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  • Dot Game and Dynamic Programming

    - by Albert Diego
    I'm trying to solve a variant of the dot game with dynamic programming. The regular dot game is played with a line of dots. Each player takes either one or two dots at their respective end of the line and the person who is left with no dots to take wins. In this version of the game, each dot has a different value. Each player takes alternate turns and takes either dot at either end of the line. I want to come up with a way to use dynamic programming to find the max amount that the first player is guaranteed to win. I'm having problems grasping my head around this and trying to write a recurrence for the solution. Any help is appreciated, thanks!

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  • Finding the maximum weight subsequence of an array of positive integers?

    - by BeeBand
    I'm tring to find the maximum weight subsequence of an array of positive integers - the catch is that no adjacent members are allowed in the final subsequence. The exact same question was asked here, and a recursive solution was given by MarkusQ. He provides an explanation, but can anyone help me understand how he has expanded the function? How does this solution take into consideration non-adjacent members?

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  • What is the optimum way to select the most dissimilar individuals from a population?

    - by Aaron D
    I have tried to use k-means clustering to select the most diverse markers in my population, for example, if we want to select 100 lines I cluster the whole population to 100 clusters then select the closest marker to the centroid from each cluster. The problem with my solution is it takes too much time (probably my function needs optimization), especially when the number of markers exceeds 100000. So, I will appreciate it so much if anyone can show me a new way to select markers that maximize diversity in my population and/or help me optimize my function to make it work faster. Thank you # example: library(BLR) data(wheat) dim(X) mdf<-mostdiff(t(X), 100,1,nstart=1000) Here is the mostdiff function that i used: mostdiff <- function(markers, nClust, nMrkPerClust, nstart=1000) { transposedMarkers <- as.array(markers) mrkClust <- kmeans(transposedMarkers, nClust, nstart=nstart) save(mrkClust, file="markerCluster.Rdata") # within clusters, pick the markers that are closest to the cluster centroid # turn the vector of which markers belong to which clusters into a list nClust long # each element of the list is a vector of the markers in that cluster clustersToList <- function(nClust, clusters) { vecOfCluster <- function(whichClust, clusters) { return(which(whichClust == clusters)) } return(apply(as.array(1:nClust), 1, vecOfCluster, clusters)) } pickCloseToCenter <- function(vecOfCluster, whichClust, transposedMarkers, centers, pickHowMany) { clustSize <- length(vecOfCluster) # if there are fewer than three markers, the center is equally distant from all so don't bother if (clustSize < 3) return(vecOfCluster[1:min(pickHowMany, clustSize)]) # figure out the distance (squared) between each marker in the cluster and the cluster center distToCenter <- function(marker, center){ diff <- center - marker return(sum(diff*diff)) } dists <- apply(transposedMarkers[vecOfCluster,], 1, distToCenter, center=centers[whichClust,]) return(vecOfCluster[order(dists)[1:min(pickHowMany, clustSize)]]) } }

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  • Five unique, random numbers from a subset

    - by tau
    I know similar questions come up a lot and there's probably no definitive answer, but I want to generate five unique random numbers from a subset of numbers that is potentially infinite (maybe 0-20, or 0-1,000,000). The only catch is that I don't want to have to run while loops or fill an array. My current method is to simply generate five random numbers from a subset minus the last five numbers. If any of the numbers match each other, then they go to their respective place at the end of the subset. So if the fourth number matches any other number, it will bet set to the 4th from the last number. Does anyone have a method that is "random enough" and doesn't involve costly loops or arrays? Please keep in mind this a curiosity, not some mission-critical problem. I would appreciate it if everyone didn't post "why are you having this problem?" answers. I am just looking for ideas. Thanks a lot!

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  • Where can I find soft-multiply and divide algorithms?

    - by srking
    I'm working on a micro-controller without hardware multiply and divide. I need to cook up software algorithms for these basic operations that are a nice balance of compact size and efficiency. My C compiler port will employ these algos, not the the C developers themselves. My google-fu is so far turning up mostly noise on this topic. Can anyone point me to something informative? I can use add/sub and shift instructions. Table lookup based algos might also work for me, but I'm a bit worried about cramming so much into the compiler's back-end...um, so to speak. Thanks!

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  • How can I generate an "unlimited" world?

    - by snowlord
    I would like to create a game with an endless (in reality an extremely large) world in which the player can move about. Whether or not I will ever get around to implement the game is one matter, but I find the idea interesting and would like some input on how to do it. The point is to have a world where all data is generated randomly on-demand, but in a deterministic way. Currently I focus on a large 2D map from which it should be possible to display any part without knowledge about the surrounding parts. I have implemented a prototype by writing a function that gives a random-looking, but deterministic, integer given the x and y of a pixel on the map (see my recent question about this function). Using this function I populate the map with "random" values, and then I smooth the map using a simple filter based on the surrounding pixels. This makes the map dependent on a few pixels outside its edge, but that's not a big problem. The final result is something that at least looks like a map (especially with a good altitude color map). Given this, one could maybe first generate a coarser map which is used to generate bigger differences in altitude to create mountain ranges and seas. Anyway, that was my idea, but I am sure that there exist ways to do this already and I also believe that given the specification, many of you can come up with better ideas. EDIT: Forgot the link to my question.

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  • How to compute palindrome from a stream of characters in sub-linear space/time?

    - by wrick
    I don't even know if a solution exists or not. Here is the problem in detail. You are a program that is accepting an infinitely long stream of characters (for simplicity you can assume characters are either 1 or 0). At any point, I can stop the stream (let's say after N characters were passed through) and ask you if the string received so far is a palindrome or not. How can you do this using less sub-linear space and/or time.

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  • How to find out top links in a website?

    - by Anil
    I want to know what are the best links in a site are? It may be pagerank wise or popularity wise. For example http://www.pragprog.com is a site. I want to find out what are the most relevant links this site has. The links should not be external pointing links. It should be of the same site. Do google or any similar site can tell such information?

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  • Is my program taking too much time to execute?

    - by Conrad C
    I wanted to solve a question from project euleur about finding the largest prime number of a big number. I run my code on a virtual machine on Visual studio 2012, and the code seems froze. When I step into the loop, the code works well, but when I execute it, the console is always there. It is as if the program is still running. Could it be that the program takes time to execute? My Code static void Main(string[] args) { long number = 5; for (long i = 1; i < 600851475143; i++) { if (i % 2 != 0 && i % 1 == 0 && i % i == 0) number = i; } }

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  • Python - Compress Ascii String

    - by n0idea
    I'm looking for a way to compress an ascii-based string, any help? I need also need to decompress it. I tried zlib but with no help. What can I do to compress the string into lesser length? code: def compress(request): if request.POST: data = request.POST.get('input') if is_ascii(data): result = zlib.compress(data) return render_to_response('index.html', {'result': result, 'input':data}, context_instance = RequestContext(request)) else: result = "Error, the string is not ascii-based" return render_to_response('index.html', {'result':result}, context_instance = RequestContext(request)) else: return render_to_response('index.html', {}, context_instance = RequestContext(request))

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  • Genetic programming in c++, library suggestions?

    - by shuttle87
    I'm looking to add some genetic algorithms to an Operations research project I have been involved in. Currently we have a program that aids in optimizing some scheduling and we want to add in some heuristics in the form of genetic algorithms. Are there any good libraries for generic genetic programming/algorithms in c++? Or would you recommend I just code my own? I should add that while I am not new to c++ I am fairly new to doing this sort of mathematical optimization work in c++ as the group I worked with previously had tended to use a proprietary optimization package. We have a fitness function that is fairly computationally intensive to evaluate and we have a cluster to run this on so parallelized code is highly desirable. So is c++ a good language for this? If not please recommend some other ones as I am willing to learn another language if it makes life easier. thanks!

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  • hi question about mathematics

    - by davit-datuashvili
    hi i have one question i know site mathoverflow.com and have posted question but unfortunately no one give me answer if i post here can anybody help me? it is not homework because i know somebody will say it is homework what u have tried but this is not so i dont know how solve please if it is possible i will post here ok?

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  • Constructing colours for maximum contrast

    - by Martin
    I want to draw some items on screen, each item is in one of N sets. The number of sets changes all the time, so I need to calculate N different colours which are as different as possible (to make it easy to identify what is in which set). So, for example with N = 2 my results would be black and white. With three I guess I would get all red, all green, all blue. For all four, it's less obvious what the correct answer is, and this is where I'm having trouble.

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  • Is there a good radixsort-implementation for floats in C#

    - by CommuSoft
    I have a datastructure with a field of the float-type. A collection of these structures needs to be sorted by the value of the float. Is there a radix-sort implementation for this. If there isn't, is there a fast way to access the exponent, the sign and the mantissa. Because if you sort the floats first on mantissa, exponent, and on exponent the last time. You sort floats in O(n).

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  • Reverse regular expressions to generate data

    - by Anton Gogolev
    In one of the StackOverflow Podcasts (the one where guys were discussing data generation for testing DBs -- either #11 or #12), Jeff mentioned something like "reverse regular expressions", which are used exactly for that purpose: given a regex, produce a string which will eventually match said regex. What is the correct term for this whole concept? Is this a well-known concept?

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  • Effecient data structure design

    - by Sway
    Hi there, I need to match a series of user inputed words against a large dictionary of words (to ensure the entered value exists). So if the user entered: "orange" it should match an entry "orange' in the dictionary. Now the catch is that the user can also enter a wildcard or series of wildcard characters like say "or__ge" which would also match "orange" The key requirements are: * this should be as fast as possible. * use the smallest amount of memory to achieve it. If the size of the word list was small I could use a string containing all the words and use regular expressions. however given that the word list could contain potentially hundreds of thousands of enteries I'm assuming this wouldn't work. So is some sort of 'tree' be the way to go for this...? Any thoughts or suggestions on this would be totally appreciated! Thanks in advance, Matt

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  • Classical task-scheduling assignment

    - by Bruno
    I am working on a flight scheduling app (disclaimer: it's for a college project, so no code answers, please). Please read this question w/ a quantum of attention before answering as it has a lot of peculiarities :( First, some terminology issues: You have planes and flights, and you have to pair them up. For simplicity's sake, we'll assume that a plane is free as soon as the flight using it prior lands. Flights are seen as tasks: They have a duration They have dependencies They have an expected date/time for beginning Planes can be seen as resources to be used by tasks (or flights, in our terminology). Flights have a specific type of plane needed. e.g. flight 200 needs a plane of type B. Planes obviously are of one and only one specific type, e.g., Plane Airforce One is of type C. A "project" is the set of all the flights by an airline in a given time period. The functionality required is: Finding the shortest possible duration for a said project The earliest and latest possible start for a task (flight) The critical tasks, with basis on provided data, complete with identifiers of preceding tasks. Automatically pair up flights and planes, so as to get all flights paired up with a plane. (Note: the duration of flights is fixed) Get a Gantt diagram with the projects scheduling, in which all flights begin as early as possible, showing all previously referred data graphically (dependencies, time info, etc.) So the questions is: How in the world do I achieve this? Particularly: We are required to use a graph. What do the graph's edges and nodes respectively symbolise? Are we required to discard tasks to achieve the critical tasks set? If you could also recommend some algorithms for us to look up, that'd be great.

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  • Find common nodes from two linked lists using recursion

    - by Dan
    I have to write a method that returns a linked list with all the nodes that are common to two linked lists using recursion, without loops. For example, first list is 2 - 5 - 7 - 10 second list is 2 - 4 - 8 - 10 the list that would be returned is 2 - 10 I am getting nowhere with this.. What I have been think of was to check each value of the first list with each value of the second list recursively but the second list would then be cut by one node everytime and I cannot compare the next value in the first list with the the second list. I hope this makes sense... Can anyone help?

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  • Reverse engineering a bezier curve

    - by Martin
    Given a few sample points on a bézier curve, is it possible to work out the set of possible parameters of the curve? In my specific application there is a limited set of endpoints the curve may have, so I want to generate the set of possible curves, enumerate all of them and pick out all the ones which may end on a valid end point.

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  • Latex: vertical line in lstlistings

    - by Helltone
    I want to have a vertical line for indentation in the lstlisting environment, similar to what one can get in algorithm2e. I tried doing something like the code below, but the the |'s are not contiguous and the result is ugly. \lstset{ ... showtabs=true, tabsize=3, tab=\hfill$|$\hfill, ... }

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  • Find numbers that equals a sum in an array

    - by valli-R
    I want to find the first set of integers in an array X that the sum equals a given number N. For example: X = {5, 13, 24, 9, 3, 3} N = 28 Solution = {13, 9, 3, 3} Here what I have so far : WARNING, I know it uses global and it is bad,that's not the point of the question. <?php function s($index = 0, $total = 0, $solution = '') { global $numbers; global $sum; echo $index; if($total == 28) { echo '<br/>'.$solution.' = '.$sum.'<br/>'; } elseif($index < count($numbers) && $total != 28) { s($index + 1, $total, $solution); s($index + 1, $total + $numbers[$index], $solution.' '.$numbers[$index]); } } $numbers = array(5, 13, 24, 9, 3, 3); $sum = 28; s(); ?> I don't get how I can stop the process when it finds the solution.. I know I am not far from good solution.. Thanks in advance

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