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  • Context-sensitive grammar for specific language

    - by superagio
    How can I construct a grammar that generates this language? Construct a grammar that generates L: L = {a^n b^m c^k|k>n, k>m} I believe my productions should go along this lines: S-> ABCC A-> a|aBC|BC B-> b|bBC C-> c|Cc CB->BC The idea is to start with 2 c and keep always one more c, and then with C-c|Cc ad as much c as i want. How can my production for C remember the numbers of m and n.

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  • Proving that the distance values extracted in Dijkstra's algorithm is non-decreasing?

    - by Gail
    I'm reviewing my old algorithms notes and have come across this proof. It was from an assignment I had and I got it correct, but I feel that the proof certainly lacks. The question is to prove that the distance values taken from the priority queue in Dijkstra's algorithm is a non-decreasing sequence. My proof goes as follows: Proof by contradiction. Fist, assume that we pull a vertex from Q with d-value 'i'. Next time, we pull a vertex with d-value 'j'. When we pulled i, we have finalised our d-value and computed the shortest-path from the start vertex, s, to i. Since we have positive edge weights, it is impossible for our d-values to shrink as we add vertices to our path. If after pulling i from Q, we pull j with a smaller d-value, we may not have a shortest path to i, since we may be able to reach i through j. However, we have already computed the shortest path to i. We did not check a possible path. We no longer have a guaranteed path. Contradiction.

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  • Generating All Permutations of Character Combinations when # of arrays and length of each array are

    - by Jay
    Hi everyone, I'm not sure how to ask my question in a succinct way, so I'll start with examples and expand from there. I am working with VBA, but I think this problem is non language specific and would only require a bright mind that can provide a pseudo code framework. Thanks in advance for the help! Example: I have 3 Character Arrays Like So: Arr_1 = [X,Y,Z] Arr_2 = [A,B] Arr_3 = [1,2,3,4] I would like to generate ALL possible permutations of the character arrays like so: XA1 XA2 XA3 XA4 XB1 XB2 XB3 XB4 YA1 YA2 . . . ZB3 ZB4 This can be easily solved using 3 while loops or for loops. My question is how do I solve for this if the # of arrays is unknown and the length of each array is unknown? So as an example with 4 character arrays: Arr_1 = [X,Y,Z] Arr_2 = [A,B] Arr_3 = [1,2,3,4] Arr_4 = [a,b] I would need to generate: XA1a XA1b XA2a XA2b XA3a XA3b XA4a XA4b . . . ZB4a ZB4b So the Generalized Example would be: Arr_1 = [...] Arr_2 = [...] Arr_3 = [...] . . . Arr_x = [...] Is there a way to structure a function that will generate an unknown number of loops and loop through the length of each array to generate the permutations? Or maybe there's a better way to think about the problem? Thanks Everyone!

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  • Finding the nth number of primes

    - by Braxton Smith
    I can not figure out why this won't work. Please help me from math import sqrt pN = 0 numPrimes = 0 num = 1 def checkPrime(x): '''Check\'s whether a number is a prime or not''' prime = True if(x==2): prime = True elif(x%2==0): prime=False else: root=int(sqrt(x)) for i in range(3,root,2): if(x%i==0): prime=False break return prime n = int(input("Find n number of primes. N being:")) while( numPrimes != n ): if( checkPrime( num ) == True ): numPrimes += 1 pN = num print("{0}: {1}".format(numPrimes,pN)) num += 1 print("Prime {0} is: {1}".format(n,pN))

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  • Examples of monoids/semigroups in programming

    - by jkff
    It is well-known that monoids are stunningly ubiquitous in programing. They are so ubiquitous and so useful that I, as a 'hobby project', am working on a system that is completely based on their properties (distributed data aggregation). To make the system useful I need useful monoids :) I already know of these: Numeric or matrix sum Numeric or matrix product Minimum or maximum under a total order with a top or bottom element (more generally, join or meet in a bounded lattice, or even more generally, product or coproduct in a category) Set union Map union where conflicting values are joined using a monoid Intersection of subsets of a finite set (or just set intersection if we speak about semigroups) Intersection of maps with a bounded key domain (same here) Merge of sorted sequences, perhaps with joining key-equal values in a different monoid/semigroup Bounded merge of sorted lists (same as above, but we take the top N of the result) Cartesian product of two monoids or semigroups List concatenation Endomorphism composition. Now, let us define a quasi-property of an operation as a property that holds up to an equivalence relation. For example, list concatenation is quasi-commutative if we consider lists of equal length or with identical contents up to permutation to be equivalent. Here are some quasi-monoids and quasi-commutative monoids and semigroups: Any (a+b = a or b, if we consider all elements of the carrier set to be equivalent) Any satisfying predicate (a+b = the one of a and b that is non-null and satisfies some predicate P, if none does then null; if we consider all elements satisfying P equivalent) Bounded mixture of random samples (xs+ys = a random sample of size N from the concatenation of xs and ys; if we consider any two samples with the same distribution as the whole dataset to be equivalent) Bounded mixture of weighted random samples Which others do exist?

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  • Cropping image with ImageScience

    - by fl00r
    ImageScience is cool and light. I am using it in my sinatra app. But I can't understand how can I crop image with not square form and how can I make thumbnail with two dimensions. As I found on ImageScience site: ImageScience.with_image(file) do |img| img.cropped_thumbnail(100) do |thumb| thumb.save "#{file}_cropped.png" end img.thumbnail(100) do |thumb| thumb.save "#{file}_thumb.png" end img.resize(100, 150) do |img2| img2.save "#{file}_resize.png" end end I can crop thumb and resize thumb only with ONE dimension but I want to use two, as in RMagick. For example I want to crop 100x200px box from image, or I want to make thumbnail with width or height not bigger then 300 (width) or 500 (height) pixels.

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  • Why is it useful to count the number of bits?

    - by Scorchin
    I've seen the numerous questions about counting the number of set bits in a insert type of input, but why is it useful? For those looking for algorithms about bit counting, look here: http://stackoverflow.com/questions/1517848/counting-common-bits-in-a-sequence-of-unsigned-longs http://stackoverflow.com/questions/472325/fastest-way-to-count-number-of-bit-transitions-in-an-unsigned-int http://stackoverflow.com/questions/109023/best-algorithm-to-count-the-number-of-set-bits-in-a-32-bit-integer

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  • Using Dijkstra's algorithm with negative edges?

    - by Riddler
    Most books explain the reason the algorithm doesn't work with negative edges as nodes are deleted from the priority queue after the node is arrived at since the algorithm assumes the shortest distance has been found. However since negative edges can reduce the distance, a future shorter distance might be found; but since the node is deleted it cannot be updated. Wouldn't an obvious solution to this be to not delete the node? Why not keep the node in the queue, so if a future shorter distance is found, it can be updated? If I am misunderstanding the problem, what is preventing the algorithm from being used with negative edges?

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  • Real world example of Unification in First Order Logic?

    - by Sebi
    I know this is only part of a programming question, but at the moment, I'm doing a little bit of logic programming. One thing I still don't understand correctly is Unification in First Order Logic. I read the Wikipedia article and it is more or less clear that the purpose is searching a term that unifies two sentences... There are also examples in this article but I just don't get the point why this should be useful. Can anyone give an example with real world objects instead of A, B, C,, etc.? I hope this will help me to understand. Thanks

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  • Moderating computer-addiction through programming

    - by every_answer_gets_a_point
    i have an addiction to be on the computer all the time. it doesn't matter what i am doing as long as i am in front of it. i feel like the whole world is here and this is all that matters. i found that through some intellectual stimulation, like writing algorithms, it has helped me to be more satisfied with the time on the computer and i dont need it as much. if any of you have had experience with reliving your computer anxiety through writing code, can you tell me exactly what you wrote, and what you may recommend i work on? thank you for your programming advice

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  • Solving the water jug problem

    - by Amit
    While reading through some lecture notes on preliminary number theory, I came across the solution to water jug problem (with two jugs) which is summed as thus: Using the property of the G.C.D of two numbers that GCD(a,b) is the smallest possible linear combination of a and b, and hence a certain quantity Q is only measurable by the 2 jugs, iff Q is a n*GCD(a,b), since Q=sA + tB, where: n = a positive integer A = capacity of jug A B= capacity of jug B And, then the method to the solution is discussed Another model of the solution is to model the various states as a state-space search problem as often resorted to in Artificial Intelligence. My question is: What other known methods exist which models the solution, and how? Google didn't throw up much.

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  • Rules Engine vs Expert System

    - by User1
    What is the difference between a rules engine and an expert system? Example1: Let's say that I have a program that determines the expiration date of a new driver's license. It takes inputs like visa expiration date, passport number, birthday, etc. It determines the expiration date of the driver's license from this input. It can even give an error if the input did not have enough valid identifications to allow a new driver's license. Example2: Let's say I am making an online version of the game Monopoly. I want the ability to change the rules of the game (say $400 for passing go or no one can buy properties until they land on the same property twice, etc). I have a module in the code to handle these rules. Are these both rules engines or are they expert systems? They both seem so similar. Is it just a synonym?

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  • Undefined Variable in Matlab

    - by OrangeRind
    The Following is the basic skeleton for my MATLAB program. Each box is a class definition. Scroll down for the error. Note: Each Class has a custom constructor which does not require an external parameter The Error Undefined function or variable 'Troom'. Error in == wallwall.wall at 31 function o = wall(Tr) Error in == mainfile at 5 w1 = wall(); This comes when I create an object of Class wall from another file "mainfile" Question Why is this happening? Am I getting wrong in the concepts of OOP for Matlab specific? How do I resolve this? Thanks in Advance!

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  • Algorithm for optimally choosing actions to perform a task

    - by Jules
    There are two data types: tasks and actions. An action costs a certain time to complete, and a set of tasks this actions consists of. A task has a set of actions, and our job is to choose one of them. So: class Task { Set<Action> choices; } class Action { float time; Set<Task> dependencies; } For example the primary task could be "Get a house". The possible actions for this task: "Buy a house" or "Build a house". The action "Build a house" costs 10 hours and has the dependencies "Get bricks" and "Get cement", etcetera. The total time is the sum of all the times of the actions required to perform. We want to choose actions such that the total time is minimal. Note that the dependencies can be diamond shaped. For example "Get bricks" could require "Get a car" (to transport the bricks) and "Get cement" would also require a car. Even if you do "Get bricks" and "Get cement" you only have to count the time it takes to get a car once. Note also that the dependencies can be circular. For example "Money" - "Job" - "Car" - "Money". This is no problem for us, we simply select all of "Money", "Job" and "Car". The total time is simply the sum of the time of these 3 things. Mathematical description: Let actions be the chosen actions. valid(task) = ?action ? task.choices. (action ? actions ? ?tasks ? action.dependencies. valid(task)) time = sum {action.time | action ? actions} minimize time subject to valid(primaryTask)

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  • Recognizing terminals in a CFG production previously not defined as tokens.

    - by kmels
    I'm making a generator of LL(1) parsers, my input is a CoCo/R language specification. I've already got a Scanner generator for that input. Suppose I've got the following specification: COMPILER 1. CHARACTERS digit="0123456789". TOKENS number = digit{digit}. decnumber = digit{digit}"."digit{digit}. PRODUCTIONS Expression = Term{"+"Term|"-"Term}. Term = Factor{"*"Factor|"/"Factor}. Factor = ["-"](Number|"("Expression")"). Number = (number|decnumber). END 1. So, if the parser generated by this grammar receives a word "1+1", it'd be accepted i.e. a parse tree would be found. My question is, the character "+" was never defined in a token, but it appears in the non-terminal "Expression". How should my generated Scanner recognize it? It would not recognize it as a token. Is this a valid input then? Should I add this terminal in TOKENS and then consider an error routine for a Scanner for it to skip it? How does usual language specifications handle this?

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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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