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  • recursion tree and binary tree cost calculation

    - by Tony
    Hi all, I've got the following recursion: T(n) = T(n/3) + T(2n/3) + O(n) The height of the tree would be log3/2 of 2. Now the recursion tree for this recurrence is not a complete binary tree. It has missing nodes lower down. This makes sense to me, however I don't understand how the following small omega notation relates to the cost of all leaves in the tree. "... the total cost of all leaves would then be Theta (n^log3/2 of 2) which, since log3/2 of 2 is a constant strictly greater then 1, is small omega(n lg n)." Can someone please help me understand how the Theta(n^log3/2 of 2) becomes small omega(n lg n)?

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  • Divide and conquer method to compute roots [SOLVED]

    - by hellsoul153
    Hello, Knowing that we can use Divide-and-Conquer algorithm to compute large exponents, for exemple 2 exp 100 = 2 exp(50) * 2 exp(50), which is quite more efficient, is this method efficient using roots ? For exemple 2 exp (1/100) = (2 exp(1/50)) exp(1/50) ? In other words, I'm wondering if (n exp(1/x)) is more efficient to (n exp(1/y)) for x < y and where x and y are integers.

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  • The Definition of Regular Languages

    - by AraK
    Good Day, I have tried, and burned my brain to understand the definition of Regular Languages in Discrete Mathematics and its Applications(Rosen) without reaching the goal of understanding why the definition is like that in this book. On page(789), I am rephrasing the definition: Type 3 grammars are defined as: w1 --> w2 Where w1 is a non-terminal, and w2 is of the form: w2 = aB w2 = a Where B is a non-terminal, and a is a terminal. A special case is when w1 is the starting symbol and w2 is lambda(the empty string): w1 = S S --> lambda Two questions I couldn't find an answer for. First, Why can't w2 be of the form Ba. Second, Why lambda is only allowed for the starting symbol only. The book states that, regular languages are equivalent to Finite State Automaton, and we can easily see that a we can build FSA for both cases. I took a look at other resources, and these restrictions don't exist in these resources. Thanks,

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  • Core principles, rules, and habits for CS students

    - by Asad Butt
    No doubt there is a lot to read on blogs, in books, and on Stack Overflow, but can we identify some guidelines for CS students to use while studying? For me these are: Finish your course books early and read 4-5 times more material relative to your course work. Programming is the one of the fastest evolving professions. Follow the blogs on a daily basis for the latest updates, news, and technologies. Instead of relying on assignments and exams, do at least one extra, non-graded, small to medium-sized project for every programming course. Fight hard for internships or work placements even if they are unpaid, since 3 months of work 1 year at college. Practice everything, every possible and impossible way. Try doing every bit of your assignments project yourself; i.e. fight for every inch. Rely on documentation as the first source for help and samples, Google, and online forums as the last source. Participate often in online communities and forums to learn the best possible approach for every solution to your problem. (After doing your bit.) Make testing one of your habits as it is getting more important everyday in programming. Make writing one of your habits. Write something productive once or twice a week and publish it.

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  • How is a new programming language actually formed/created ?

    - by hory.incpp
    Fortran-Algol-Cpl-Bcpl-C-C++-Java ..... Seems like every language is built upon an ancestor language. My question : New languages extend parent ones or there is some kind of a trick? e.g. System.out.print() in Java ; is it actually printf() in C, and so on (printf is actually .. in Cpl)? If so, doesn't this make every further language be slower and need more memory? What separates a new language from a framework?

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  • Python: writing a program to compute the area of a circle and square

    - by user1672504
    I have a question with an assignment. I'm not sure how to write this program and I really need help! Could someone help me with this? This is the assignment: Write a program that asks the user to enter two values: an integer choice and a real number x. If choice is 1, compute and display the area of a circle of radius x. If choice is 2, compute and display the are of a square with sides of length x. If choice is neither 1, nor 2, will display the text Invalid choice. Sample run: Enter choice: 2 Enter x: 8 The area is: 64.0 Sample run: Enter choice: 1 Enter x: 8 The area is: 201.06176 My attempt: choice = input ('Enter Choice:') choice_1 = int (choice) if (choice_1==1): radius = (int) print('Enter x:',radius) pi = 3.14159 area = ( radius ** 2 ) * pi print ( 'The Area is=' , area )

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  • What are the lesser known but cool data structures ?

    - by f3lix
    There a some data structures around that are really cool but are unknown to most programmers. Which are they? Everybody knows linked lists, binary trees, and hashes, but what about Skip lists, Bloom filters for example. I would like to know more data structures that are not so common, but are worth knowing because they rely on great ideas and enrich a programmer's tool box. PS: I am also interested on techniques like Dancing links which make interesting use of the properties of a common data structure. EDIT: Please try to include links to pages describing the data structures in more detail. Also, try to add a couple of words on why a data structures is cool (as Jonas Kölker already pointed out). Also, try to provide one data-structure per answer. This will allow the better data structures to float to the top based on their votes alone.

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  • Is it possible to have regexp that matches all valid regular expressions?

    - by Juha Syrjälä
    Is it possible to detect if a given string is valid regular expression, using just regular expressions? Say I have some strings, that may or may not be a valid regular expressions. I'd like to have a regular expression matches those string that correspond to valid regular expression. Is that possible? Or do I have use some higher level grammar (i.e. context free language) to detect this? Does it affect if I am using some extended version of regexps like Perl regexps? If that is possible, what the regexp matching regexp is?

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  • Balancing a Binary Tree (AVL)

    - by Gustavo Carreno
    Ok, this is another one in the theory realm for the CS guys around. In the 90's I did fairly well in implementing BST's. The only thing I could bever get my head around was the intricacy of the algorithm to balance a Binary Tree (AVL). Can you guys help me on this?

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  • What is the most easy way to get in advanced Type Theory.

    - by Bubba88
    Of course, by 'advanced' I mean here just something beyond what every programmer does know. I'm currently more-or-less comfortable with the basics and want to understand the most important, most elegant and most practically applicable achievements of modern type theory. I just do not have much time, desire and mental powers to study all the formalistics more thoroughly and that may change in the future. But there is something really attractive for me in that branch, that just forces to ask silly questions like this :) Thank you very much!

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  • Learning material on SAT

    - by Jules
    What are good documents to read on SAT solvers. I have not been able to find good material via Google. The documents I found were either birds eye view, too advanced or corrupted PDF files... Which papers/documents do you recommend to learn about the algorithms in modern practical SAT solvers?

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  • Fitch Format Proofs - any resources around?

    - by devoured elysium
    I am currently studying Fitch Format first order logic proofs. My lecturer follows closely Language, Proof and Logic by Jon Barwise. I am trying to do some proofs but I am having some trouble getting to understand how to do these proofs. As I have already read what Language Proof and Logic has to offer, I'd like to know if there are any other books or resources around that use the Fitch format for their formal proofs. Plus, having solved exercises would be of great(!) help. Thanks

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  • What makes people think that NNs have more computational power than existing models?

    - by Bubba88
    I've read in Wikipedia that neural-network functions defined on a field of arbitrary real/rational numbers (along with algorithmic schemas, and the speculative `transrecursive' models) have more computational power than the computers we use today. Of course it was a page of russian wikipedia (ru.wikipedia.org) and that may be not properly proven, but that's not the only source of such.. rumors Now, the thing that I really do not understand is: How can a string-rewriting machine (NNs are exactly string-rewriting machines just as Turing machines are; only programming language is different) be more powerful than a universally capable U-machine? Yes, the descriptive instrument is really different, but the fact is that any function of such class can be (easily or not) turned to be a legal Turing-machine. Am I wrong? Do I miss something important? What is the cause of people saying that? I do know that the fenomenum of undecidability is widely accepted today (though not consistently proven according to what I've read), but I do not really see a smallest chance of NNs being able to solve that particular problem. Add-in: Not consistently proven according to what I've read - I meant that you might want to take a look at A. Zenkin's (russian mathematician) papers after mid-90-s where he persuasively postulates the wrongness of G. Cantor's concepts, including transfinite sets, uncountable sets, diagonalization method (method used in the proof of undecidability by Turing) and maybe others. Even Goedel's incompletness theorems were proven in right way in only 21-st century.. That's all just to plug Zenkin's work to the post cause I don't know how widespread that knowledge is in CS community so forgive me if that did look stupid. Thank you!

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  • A Simulator for a non-deterministic Push-Down Automaton

    - by shake
    Well, i need to make simulator for non-deterministic Push-Down Automaton. Everything is okey, i know i need to do recursion or something similar. But i do not know how to make that function which would simulate automaton. I got everything else under control, automaton generator, stack ... I am doing it in java, so this is maybe only issue that man can bump on, and i did it. So if anyone have done something similar, i could use advices. This is my current organisation of code: C lasses: class transit: list -contains non deterministic transitions state input sign stack sign class generator it generate automaton from file clas NPA public boolean start() - this function i am having trouble with Of course problem of separate stacks, and input for every branch. I tried to solve it with collection of objects NPA and try to start every object, but it doesn work :((..

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  • How do I implement graphs and graph algorithms in a functional programming language?

    - by brad
    Basically, I know how to create graph data structures and use Dijkstra's algorithm in programming languages where side effects are allowed. Typically, graph algorithms use a structure to mark certain nodes as 'visited', but this has side effects, which I'm trying to avoid. I can think of one way to implement this in a functional language, but it basically requires passing around large amounts of state to different functions, and I'm wondering if there is a more space-efficient solution.

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  • Specifying Language for a grammar

    - by darkie15
    Hi All, Is there any specific methodology followed to specify a language for given grammar ?? i.e. Is it necessary to run all the production rules given in a grammar to determine the language it represents? I don't have an example as such since the one I am working on is a homework question. Regards, darkie15

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  • What problems have you solved using constraint programming?

    - by knorv
    I'd like to know about specific problems you - the SO reader - have solved using constraint programming and what constraint logic language you used. Questions: What problems have you used constraint programming to solve? What constraint logic language did you use? I'm looking for first-hand experiences, so please do not answer unless you have that.

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  • What is better for a student programming in C++ to learn for writing GUI: C# vs QT?

    - by flashnik
    I'm a teacher(instructor) of CS in the university. The course is based on Cormen and Knuth and students program algorithms in C++. But sometimes it is good to show how an algorithm works or just a result of task through GUI. Also in my opinion it's very imporant to be able to write full programs. They will have courses concerning GUI but a three years, later, in fact, before graduatuion. I think that they should be able to write simple GUI applications earlier. So I want to teach them it. How do you think, what is more useful for them to learn: programming GUI with QT or writing GUI in C# and calling unmanaged C++ library?

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  • List of fundamental data structures - what am I missing?

    - by jboxer
    I've been studying my fundamental data structures a bunch recently, trying to make sure I've got them down cold. By "fundamental", I mean the real basic ones. Fancy ones like Red-Black Trees and Bloom Filters are clearly worth knowing, but they're usually either enhancements of fundamental ones (Red-Black Trees are binary search trees with special properties to keep them balanced) or they're only useful in very specific situations (Bloom Filters). So far, I'm "fluent" in the following data structures: Arrays Linked Lists Stacks/Queues Binary Search Trees Heaps/Priority Queues Hash Tables However, I feel like I'm missing something. Are there any fundamental ones that I'm forgetting about? EDIT: Added these after posting the question Strings (suggested by catchmeifyoutry) Sets (suggested by Peter) Graphs (suggested by Nick D and aJ) B-Trees (Suggested by tloach) I'm a little on-the-fence about whether these are too fancy or not, but I think they're different enough from the fundamental structures (and important enough) to be worth studying as fundamental.

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  • Do invariant assertions fit into C# programming?

    - by P.Brian.Mackey
    In the book coders at work, the author asks "How do you use invariants in your code". Please explain what this question means. I saw class invariants on wiki, but the example is in Java and I am not skilled enough in Java to relate this example to C#. .NET 4.0 introduces invariance, covariance, and contravariance and is well explained here. Invariance is so broad. The authors usage of the word seems unit test related. For those that read the book, what does the author mean? Are we talking about making an assumption and simply testing the validity after the unit test?

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  • Learning material on SAT (Boolean Satisfiability Problem)

    - by Jules
    What are good documents to read on SAT (Boolean satisfiability problem) solvers. I have not been able to find good material via Google. The documents I found were either birds eye view, too advanced or corrupted PDF files... Which papers/documents do you recommend to learn about the algorithms in modern practical SAT solvers?

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  • P-NP-Problem: What are the most promising methods?

    - by phimuemue
    Hello everybody, I know that P=NP has not been solved up to now, but can anybody tell me something about the following: What are currently the most promising mathematical / computer scientific methods that could be helpful to tackle this problem? Or are there even none such methods known to be potentially helpful up to now? Is there any (free) compendium on this topic where I can find all / most of the research done in this area?

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  • Learning networking fundamentals

    - by bplus
    Not having a CS degree has left large holes in my programming related knowledge. In particular I'd really like to learn some of the computer networking stuff I would have got in a good CS degree. The problem I really have is "not knowing what I don't know". So far I know I don't know anything about the following (as far as computer networks are concearned) -sockets -ports -internet protocol (the whole IP stack I keep hearing about). Can anyone add more to the list? Can anyone suggest a project (writing a toy web server?) Thanks in advance

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