details on the transformation step? Thanks in advance.

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• Detecting Handlers of a jQuery "Live" Event

  - by Anderson De Andrade

  Using: $('#foo').data('events').click We are able to access an iterative object of click handlers added to the element '#foo' but only when they were added with .bind() Is there a way to get the handlers for an event added with .live()? Is there any other way to know if an element has a click handler assigned?

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• Building a life-critical System using Agile

  - by Ben Breen

  Looking at the general trend of comments in my question about Building an Aircraft using Agile, the biggest problem other than cost appears to be safety. Do people feel that it is not possible to build a safe system (or prove it is safe) using agile? Doesn’t all the iterative testing mitigate this? Is it likely that a piece of software developed using agile will never be as reliable as counterparts such as waterfall?

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• how to do this problem?

  - by Sachin Tendulkar

  Write an iterative program that finds the largest number of McNuggets that cannot be bought in exact quantity. Your program should print the answer in the following format (where the correct number is provided in place of n): "Largest number of McNuggets that cannot be bought in exact quantity: n"

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• More Fun With Math

  - by PointsToShare

  More Fun with Math   The runaway student – three different ways of solving one problem Here is a problem I read in a Russian site: A student is running away. He is moving at 1 mph. Pursuing him are a lion, a tiger and his math teacher. The lion is 40 miles behind and moving at 6 mph. The tiger is 28 miles behind and moving at 4 mph. His math teacher is 30 miles behind and moving at 5 mph. Who will catch him first? Analysis Obviously we have a set of three problems. They are all basically the same, but the details are different. The problems are of the same class. Here is a little excursion into computer science. One of the things we strive to do is to create solutions for classes of problems rather than individual problems. In your daily routine, you call it re-usability. Not all classes of problems have such solutions. If a class has a general (re-usable) solution, it is called computable. Otherwise it is unsolvable. Within unsolvable classes, we may still solve individual (some but not all) problems, albeit with different approaches to each. Luckily the vast majority of our daily problems are computable, and the 3 problems of our runaway student belong to a computable class. So, let’s solve for the catch-up time by the math teacher, after all she is the most frightening. She might even make the poor runaway solve this very problem – perish the thought! Method 1 – numerical analysis. At 30 miles and 5 mph, it’ll take her 6 hours to come to where the student was to begin with. But by then the student has advanced by 6 miles. 6 miles require 6/5 hours, but by then the student advanced by another 6/5 of a mile as well. And so on and so forth. So what are we to do? One way is to write code and iterate it until we have solved it. But this is an infinite process so we’ll end up with an infinite loop. So what to do? We’ll use the principles of numerical analysis. Any calculator – your computer included – has a limited number of digits. A double floating point number is good for about 14 digits. Nothing can be computed at a greater accuracy than that. This means that we will not iterate ad infinidum, but rather to the point where 2 consecutive iterations yield the same result. When we do financial computations, we don’t even have to go that far. We stop at the 10th of a penny.  It behooves us here to stop at a 10th of a second (100 milliseconds) and this will how we will avoid an infinite loop. Interestingly this alludes to the Zeno paradoxes of motion – in particular “Achilles and the Tortoise”. Zeno says exactly the same. To catch the tortoise, Achilles must always first come to where the tortoise was, but the tortoise keeps moving – hence Achilles will never catch the tortoise and our math teacher (or lion, or tiger) will never catch the student, or the policeman the thief. Here is my resolution to the paradox. The distance and time in each step are smaller and smaller, so the student will be caught. The only thing that is infinite is the iterative solution. The race is a convergent geometric process so the steps are diminishing, but each step in the solution takes the same amount of effort and time so with an infinite number of steps, we’ll spend an eternity solving it.  This BTW is an original thought that I have never seen before. But I digress. Let’s simply write the code to solve the problem. To make sure that it runs everywhere, I’ll do it in JavaScript. function LongCatchUpTime(D, PV, FV) // D is Distance; PV is Pursuers Velocity; FV is Fugitive’ Velocity {     var t = 0;     var T = 0;     var d = parseFloat(D);     var pv = parseFloat (PV);     var fv = parseFloat (FV);     t = d / pv;     while (t > 0.000001) //a 10th of a second is 1/36,000 of an hour, I used 1/100,000     {         T = T + t;         d = t * fv;         t = d / pv;     }     return T;     } By and large, the higher the Pursuer’s velocity relative to the fugitive, the faster the calculation. Solving this with the 10th of a second limit yields: 7.499999232000001 Method 2 – Geometric Series. Each step in the iteration above is smaller than the next. As you saw, we stopped iterating when the last step was small enough, small enough not to really matter.  When we have a sequence of numbers in which the ratio of each number to its predecessor is fixed we call the sequence geometric. When we are looking at the sum of sequence, we call the sequence of sums series.  Now let’s look at our student and teacher. The teacher runs 5 times faster than the student, so with each iteration the distance between them shrinks to a fifth of what it was before. This is a fixed ratio so we deal with a geometric series.  We normally designate this ratio as q and when q is less than 1 (0 < q < 1) the sum of  + … +  is  – 1) / (q – 1). When q is less than 1, it is easier to use ) / (1 - q). Now, the steps are 6 hours then 6/5 hours then 6/5*5 and so on, so q = 1/5. And the whole series is multiplied by 6. Also because q is less than 1 , 1/  diminishes to 0. So the sum is just  / (1 - q). or 1/ (1 – 1/5) = 1 / (4/5) = 5/4. This times 6 yields 7.5 hours. We can now continue with some algebra and take it back to a simpler formula. This is arduous and I am not going to do it here. Instead let’s do some simpler algebra. Method 3 – Simple Algebra. If the time to capture the fugitive is T and the fugitive travels at 1 mph, then by the time the pursuer catches him he travelled additional T miles. Time is distance divided by speed, so…. (D + T)/V = T  thus D + T = VT  and D = VT – T = (V – 1)T  and T = D/(V – 1) This “strangely” coincides with the solution we just got from the geometric sequence. This is simpler ad faster. Here is the corresponding code. function ShortCatchUpTime(D, PV, FV) {     var d = parseFloat(D);     var pv = parseFloat (PV);     var fv = parseFloat (FV);     return d / (pv - fv); } The code above, for both the iterative solution and the algebraic solution are actually for a larger class of problems.  In our original problem the student’s velocity (speed) is 1 mph. In the code it may be anything as long as it is less than the pursuer’s velocity. As long as PV > FV, the pursuer will catch up. Here is the really general formula: T = D / (PV – FV) Finally, let’s run the program for each of the pursuers.  It could not be worse. I know he’d rather be eaten alive than suffering through yet another math lesson. See the code run? Select  “Catch Up Time” in www.mgsltns.com/games.htm The host is running on Unix, so the link is case sensitive. That’s All Folks

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