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  • Diophantine Equation [closed]

    - by ANIL
    In mathematics, a Diophantine equation (named for Diophantus of Alexandria, a third century Greek mathematician) is a polynomial equation where the variables can only take on integer values. Although you may not realize it, you have seen Diophantine equations before: one of the most famous Diophantine equations is: X^n+Y^n=Z^n We are not certain that McDonald's knows about Diophantine equations (actually we doubt that they do), but they use them! McDonald's sells Chicken McNuggets in packages of 6, 9 or 20 McNuggets. Thus, it is possible, for example, to buy exactly 15 McNuggets (with one package of 6 and a second package of 9), but it is not possible to buy exactly 16 nuggets, since no non- negative integer combination of 6's, 9's and 20's adds up to 16. To determine if it is possible to buy exactly n McNuggets, one has to solve a Diophantine equation: find non-negative integer values of a, b, and c, such that 6a + 9b + 20c = n. Problem 1 Show that it is possible to buy exactly 50, 51, 52, 53, 54, and 55 McNuggets, by finding solutions to the Diophantine equation. You can solve this in your head, using paper and pencil, or writing a program. However you chose to solve this problem, list the combinations of 6, 9 and 20 packs of McNuggets you need to buy in order to get each of the exact amounts. Given that it is possible to buy sets of 50, 51, 52, 53, 54 or 55 McNuggets by combinations of 6, 9 and 20 packs, show that it is possible to buy 56, 57,..., 65 McNuggets. In other words, show how, given solutions for 50-55, one can derive solutions for 56-65. Problem 2 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" Hints: Hypothesize possible instances of numbers of McNuggets that cannot be purchased exactly, starting with 1 For each possible instance, called n, a. Test if there exists non-negative integers a, b, and c, such that 6a+9b+20c = n. (This can be done by looking at all feasible combinations of a, b, and c) b. If not, n cannot be bought in exact quantity, save n When you have found six consecutive values of n that in fact pass the test of having an exact solution, the last answer that was saved (not the last value of n that had a solution) is the correct answer, since you know by the theorem that any amount larger can also be bought in exact quantity

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  • Sublinear Extra Space MergeSort

    - by hulkmeister
    I am reviewing basic algorithms from a book called Algorithms by Robert Sedgewick, and I came across a problem in MergeSort that I am, sad to say, having difficulty solving. The problem is below: Sublinear Extra Space. Develop a merge implementation that reduces that extra space requirement to max(M, N/M), based on the following idea: Divide the array into N/M blocks of size M (for simplicity in this description, assume that N is a multiple of M). Then, (i) considering the blocks as items with their first key as the sort key, sort them using selection sort; and (ii) run through the array merging the first block with the second, then the second block with the third, and so forth. The problem I have with the problem is that based on the idea Sedgewick recommends, the following set of arrays will not be sorted: {0, 10, 12}, {3, 9, 11}, {5, 8, 13}. The algorithm I use is the following: Divide the full array into subarrays of size M. Run Selection Sort on each of the subarrays. Merge each of the subarrays using the method Sedgwick recommends in (ii). (This is where I encounter the problem of where to store the results after the merge.) This leads to wanting to increase the size of the auxiliary space needed to handle at least two subarrays at a time (for merging), but based on the specifications of the problem, that is not allowed. I have also considered using the original array as space for one subarray and using the auxiliary space for the second subarray. However, I can't envision a solution that does not end up overwriting the entries of the first subarray. Any ideas on other ways this can be done? NOTE: If this is suppose to be on StackOverflow.com, please let me know how I can move it. I posted here because the question was academic.

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  • How do you avoid jumping to a solution when under pressure? [closed]

    - by GlenPeterson
    When under a particularly strict programming deadline (like an hour), if I panic at all, my tendency is to jump into coding without a real plan and hope I figure it out as I go along. Given enough time, this can work, but in an interview it's been pretty unsuccessful, if not downright counter-productive. I'm not always comfortable sitting there thinking while the clock ticks away. Is there a checklist or are there techniques to recognize when you understand the problem well enough to start coding? Maybe don't touch the keyboard for the first 5-10 minutes of the problem? At what point do you give up and code a brute-force solution with the hope of reasoning out a better solution later? A related follow-up question might be, "How do you ensure that you are solving the right problem?" Or "When is it most productive to think and design more vs. code some experiments to and figure out the design later?" EDIT: One close vote already, but I'm not sure why. I wrote this in the first person, but I doubt I'm the only programmer to ever choke in an interview. Here is a list of techniques for taking a math test and another for taking an oral exam. Maybe I'm not expressing myself well, but I'm asking if there is a similar list of techniques for handling a programming problem under pressure?

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  • Proper Translation of equation to C#

    - by Shykin
    I am trying to replicate this equation: Slope(b) = (NSXY - (SX)(SY)) / (NSX2 - (SX)2) in C# but I'm getting the following issue: If I make the average of X = 1 + 2 + 3 + 4 + 5 and the average Y = 5 + 4 + 3 + 2 + 1 it gives me a positive slope even though it is clearly counting down. If I place the same numbers into this calculator: http://www.easycalculation.com/statistics/regression.php It gives me a negative slope in the linked calculator with the same data. I'm trying to narrow down the reasons so is the following a proper translation from equation to C# code: Slope(b) = (NSXY - (SX)(SY)) / (NSX2 - (SX)2) to Slope (m) = ((x * avgX * avgY) - (avgX * avgY)) / ((x * Math.Pow(avgX, 2)) - Math.Pow(avgX, 2));

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  • Solving Diophantine Equations Using Python

    - by HARSHITH
    In mathematics, a Diophantine equation (named for Diophantus of Alexandria, a third century Greek mathematician) is a polynomial equation where the variables can only take on integer values. Although you may not realize it, you have seen Diophantine equations before: one of the most famous Diophantine equations is: We are not certain that McDonald's knows about Diophantine equations (actually we doubt that they do), but they use them! McDonald's sells Chicken McNuggets in packages of 6, 9 or 20 McNuggets. Thus, it is possible, for example, to buy exactly 15 McNuggets (with one package of 6 and a second package of 9), but it is not possible to buy exactly 16 nuggets, since no non- negative integer combination of 6's, 9's and 20's adds up to 16. To determine if it is possible to buy exactly n McNuggets, one has to solve a Diophantine equation: find non-negative integer values of a, b, and c, such that 6a + 9b + 20c = n. 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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  • How to fix “Collection was modified; enumeration operation may not execute. “when using Copy.asmx in SharePoint2010

    - by ybbest
    Problem: In my current project, we use copy.asmx web services in SharePoint2010 to upload a document to a document library. In one of the document library, when uploading a document with a choice field, it blows up and the error message is Collection was modified; enumeration operation may not execute. Analysis: After some research , we found out the problem is that we have 2 content types that both have a field called Document Type , although the internal name are different but the display name are exactly the same and this cause the problem. I am still not too sure why, it could possibly a SharePoint bug. Solution: After rename one of the field display name to a different name, it works like a charm. You can download source code with the problem here and source code without the problem here.

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  • Finding a problem in some task [closed]

    - by nagisa
    Recently I competed in nation wide programming contest finals. Not unexpectedly all problems were algorithmic. I lost (40 points out of 600. Winner got ~300). I know why I lost very well - I don't know how to find actual problem in those obfuscated tasks which are life-blood of every competition. I think that being self-taught and not well versed in algorithms got me too. As side effect of learning things myself I know how to search for information, however all I could find are couple questions about learning algorithms. For now I put Python Algorithms: Mastering Basic Algorithms in the Python Language and Analysis of Algorithms which I found in those questions to my "to read" list. That leaves my first problem of not knowing how to find a problem unsolved. Will that ability come with learning algorithms? Or does it need some special attention? Any suggestions are welcomed.

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  • Where can you find fun/educational programming challenges?

    - by tj9991
    I've searched around for different challenge sites, and most of them seem to be geared towards difficulty in problem solving logically, rather than trying to use your language of choice to do something you haven't used it for. Their center is around mathematics rather than function design. Some kind of point system for correctly solving challenges, or solving them the most efficient/smallest would be neat as well. Listed sites Project Euler TopCoder UVa Online Judge Challenges with Python Google Code Jam Programming Challenges Less Than Dot ACM's Programing Contest archive USACO problems ITA Software's puzzle page Refactor My Code Ruby Quiz

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  • How would you refactor nested IF Statements?

    - by saunderl
    I was cruising around the programming blogosphere when I happened upon this post about GOTO's: http://giuliozambon.blogspot.com/2010/12/programmers-tabu.html Here the writer talks about how "one must come to the conclusion that there are situations where GOTOs make for more readable and more maintainable code" and then goes on to show an example similar to this: if (Check#1) { CodeBlock#1 if (Check#2) { CodeBlock#2 if (Check#3) { CodeBlock#3 if (Check#4) { CodeBlock#4 if (Check#5) { CodeBlock#5 if (Check#6) { CodeBlock#6 if (Check#7) { CodeBlock#7 } else { rest - of - the - program } } } } } } } The writer then proposes that using GOTO's would make this code much easier to read and maintain. I personally can think of at least 3 different ways to flatten it out and make this code more readable without resorting to flow-breaking GOTO's. Here are my two favorites. 1 - Nested Small Functions. Take each if and its code block and turn it into a function. If the boolean check fails, just return. If it passes, then call the next function in the chain. (Boy, that sounds a lot like recursion, could you do it in a single loop with function pointers?) 2 - Sentinal Variable. To me this is the easyest. Just use a blnContinueProcessing variable and check to see if it is still true in your if check. Then if the check fails, set the variable to false. How many different ways can this type of coding problem be refactored to reduce nesting and increase maintainability?

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  • Which problem(s) do YOU want to see solved?

    - by buu700
    My team and I are meeting tonight to come up with a business plan and some community input would be amazing. I've been mulling over this issue for the past few months and bouncing ideas off of others, and now I'd finally like some input from the community. I have come up with a fair selection of ideas, but most of those amount to either fun projects which could potentially be profitable, or otherwise solid business models that have one or two major hurdles (usually related to resources or legality). For our team meeting tonight, my idea is to take inventory of our available skills, resources, and compelling problems which interest us. The last is where I would greatly appreciate some community input. Hell, even entire business ideas/plans would be appreciated. No matter how big or small your thoughts, any input would be appreciated. We're a team of computer scientists, so our business will be primarily based around software/technology/Web solutions. Among my relevant available resources (entire Internet aside), I have the following: A pretty reliable connection to an SEO company a large production company. A stash of fairly powerful server hardware. A fast network with static IPs. The backend for Hackswipe, which includes credit card payment processing and a Google Voice-based SMS gateway. This work in progress design for something completely unrelated but which is backed by some fairly decent infrastructure. Direct access to the experts in just about any relevant field (on-campus Carnegie Mellon professors). A sexual relationship with the baron of a small nation. For further down the line, some investor relationships. Not likely to be so relevant, but a decent social media presence (Stack Overflow reputation, modship in some major reddits, various tech forums). The source code for Eugene fucking McCabe. Pooled with the other team members, the list of projects we can build off of would be longer (including an Android app). So, what are your thoughts? Crossposted to reddit

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  • Automatically analyze excel files

    - by dole doug
    I have to replicate a manual generation of a large number of excel files. I started to manually track the relations between cells ( files, formulas, etc). I also had a talk with the person which generates those files. For now I have a general understanding about how the excel files are generated, but "devil is in the details". I assume that I can write a script which will generate the hierarchy between cells and files, but this might require the same effort as manually noticing the relations. Also, I'm afraid that I'm not too experienced and my app is more prone to error approach than a manual analyze. How to handle this problem? Do you know about an open source project which analyze the excel files in a recursive mode following the formulas ?

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  • Is "White-Board-Coding" inappropriate during interviews?

    - by Eoin Campbell
    This is a somewhat subjective quesiton but I'd love to hear feedback/opinions from either interviewers/interviewees on the topic. We split our technical part into 4 parts. Write Code, Read & Analyse Code, Design Session & Code on the white board. For the last part what we ask interviewees to do is write a small code snippet (4-5 lines) on the whiteboard and explain as they go through it. Let me be clear the purpose is not to catch people out. We're not looking for perfect syntax. Hell it can even be pseudo-code. but the point is to give them a very simple problem and see if their brain can communicate the solution to us. By simple problems I mean "Reverse a string", "FizzBuzz" etc... EDIT Just with regards the comment about Pseudo-Code. We always ask for an explicit language first. We;re a .NET C# house. we've only said "pseudo-code" where someone has been blanking/really struggling with the code. My question is "Is it innappropriate / unreasonable to expect a programmer to write a code snippet on a whiteboard during an interview ?"

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  • programming manner to solve problem

    - by gcc
    Everyone has style(s)/technique(s) to approach/solve real world problems. This/these technique(s) distinguish(es) us from other people or other programmers. (Actually, I think it make us a wanted/ great programmer/computer science ) To improve, we read a lot of books (ex : programming style, how to solve program, how to approach problem, software and algorithm). Can I learn your technique? In other words, if someone gives you a problem, at first step, what are you doing to solve it? (In all honesty, I want learn in what manner you are looking problem )

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  • My first time in the gambling industry

    - by sfrj
    I am a Java enterprise developer with almost 3 years of professional experience. Soon i am going to have a face to face interview with a company in the gambling industry. I already did successfully a phone screening and now for the personal interview i suppose they will ask me about some kind of white board problem or system design task. I think i am in the right place to ask about this, and would appreciate a lot if someone would give me some tips or share something related to his own experience. The things i am more interested in regarding my interview are: What are the most common challenges for programmers, in this industry? Any idea or suggestion on a white board problem they may ask me? Could you point me to some links where i can find information on the topic or sample problems in this industry?. I personally find this question very interesting not just for me. Also i think, the given answers can help also others in a similar situation. Just what i want to say whit this last comment is: Please avoid, answers like: www.google.com and so on...

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  • How to save during real-time collaboration

    - by dev.e.loper
    I want multiple users to edit same document. Problem I'm facing is when a new user joins, he might see an outdated document. How do I make sure that new users get most recent changes? Some solutions I thought of: Save on every change. I don't like this solution because it will slow things down on UI and put load on db. When new user joins, trigger save on all other clients. After other clients saved, load document. With this there can be inconsistency still. Any other suggestions would be helpful.

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  • Should I be worried if I solve a lot of my problems the same way?

    - by Bryan Harrington
    I really enjoy programming games and puzzle creators/games. I find myself engineering a lot of these problems the same way and ultimately using similar technique to program them that I'm really comfortable with. To give you brief insight, I like to create graphs where nodes are represented with objects. These object hold data such as coordinates, positions and of course references to other neighboring objects. I'll place them all in a data structure and make decisions on this information in a "game loop". While this is a brief example, its not exact in all situations. It's just one way I feel really comfortable with. Is this bad?

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  • Calculating 3d rotation around random axis

    - by mitim
    This is actually a solved problem, but I want to understand why my original method didn't work (hoping someone with more knowledge can explain). (Keep in mind, I've not very experienced in 3d programming, having only played with the very basic for a little bit...nor do I have a lot of mathematical experience in this area). I wanted to animate a point rotating around another point at a random axis, say a 45 degrees along the y axis (think of an electron around a nucleus). I know how to rotate using the transform matrix along the X, Y and Z axis, but not an arbitrary (45 degree) axis. Eventually after some research I found a suggestion: Rotate the point by -45 degrees around the Z so that it is aligned. Then rotate by some increment along the Y axis, then rotate it back +45 degrees for every frame tick. While this certainly worked, I felt that it seemed to be more work then needed (too many method calls, math, etc) and would probably be pretty slow at runtime with many points to deal with. I thought maybe it was possible to combine all the rotation matrixes involve into 1 rotation matrix and use that as a single operation. Something like: [ cos(-45) -sin(-45) 0] [ sin(-45) cos(-45) 0] rotate by -45 along Z [ 0 0 1] multiply by [ cos(2) 0 -sin(2)] [ 0 1 0 ] rotate by 2 degrees (my increment) along Y [ sin(2) 0 cos(2)] then multiply that result by (in that order) [ cos(45) -sin(45) 0] [ sin(45) cos(45) 0] rotate by 45 along Z [ 0 0 1] I get 1 mess of a matrix of numbers (since I was working with unknowns and 2 angles), but I felt like it should work. It did not and I found a solution on wiki using a different matirx, but that is something else. I'm not sure if maybe I made an error in multiplying, but my question is: this is actually a viable way to solve the problem, to take all the separate transformations, combine them via multiplying, then use that or not?

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  • Steps to create a solution for a problem

    - by Mr_Green
    I am a trainee. According to my teacher, he says that to solve a problem we should go with steps to solve it like Create Algorithm (optional) Create a Datatable: By analyzing the problem, create main concepts in those problem as columns and the related issues in the main concept as rows. Create a Flowchart based on the Datatable. (when creating flow chart, think that you are in that situation and design it in your brain) By seeing the Flowchart, solve the problem. These steps should always consider by a programmer if he/she wants to become a Software designer (not programmer). Because the above approach gives an efficient way of finding solution to a problem even the problem is small. According to him, this way of approach also works in real time scenario's. My question is: Is this really an efficient way? please share also your thoughts. Keeping beside my question I just want to share some thoughts of my teacher with you who is a good mentor for me.

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  • algorithm for project euler problem no 18

    - by Valentino Ru
    Problem number 18 from Project Euler's site is as follows: By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23. 3 7 4 2 4 6 8 5 9 3 That is, 3 + 7 + 4 + 9 = 23. Find the maximum total from top to bottom of the triangle below: 75 95 64 17 47 82 18 35 87 10 20 04 82 47 65 19 01 23 75 03 34 88 02 77 73 07 63 67 99 65 04 28 06 16 70 92 41 41 26 56 83 40 80 70 33 41 48 72 33 47 32 37 16 94 29 53 71 44 65 25 43 91 52 97 51 14 70 11 33 28 77 73 17 78 39 68 17 57 91 71 52 38 17 14 91 43 58 50 27 29 48 63 66 04 68 89 53 67 30 73 16 69 87 40 31 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o) The formulation of this problems does not make clear if the "Traversor" is greedy, meaning that he always choosed the child with be higher value the maximum of every single walkthrough is asked The NOTE says, that it is possible to solve this problem by trying every route. This means to me, that is is also possible without! This leads to my actual question: Assumed that not the greedy one is the max, is there any algorithm that finds the max walkthrough value without trying every route and that doesn't act like the greedy algorithm? I implemented an algorithm in Java, putting the values first in a node structure, then applying the greedy algorithm. The result, however, is cosidered as wrong by Project Euler. sum = 0; void findWay(Node node){ sum += node.value; if(node.nodeLeft != null && node.nodeRight != null){ if(node.nodeLeft.value > node.nodeRight.value){ findWay(node.nodeLeft); }else{ findWay(node.nodeRight); } } }

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  • How to stop getting too focused on a train of thought when programming?

    - by LDM91
    I often find myself getting too focused on a train of thought when programming, which results in me having what I guess could be described as "tunnel vision". As a result of this I miss important details/clues, which means I waste a fair amount of time before finally deciding the path I'm taking to solve the task is wrong. Afterwards, I take a step back which almost always results in me discovering what I've missed in a lot less time.. It's becoming really frustrating as it feels like I'm wasting a lot of time and effort, so I was wondering if anyone else had experienced similar issues, and had some suggestions to stop going down dead ends and programming "blindly" as it were!

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  • Genetic Algorithm new generation exponentially increasing

    - by Rdz
    I'm programming Genetic Algorithm in C++ and after searching all kind of ways of doing GA'a operators (selection, crossover, mutation) I came up with a doubt. Let's say I have an initial population of 500. My selection will consist in getting the top 20% of 500(based on best fitness). So I get 100 individuals to mate. When I do the crossover I'll get 2 children where both together have 50% of surviving. So far so good. I start the mutation, and everything's ok.. Now when I start choosing the Next generation, I see that I have a big number of children (in this case, 4950 if you wanna know). Now the thing is, every time I run GA, if I send all the children to the next generation, the number of individuals per generation will increase exponentially. So there must be a way of choosing the children to fulfill a new generation without getting out of this range of the initial population. What I'm asking here is if there is anyway of choosing the children to fill the new generations OR should I choose somehow (and maybe reduce) the parents to mate so I don't get so many children in the end. Thanks :)

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  • How do you properly word a Google search when you don't even have a solution in mind? [closed]

    - by Bruno Romaszkiewicz
    So, I'm stuck on a problem, looking for a solution, my rubber duck can't help me, my co-workers can't help me. Next natural step is research, right? Google can help me, He always can. Or so I'm told. My problem is, I never found much use for Google when looking for a programming solution, it's very useful for finding how to implement one, but when you don't even know where to start, how do you properly word a Google search? Is there any other option?

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  • How to avoid jumping to a solution when under pressure? [closed]

    - by GlenPeterson
    When under a particularly strict programming deadline (like an hour), if I panic at all, my tendency is to jump into coding without a real plan and hope I figure it out as I go along. Given enough time, this can work, but in an interview it's been pretty unsuccessful, if not downright counter-productive. I'm not always comfortable sitting there thinking while the clock ticks away. Is there a checklist or are there techniques to recognize when you understand the problem well enough to start coding? Maybe don't touch the keyboard for the first 5-10 minutes of the problem? At what point do you give up and code a brute-force solution with the hope of reasoning out a better solution later? When is it most productive to think and design more vs. code some experiments to and figure out the design later? Here is a list of techniques for taking a math test and another for taking an oral exam. Is there is a similar list of techniques for handling a programming problem under pressure? ANSWERS: I think this is a valid answer: How To Solve It. I found the link as an answer to Steps to solve or approach towards a solution. There were also some really good tips at Is thinking out loud during an interview really the best strategy?. A great and concise argument for TDD is the first answer to TDD Writing code vs Figuring out the answer to a problem?. My question may be a near-duplicate of that one.

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