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  • 8-direction path finding algorithm

    - by frinkz
    I'm having trouble finding the right pathfinding algorithm for some AI I'm working on. I have players on a pitch, moving around freely (not stuck to a grid), but they are confined to moving in 8 directions (N NE E etc.) I was working on using A*, and a graph for this. But I realised, every node on the graph is equally far apart, and all the edges have the same weight - since the pitch is rectangular. And the number of nodes is enormous (being a large pitch, with them able to move between 1 pixel and another) I figured there must be another algorithm, optimised for this sort of thing?

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  • Algorithm: efficient way to remove duplicate integers from an array

    - by ejel
    I got this problem from an interview with Microsoft. Given an array of random integers, write an algorithm in C that removes duplicated numbers and return the unique numbers in the original array. E.g Input: {4, 8, 4, 1, 1, 2, 9} Output: {4, 8, 1, 2, 9, ?, ?} One caveat is that the expected algorithm should not required the array to be sorted first. And when an element has been removed, the following elements must be shifted forward as well. Anyway, value of elements at the tail of the array where elements were shifted forward are negligible. Update: The result must be returned in the original array and helper data structure (e.g. hashtable) should not be used. However, I guess order preservation is not necessary. Update2: For those who wonder why these impractical constraints, this was an interview question and all these constraints are discussed during the thinking process to see how I can come up with different ideas.

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  • Classical Round Table algorithm?

    - by user1795954
    Coins with different value are spread in circle around a round table . We can choose any coin such that for any two adjacent pair of coins , atleast one must be selected (both maybe selected too) . In such condition we have to find minimum possible value of coins selected . I have to respect time complexity so instead of using naive recursive bruteforce , i tried doing it using dynamic programming . But i get Wrong Answer - my algorithm is incorrect . If someone could suggest an algorithm to do it dynamically , i could code myself in c++ . Also maximum number of coins is 10^6 , so i think O(n) solution exists .

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  • Algorithm for evaluating nested logical expression

    - by TravelingSalesman
    I have a logical expression that I would like to evaluate. The expression can be nested and consists of T (True) or F (False) and parenthesis. The parenthesis "(" means "logical OR". Two terms TF beside each others (or any other two combinations beside each others), should be ANDED (Logical AND). For example, the expression: ((TFT)T) = true I need an algorithm for solving this problem. I thought of converting the expression first to disjunctive or conjunctive normal form and then I can easily evaluate the expression. However, I couldn't find an algorithm that normalizes the expression. Any suggestions? Thank you. The problem statement can be found here: https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=2&category=378&page=show_problem&problem=2967

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  • Coming Up with a Good Algorithm for a Simple Idea

    - by mkoryak
    I need to come up with an algorithm that does the following: Lets say you have an array of positive numbers (e.g. [1,3,7,0,0,9]) and you know beforehand their sum is 20. You want to abstract some average amount from each number such that the new sum would be less by 7. To do so, you must follow these rules: you can only subtract integers the resulting array must not have any negative values you can not make any changes to the indices of the buckets. The more uniformly the subtraction is distributed over the array the better. Here is my attempt at an algorithm in JavaScript + underscore (which will probably make it n^2): function distributeSubtraction(array, goal){ var sum = _.reduce(arr, function(x, y) { return x + y; }, 0); if(goal < sum){ while(goal < sum && goal > 0){ var less = ~~(goal / _.filter(arr, _.identity).length); //length of array without 0s arr = _.map(arr, function(val){ if(less > 0){ return (less < val) ? val - less : val; //not ideal, im skipping some! } else { if(goal > 0){ //again not ideal. giving preference to start of array if(val > 0) { goal--; return val - 1; } } else { return val; } } }); if(goal > 0){ var newSum = _.reduce(arr, function(x, y) { return x + y; }, 0); goal -= sum - newSum; sum = newSum; } else { return arr; } } } else if(goal == sum) { return _.map(arr, function(){ return 0; }); } else { return arr; } } var goal = 7; var arr = [1,3,7,0,0,9]; var newArray = distributeSubtraction(arr, goal); //returned: [0, 1, 5, 0, 0, 7]; Well, that works but there must be a better way! I imagine the run time of this thing will be terrible with bigger arrays and bigger numbers. edit: I want to clarify that this question is purely academic. Think of it like an interview question where you whiteboard something and the interviewer asks you how your algorithm would behave on a different type of a dataset.

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  • Fast partial sorting algorithm

    - by trican
    I'm looking for a fast way to do a partial sort of 81 numbers - Ideally I'm looking to extract the lowest 16 values (its not necessary for the 16 to be in the absolutely correct order). The target for this is dedicated hardware in an FPGA - so this slightly complicated matters as I want the area of the resultant implementation as small as possible. I looked at and implemented the odd-even merge sort algorithm, but I'm ideally looking for anything that might be more efficient for my needs (trade algorithm implementation size for a partial sort giving lowest 16, not necessarily in order as opposed to a full sort) Any suggestions would be very welcome Many thanks

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  • Algorithm to determine coin combinations

    - by A.J.
    I was recently faced with a prompt for a programming algorithm that I had no idea what to do for. I've never really written an algorithm before, so I'm kind of a newb at this. The problem said to write a program to determine all of the possible coin combinations for a cashier to give back as change based on coin values and number of coins. For example, there could be a currency with 4 coins: a 2 cent, 6 cent, 10 cent and 15 cent coins. How many combinations of this that equal 50 cents are there? The language I'm using is C++, although that doesn't really matter too much. edit: This is a more specific programming question, but how would I analyze a string in C++ to get the coin values? They were given in a text document like 4 2 6 10 15 50 (where the numbers in this case correspond to the example I gave)

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  • I need an algorithm to find the best path

    - by user242635
    I need an algorithm to find the best solution of a path finding problem. The problem can be stated as: At the starting point I can proceed along multiple different paths. At each step there are another multiple possible choices where to proceed. There are two operations possible at each step: A boundary condition that determine if a path is acceptable or not. A condition that determine if the path has reached the final destination and can be selected as the best one. At each step a number of paths can be eliminated, letting only the "good" paths to grow. I hope this sufficiently describes my problem, and also a possible brute force solution. My question is: is the brute force is the best/only solution to the problem, and I need some hint also about the best coding structure of the algorithm.

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  • Should I use a modified singleton design pattern that only allows one reference to its instance?

    - by Graham
    Hi, I have a class that would normally just generate factory objects, however this class should only used once throughout the program in once specifix place. What is the best design pattern to use in this instance? I throught that having a modified singleton design which only allows one reference to instance throughout the program would be the correct way to go. So only the first call to getInstance() returns the factory library. Is this a good or bad idea? Have I missed out another fundermental design pattern for solving this problem? Thanks for your help.

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  • How do I set up MVP for a Winforms solution?

    - by JonWillis
    Question moved from Stackoverflow - http://stackoverflow.com/questions/4971048/how-do-i-set-up-mvp-for-a-winforms-solution I have used MVP and MVC in the past, and I prefer MVP as it controls the flow of execution so much better in my opinion. I have created my infrastructure (datastore/repository classes) and use them without issue when hard coding sample data, so now I am moving onto the GUI and preparing my MVP. Section A I have seen MVP using the view as the entry point, that is in the views constructor method it creates the presenter, which in turn creates the model, wiring up events as needed. I have also seen the presenter as the entry point, where a view, model and presenter are created, this presenter is then given a view and model object in its constructor to wire up the events. As in 2, but the model is not passed to the presenter. Instead the model is a static class where methods are called and responses returned directly. Section B In terms of keeping the view and model in sync I have seen. Whenever a value in the view in changed, i.e. TextChanged event in .Net/C#. This fires a DataChangedEvent which is passed through into the model, to keep it in sync at all times. And where the model changes, i.e. a background event it listens to, then the view is updated via the same idea of raising a DataChangedEvent. When a user wants to commit changes a SaveEvent it fires, passing through into the model to make the save. In this case the model mimics the view's data and processes actions. Similar to #b1, however the view does not sync with the model all the time. Instead when the user wants to commit changes, SaveEvent is fired and the presenter grabs the latest details and passes them into the model. in this case the model does not know about the views data until it is required to act upon it, in which case it is passed all the needed details. Section C Displaying of business objects in the view, i.e. a object (MyClass) not primitive data (int, double) The view has property fields for all its data that it will display as domain/business objects. Such as view.Animals exposes a IEnumerable<IAnimal> property, even though the view processes these into Nodes in a TreeView. Then for the selected animal it would expose SelectedAnimal as IAnimal property. The view has no knowledge of domain objects, it exposes property for primitive/framework (.Net/Java) included objects types only. In this instance the presenter will pass an adapter object the domain object, the adapter will then translate a given business object into the controls visible on the view. In this instance the adapter must have access to the actual controls on the view, not just any view so becomes more tightly coupled. Section D Multiple views used to create a single control. i.e. You have a complex view with a simple model like saving objects of different types. You could have a menu system at the side with each click on an item the appropriate controls are shown. You create one huge view, that contains all of the individual controls which are exposed via the views interface. You have several views. You have one view for the menu and a blank panel. This view creates the other views required but does not display them (visible = false), this view also implements the interface for each view it contains (i.e. child views) so it can expose to one presenter. The blank panel is filled with other views (Controls.Add(myview)) and ((myview.visible = true). The events raised in these "child"-views are handled by the parent view which in turn pass the event to the presenter, and visa versa for supplying events back down to child elements. Each view, be it the main parent or smaller child views are each wired into there own presenter and model. You can literately just drop a view control into an existing form and it will have the functionality ready, just needs wiring into a presenter behind the scenes. Section E Should everything have an interface, now based on how the MVP is done in the above examples will affect this answer as they might not be cross-compatible. Everything has an interface, the View, Presenter and Model. Each of these then obviously has a concrete implementation. Even if you only have one concrete view, model and presenter. The View and Model have an interface. This allows the views and models to differ. The presenter creates/is given view and model objects and it just serves to pass messages between them. Only the View has an interface. The Model has static methods and is not created, thus no need for an interface. If you want a different model, the presenter calls a different set of static class methods. Being static the Model has no link to the presenter. Personal thoughts From all the different variations I have presented (most I have probably used in some form) of which I am sure there are more. I prefer A3 as keeping business logic reusable outside just MVP, B2 for less data duplication and less events being fired. C1 for not adding in another class, sure it puts a small amount of non unit testable logic into a view (how a domain object is visualised) but this could be code reviewed, or simply viewed in the application. If the logic was complex I would agree to an adapter class but not in all cases. For section D, i feel D1 creates a view that is too big atleast for a menu example. I have used D2 and D3 before. Problem with D2 is you end up having to write lots of code to route events to and from the presenter to the correct child view, and its not drag/drop compatible, each new control needs more wiring in to support the single presenter. D3 is my prefered choice but adds in yet more classes as presenters and models to deal with the view, even if the view happens to be very simple or has no need to be reused. i think a mixture of D2 and D3 is best based on circumstances. As to section E, I think everything having an interface could be overkill I already do it for domain/business objects and often see no advantage in the "design" by doing so, but it does help in mocking objects in tests. Personally I would see E2 as a classic solution, although have seen E3 used in 2 projects I have worked on previously. Question Am I implementing MVP correctly? Is there a right way of going about it? I've read Martin Fowler's work that has variations, and I remember when I first started doing MVC, I understood the concept, but could not originally work out where is the entry point, everything has its own function but what controls and creates the original set of MVC objects.

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  • Should we write detailed architecture design or just an outline when designing a program?

    - by EpsilonVector
    When I'm doing design for a task, I keep fighting this nagging feeling that aside from being a general outline it's going to be more or less ignored in the end. I'll give you an example: I was writing a frontend for a device that has read/write operations. It made perfect sense in the class diagram to give it a read and a write function. Yet when it came down to actually writing them I realized they were literally the same function with just one line of code changed (read vs write function call), so to avoid code duplication I ended up implementing a do_io function with a parameter that distinguishes between operations. Goodbye original design. This is not a terribly disruptive change, but it happens often and can happen in more critical parts of the program as well, so I can't help but wondering if there's a point to design more detail than a general outline, at least when it comes to the program's architecture (obviously when you are specifying an API you have to spell everything out). This might be just the result of my inexperience in doing design, but on the other hand we have agile methodologies which sort of say "we give up on planning far ahead, everything is going to change in a few days anyway", which is often how I feel. So, how exactly should I "use" design?

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  • As an indie game dev, what processes are the best for soliciting feedback on my design/spec/idea? [closed]

    - by Jess Telford
    Background I have worked in a professional environment where the process usually goes like the following: Brain storm idea Solidify the game mechanics / design Iterate on design/idea to create a more solid experience Spec out the details of the design/idea Build it Step 3. is generally done with the stakeholders of the game (developers, designers, investors, publishers, etc) to reach an 'agreement' which meets the goals of all involved. Due to this process involving a series of often opposing and unique view points, creative solutions can surface through discussion / iteration. This is backed up by a process for collating the changes / new ideas, as well as structured time for discussion. As a (now) indie developer, I have to play the role of all the stakeholders (developers, designers, investors, publishers, etc), and often find myself too close to the idea / design to do more than minor changes, which I feel to be local maxima when it comes to the best result (I'm looking for the global maxima, of course). I have read that ideas / game designs / unique mechanics are merely multipliers of execution, and that keeping them secret is just silly. In sharing the idea with others outside the realm of my own thinking, I hope to replicate the influence other stakeholders have. I am struggling with the collation of changes / new ideas, and any kind of structured method of receiving feedback. My question: As an indie game developer, how and where can I share my ideas/designs to receive meaningful / constructive feedback? How can I successfully collate the feedback into a new iteration of the design? Are there any specialized websites, etc?

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  • Where can I find design exercises to work on?

    - by Oak
    I feel it's important to continue practicing my problem-solving skills. Writing my own mini-projects is one way, but another is to try and solve problems posted online. It's easy to find interesting programming quizzes online that require applying clever algorithms to solve - Project Euler is one well-known example. However, in a lot of real-life projects the design of the software - especially in the initial phases - has a large impact and at later stages it cannot be tweaked as easily as plain algorithms. In order to improve these skills, I'm looking for any collection of design problems. When I say "design", I mean the abstract design of a software solution - for example what modules will there be and what are the dependencies between them, how data will flow in the program, what sort of data needs to be saved in the database, etc. Design problems are those problems that are critical to solve in the early stages of any project, but their solution is a whiteboard diagram without a single line of code. Of course these sort of problems do not have a single correct solution, but I'll be especially happy with any place that also displays pros and cons of the typical solutions that might be used to approach the problem.

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  • What modelling technique do you use for your continuous design?

    - by d3prok
    Together with my teammates, I'm trying to self-learn XP and apply its principles. We're successfully working in TDD and happily refactoring our code and design. However we're having problems with the overall view of the design of the project. Lately we were wondering what would be the "good" practices for an effective continuous design of the code. We're not strictly seeking the right model, like CRC cards, communication diagrams, etc., instead we're looking for a technique to constantly collaborate on the high level view of the system (not too high though). I'll try to explain myself better: I'm actually interested in the way CRC cards are used to brainstorm a model and I would mix them with some very rough UML diagrams (that we already use). However, what we're looking for are some principles for deciding when, how and how much to model during our iterations. Have you any suggestion on this matter? For example, when your teammates and you know you need a design session and how your meetings work?

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  • Is there any algorithm for finding LINES by PIXEL COLORS on picture?

    - by Ole Jak
    So I have Image like this I want to get something like this (I hevent drawn all lines I want but I hope you can get my idea) I need algorithm for finding all straight lines on it by just reading colors of pixels. No hard math, no Haar, no Hough. Some algorithm which would be based on points colors. I want to give to algorithm parameters like min line length and max line distortion. I want to get relative to picture pixel coords start and end points of lines. So I need algorithm for finding straight lines of different colors on picture. Algorithm which would be based on idea of image of different colors and Lines of static colors. Yes - such algorithm will not work for images with lots of shadows and lights. But It willl probably be fast (I hope so). Is there any such algorithm?

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  • Minimum-Waste Print Job Grouping Algorithm?

    - by Matt Mc
    I work at a publishing house and I am setting up one of our presses for "ganging", in other words, printing multiple jobs simultaneously. Given that different print jobs can have different quantities, and anywhere from 1 to 20 jobs might need to be considered at a time, the problem would be to determine which jobs to group together to minimize waste (waste coming from over-printing on smaller-quantity jobs in a given set, that is). Given the following stable data: All jobs are equal in terms of spatial size--placement on paper doesn't come into consideration. There are three "lanes", meaning that three jobs can be printed simultaneously. Ideally, each lane has one job. Part of the problem is minimizing how many lanes each job is run on. If necessary, one job could be run on two lanes, with a second job on the third lane. The "grouping" waste from a given set of jobs (let's say the quantities of them are x, y and z) would be the highest number minus the two lower numbers. So if x is the higher number, the grouping waste would be (x - y) + (x - z). Otherwise stated, waste is produced by printing job Y and Z (in excess of their quantities) up to the quantity of X. The grouping waste would be a qualifier for the given set, meaning it could not exceed a certain quantity or the job would simply be printed alone. So the question is stated: how to determine which sets of jobs are grouped together, out of any given number of jobs, based on the qualifiers of 1) Three similar quantities OR 2) Two quantities where one is approximately double the other, AND with the aim of minimal total grouping waste across the various sets. (Edit) Quantity Information: Typical job quantities can be from 150 to 350 on foreign languages, or 500 to 1000 on English print runs. This data can be used to set up some scenarios for an algorithm. For example, let's say you had 5 jobs: 1000, 500, 500, 450, 250 By looking at it, I can see a couple of answers. Obviously (1000/500/500) is not efficient as you'll have a grouping waste of 1000. (500/500/450) is better as you'll have a waste of 50, but then you run (1000) and (250) alone. But you could also run (1000/500) with 1000 on two lanes, (500/250) with 500 on two lanes and then (450) alone. In terms of trade-offs for lane minimization vs. wastage, we could say that any grouping waste over 200 is excessive. (End Edit) ...Needless to say, quite a problem. (For me.) I am a moderately skilled programmer but I do not have much familiarity with algorithms and I am not fully studied in the mathematics of the area. I'm I/P writing a sort of brute-force program that simply tries all options, neglecting any option tree that seems to have excessive grouping waste. However, I can't help but hope there's an easier and more efficient method. I've looked at various websites trying to find out more about algorithms in general and have been slogging my way through the symbology, but it's slow going. Unfortunately, Wikipedia's articles on the subject are very cross-dependent and it's difficult to find an "in". The only thing I've been able to really find would seem to be a definition of the rough type of algorithm I need: "Exclusive Distance Clustering", one-dimensionally speaking. I did look at what seems to be the popularly referred-to algorithm on this site, the Bin Packing one, but I was unable to see exactly how it would work with my problem. Any help is appreciated. :)

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  • Has anyone ever worked with a UX designer who also did the graphic design, is it a good combination?

    - by Ami
    I need to design a new framework for web based apps, including both UX guidelines and the art/graphic design guidelines such as what menus will look like, headers, colors, fonts etc. The UX designers I met, were unable to provide the artistic side, and the graphic designers didn't have the UX skills. Should I continue to look for one person with both skills, or is it better broken to two separate tasks?

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  • Cloud Computing Forces Better Design Practices

    - by Herve Roggero
    Is cloud computing simply different than on premise development, or is cloud computing actually forcing you to create better applications than you normally would? In other words, is cloud computing merely imposing different design principles, or forcing better design principles?  A little while back I got into a discussion with a developer in which I was arguing that cloud computing, and specifically Windows Azure in his case, was forcing developers to adopt better design principles. His opinion was that cloud computing was not yielding better systems; just different systems. In this blog, I will argue that cloud computing does force developers to use better design practices, and hence better applications. So the first thing to define, of course, is the word “better”, in the context of application development. Looking at a few definitions online, better means “superior quality”. As it relates to this discussion then, I stipulate that cloud computing can yield higher quality applications in terms of scalability, everything else being equal. Before going further I need to also outline the difference between performance and scalability. Performance and scalability are two related concepts, but they don’t mean the same thing. Scalability is the measure of system performance given various loads. So when developers design for performance, they usually give higher priority to a given load and tend to optimize for the given load. When developers design for scalability, the actual performance at a given load is not as important; the ability to ensure reasonable performance regardless of the load becomes the objective. This can lead to very different design choices. For example, if your objective is to obtains the fastest response time possible for a service you are building, you may choose the implement a TCP connection that never closes until the client chooses to close the connection (in other words, a tightly coupled service from a connectivity standpoint), and on which a connection session is established for faster processing on the next request (like SQL Server or other database systems for example). If you objective is to scale, you may implement a service that answers to requests without keeping session state, so that server resources are released as quickly as possible, like a REST service for example. This alternate design would likely have a slower response time than the TCP service for any given load, but would continue to function at very large loads because of its inherently loosely coupled design. An example of a REST service is the NO-SQL implementation in the Microsoft cloud called Azure Tables. Now, back to cloud computing… Cloud computing is designed to help you scale your applications, specifically when you use Platform as a Service (PaaS) offerings. However it’s not automatic. You can design a tightly-coupled TCP service as discussed above, and as you can imagine, it probably won’t scale even if you place the service in the cloud because it isn’t using a connection pattern that will allow it to scale [note: I am not implying that all TCP systems do not scale; I am just illustrating the scalability concepts with an imaginary TCP service that isn’t designed to scale for the purpose of this discussion]. The other service, using REST, will have a better chance to scale because, by design, it minimizes resource consumption for individual requests and doesn’t tie a client connection to a specific endpoint (which means you can easily deploy this service to hundreds of machines without much trouble, as long as your pockets are deep enough). The TCP and REST services discussed above are both valid designs; the TCP service is faster and the REST service scales better. So is it fair to say that one service is fundamentally better than the other? No; not unless you need to scale. And if you don’t need to scale, then you don’t need the cloud in the first place. However, it is interesting to note that if you do need to scale, then a loosely coupled system becomes a better design because it can almost always scale better than a tightly-coupled system. And because most applications grow overtime, with an increasing user base, new functional requirements, increased data and so forth, most applications eventually do need to scale. So in my humble opinion, I conclude that a loosely coupled system is not just different than a tightly coupled system; it is a better design, because it will stand the test of time. And in my book, if a system stands the test of time better than another, it is of superior quality. Because cloud computing demands loosely coupled systems so that its underlying service architecture can be leveraged, developers ultimately have no choice but to design loosely coupled systems for the cloud. And because loosely coupled systems are better… … the cloud forces better design practices. My 2 cents.

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  • Implementing Naïve Bayes algorithm in Java - Need some guidance

    - by techventure
    hello stackflow people As a School assignment i'm required to implement Naïve Bayes algorithm which i am intending to do in Java. In trying to understand how its done, i've read the book "Data Mining - Practical Machine Learning Tools and Techniques" which has a section on this topic but am still unsure on some primary points that are blocking my progress. Since i'm seeking guidance not solution in here, i'll tell you guys what i thinking in my head, what i think is the correct approach and in return ask for correction/guidance which will very much be appreciated. please note that i am an absolute beginner on Naïve Bayes algorithm, Data mining and in general programming so you might see stupid comments/calculations below: The training data set i'm given has 4 attributes/features that are numeric and normalized(in range[0 1]) using Weka (no missing values)and one nominal class(yes/no) 1) The data coming from a csv file is numeric HENCE * Given the attributes are numeric i use PDF (probability density function) formula. + To calculate the PDF in java i first separate the attributes based on whether they're in class yes or class no and hold them into different array (array class yes and array class no) + Then calculate the mean(sum of the values in row / number of values in that row) and standard divination for each of the 4 attributes (columns) of each class + Now to find PDF of a given value(n) i do (n-mean)^2/(2*SD^2), + Then to find P( yes | E) and P( no | E) i multiply the PDF value of all 4 given attributes and compare which is larger, which indicates the class it belongs to In temrs of Java, i'm using ArrayList of ArrayList and Double to store the attribute values. lastly i'm unsure how to to get new data? Should i ask for input file (like csv) or command prompt and ask for 4 values? I'll stop here for now (do have more questions) but I'm worried this won't get any responses given how long its got. I will really appreciate for those that give their time reading my problems and comment.

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  • help in the Donalds B. Johnson's algorithm, i cannot understand the pseudo code (PART II)

    - by Pitelk
    Hi all , i cannot understand a certain part of the paper published by Donald Johnson about finding cycles (Circuits) in a graph. More specific i cannot understand what is the matrix Ak which is mentioned in the following line of the pseudo code : Ak:=adjacency structure of strong component K with least vertex in subgraph of G induced by {s,s+1,....n}; to make things worse some lines after is mentins " for i in Vk do " without declaring what the Vk is... As far i have understand we have the following: 1) in general, a strong component is a sub-graph of a graph, in which for every node of this sub-graph there is a path to any node of the sub-graph (in other words you can access any node of the sub-graph from any other node of the sub-graph) 2) a sub-graph induced by a list of nodes is a graph containing all these nodes plus all the edges connecting these nodes. in paper the mathematical definition is " F is a subgraph of G induced by W if W is subset of V and F = (W,{u,y)|u,y in W and (u,y) in E)}) where u,y are edges , E is the set of all the edges in the graph, W is a set of nodes. 3)in the code implementation the nodes are named by integer numbers 1 ... n. 4) I suspect that the Vk is the set of nodes of the strong component K. now to the question. Lets say we have a graph G= (V,E) with V = {1,2,3,4,5,6,7,8,9} which it can be divided into 3 strong components the SC1 = {1,4,7,8} SC2= {2,3,9} SC3 = {5,6} (and their edges) Can anybody give me an example for s =1, s= 2, s= 5 what if going to be the Vk and Ak according to the code? The pseudo code is in my previous question in http://stackoverflow.com/questions/2908575/help-in-the-donalds-b-johnsons-algorithm-i-cannot-understand-the-pseudo-code and the paper can be found at http://stackoverflow.com/questions/2908575/help-in-the-donalds-b-johnsons-algorithm-i-cannot-understand-the-pseudo-code thank you in advance

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