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  • Removing the obstacle that yields the best path from a map after A* traversal

    - by David Titarenco
    I traverse a 16x16 maze using my own A* implementation. This is exactly what my program does: http://www.screenjelly.com/watch/fDQh98zMP0c?showTab=share All is well. However, after the traversal, I would like to find out what wall would give me the best alternative path. Apart from removing every block and re-running A* on the maze, what's a clever solution? I was thinking give every wall node (ignored by A*), a tentative F-value, and change the node structure to also have a n-sized list of node *tentative_parent where n is the number of walls in the maze. Could this be viable?

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  • Implementing PageRank using MapReduce

    - by Nick D.
    Hello, I'm trying to get my head around an issue with the theory of implementing the PageRank with MapReduce. I have the following simple scenario with three nodes: A B C. The adjacency matrix is here: A { B, C } B { A } The PageRank for B for example is equal to: (1-d)/N + d ( PR(A) / C(A) ) N = number of incoming links to B PR(A) = PageRank of incoming link A C(A) = number of outgoing links from page A I am fine with all the schematics and how the mapper and reducer would work but I cannot get my head around how at the time of calculation by the reducer, C(A) would be known. How will the reducer, when calculating the PageRank of B by aggregating the incoming links to B will know the number of outgoing links from each page. Does this require a lookup in some external data source?

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  • Modeling distribution of performance measurements

    - by peterchen
    How would you mathematically model the distribution of repeated real life performance measurements - "Real life" meaning you are not just looping over the code in question, but it is just a short snippet within a large application running in a typical user scenario? My experience shows that you usually have a peak around the average execution time that can be modeled adequately with a Gaussian distribution. In addition, there's a "long tail" containing outliers - often with a multiple of the average time. (The behavior is understandable considering the factors contributing to first execution penalty). My goal is to model aggregate values that reasonably reflect this, and can be calculated from aggregate values (like for the Gaussian, calculate mu and sigma from N, sum of values and sum of squares). In other terms, number of repetitions is unlimited, but memory and calculation requirements should be minimized. A normal Gaussian distribution can't model the long tail appropriately and will have the average biased strongly even by a very small percentage of outliers. I am looking for ideas, especially if this has been attempted/analysed before. I've checked various distributions models, and I think I could work out something, but my statistics is rusty and I might end up with an overblown solution. Oh, a complete shrink-wrapped solution would be fine, too ;) Other aspects / ideas: Sometimes you get "two humps" distributions, which would be acceptable in my scenario with a single mu/sigma covering both, but ideally would be identified separately. Extrapolating this, another approach would be a "floating probability density calculation" that uses only a limited buffer and adjusts automatically to the range (due to the long tail, bins may not be spaced evenly) - haven't found anything, but with some assumptions about the distribution it should be possible in principle. Why (since it was asked) - For a complex process we need to make guarantees such as "only 0.1% of runs exceed a limit of 3 seconds, and the average processing time is 2.8 seconds". The performance of an isolated piece of code can be very different from a normal run-time environment involving varying levels of disk and network access, background services, scheduled events that occur within a day, etc. This can be solved trivially by accumulating all data. However, to accumulate this data in production, the data produced needs to be limited. For analysis of isolated pieces of code, a gaussian deviation plus first run penalty is ok. That doesn't work anymore for the distributions found above. [edit] I've already got very good answers (and finally - maybe - some time to work on this). I'm starting a bounty to look for more input / ideas.

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  • Interview question: Develop an application that can display trail period expires after 30 days witho

    - by Algorist
    Hi, I saw this question in a forum about how an application can be developed that can keep track of the installation date and show trail period expired after 30 days of usage. The only constraint is not to use the external storage of any kind. Question: How to achieve this? Thanks Bala --Edit I think its easy to figure out the place to insert a question work. Anyway, I will write the question clearly. "external storage" means don't use any kind of storage like file, registry, network or anything. You only have your program.

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  • Need help with dynamic programming problem

    - by John Retallack
    I have the following problem : I am given a tree with N apples, for each apple I am given it's weight and height,I can pick apples up to a given height H,each time I pick an apple the height of every apple is increased with U(also given).I have to find out the maximum weight of apples I can pick. e.g: N=4 H=100 U=10 (height-eight) apple1: 91 10 apple2: 82 30 apple3: 93 5 apple4: 94 15 The answer is 45 : I first pick the apple with the weight of 15 then the one with the weight of 30. I would like to know if someone here could help me with giving me an hint on how I should approach this problem. Thank you.

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  • PHP: Script for generating Crossword game?

    - by Prashant
    I need an script for generating crossword game. I have a list of 8 words for which I wnat to generate a crossword game, let's say for 15 column and 15 row. I am not getting the concept of this problem. How to generate this using PHP ?? Can anyone tell me how to do that ??

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  • Visualization of Nelder-Mead algorithm in gnuplot

    - by gorczas
    Hi, does anyone know how I can achieve drawing triangle on level sets of some 3d function (something like on this image in gnuplot? When I tried doing this after reading some tutorials: gnuplot> set border 15 front linetype -1 linewidth 1.000 gnuplot> set logscale z 10 gnuplot> set view map gnuplot> set isosamples 60, 60 gnuplot> unset surface gnuplot> set contour base gnuplot> unset clabel gnuplot> set style data lines gnuplot> set ticslevel 0 gnuplot> set noztics gnuplot> set title "Trwa symulacja" gnuplot> set xlabel "x" gnuplot> set xrange [ * : * ] noreverse nowriteback gnuplot> set ylabel "y" gnuplot> set zlabel "" gnuplot> set yrange [ * : * ] noreverse nowriteback gnuplot> set zrange [ * : * ] noreverse nowriteback gnuplot> splot [-10.5:10.5] [-10.5:10.5] x**2 +y**2 with lines lc rgb "#000000" notitle,\ >'-' with lines notitle input data ('e' ends) > 5.39703780733842 0.424994542694183 29.3086374551602 input data ('e' ends) > -4.80045950473308 -8.66307635892326 98.0933034571172 input data ('e' ends) > -3.56740563691939 3.31903046267993 23.7423461905216 input data ('e' ends) > 5.39703780733842 0.424994542694183 29.3086374551602 input data ('e' ends) > e But I'm still getting warning: "Cannot contour non grid data. Please use "set dgrid3d".".

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  • Grouping consecutive identical items: IEnumerable<T> to IEnumerable<IEnumerable<T>>

    - by Romain Verdier
    I've got an interresting problem: Given an IEnumerable<string>, is it possible to yield a sequence of IEnumerable<string> that groups identical adjacent strings in one pass? Let me explain. Considering the following IEnumerable<string> (pseudo representation): {"a","b","b","b","c","c","d"} How to get an IEnumerable<IEnumerable<string>> that would yield something of the form: { // IEnumerable<IEnumerable<string>> {"a"}, // IEnumerable<string> {"a","b","b"}, // IEnumerable<string> {"c","c"}, // IEnumerable<string> {"d"} // IEnumerable<string> } The method prototype would be: public IEnumerable<IEnumerable<string>> Group(IEnumerable<string> items) { // todo } Important notes : Only one iteration over the original sequence No intermediary collections allocations (we can assume millions of strings in the original sequence, and millions consecutives identicals strings in each group) Keeping enumerators and defered execution behavior Is it possible, and how would you write it?

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  • shortest digest of a string

    - by meta
    [Description] Given a string of char type, find a shortest digest, which is defined as: a shortest sub-string which contains all the characters in the original string. [Example] A = "aaabedacd" B = "bedac" is the answer. [My solution] Define an integer table with 256 elements, which is used to record the occurring times for each kind of character in the current sub-string. Scan the whole string, statistic the total kinds of character in the given string by using the above table. Use two pointers, start, end, which are initially pointing to the start and (start + 1) of the given string. The current kinds of character is 1. Expand sub-string[start, end) at the end until it contains all kinds of character. Update the shortest digest if possible. Contract sub-string[start, end] at the start by one character each time, try to restore its digest property if necessary by step 4. The time cost is O(n), and the extra space cost is constant. Any better solution without extra space?

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  • Permutation algorithm without recursion? Java

    - by Andreas Hornig
    Hi, I would like to get all combination of a number without any repetation. Like 0.1.2, 0.2.1, 1.2.0, 1.0.2, 2.0.1, 2.1.0. I tried to find an easy scheme but couldn't find so I drawed a graph/tree for it and this screams to use recursion. But I would like to do it without, if this is possible. So could anyone please help me how to do that? Thank you in advance, Andreas

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  • How to find the longest contiguous subsequence whose reverse is also a subsequence

    - by iecut
    Suppose I have a sequence x1,x2,x3.....xn, and I want to find the longest contiguous subsequence xi,xi+1,xi+2......xi+k, whose reverse is also a subsequence of the given sequence. And if there are multiple such subsequences, then I also have to find the first. ex:- consider the sequences: abcdefgedcg here i=3 and k=2 aabcdddd here i=5, k=3 I tried looking at the original longest common subsequence problem, but that is used to compare the two sequences to find the longest common subsequence.... but here is only one sequence from which we have to find the subsequences. Please let me know what is the best way to approach this problem, to find the optimal solution.

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  • Optimizing multiple dispatch notification algorithm in C#?

    - by Robert Fraser
    Sorry about the title, I couldn't think of a better way to describe the problem. Basically, I'm trying to implement a collision system in a game. I want to be able to register a "collision handler" that handles any collision of two objects (given in either order) that can be cast to particular types. So if Player : Ship : Entity and Laser : Particle : Entity, and handlers for (Ship, Particle) and (Laser, Entity) are registered than for a collision of (Laser, Player), both handlers should be notified, with the arguments in the correct order, and a collision of (Laser, Laser) should notify only the second handler. A code snippet says a thousand words, so here's what I'm doing right now (naieve method): public IObservable<Collision<T1, T2>> onCollisionsOf<T1, T2>() where T1 : Entity where T2 : Entity { Type t1 = typeof(T1); Type t2 = typeof(T2); Subject<Collision<T1, T2>> obs = new Subject<Collision<T1, T2>>(); _onCollisionInternal += delegate(Entity obj1, Entity obj2) { if (t1.IsAssignableFrom(obj1.GetType()) && t2.IsAssignableFrom(obj2.GetType())) obs.OnNext(new Collision<T1, T2>((T1) obj1, (T2) obj2)); else if (t1.IsAssignableFrom(obj2.GetType()) && t2.IsAssignableFrom(obj1.GetType())) obs.OnNext(new Collision<T1, T2>((T1) obj2, (T2) obj1)); }; return obs; } However, this method is quite slow (measurable; I lost ~2 FPS after implementing this), so I'm looking for a way to shave a couple cycles/allocation off this. I thought about (as in, spent an hour implementing then slammed my head against a wall for being such an idiot) a method that put the types in an order based on their hash code, then put them into a dictionary, with each entry being a linked list of handlers for pairs of that type with a boolean indication whether the handler wanted the order of arguments reversed. Unfortunately, this doesn't work for derived types, since if a derived type is passed in, it won't notify a subscriber for the base type. Can anyone think of a way better than checking every type pair (twice) to see if it matches? Thanks, Robert

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  • Fastest way to calculate an X-bit bitmask?

    - by Virtlink
    I have been trying to solve this problem for a while, but couldn't with just integer arithmetic and bitwise operators. However, I think its possible and it should be fairly easy. What am I missing? The problem: to get an integer value of arbitrary length (this is not relevant to the problem) with it's X least significant bits sets to 1 and the rest to 0. For example, given the number 31, I need to get an integer value which equals 0x7FFFFFFF (31 least significant bits are 1 and the rest zeros). Of course, using a loop OR-ing a shifted 1 to an integer X times will do the job. But that's not the solution I'm looking for. It should be more in the direction of (X << Y - 1), thus using no loops.

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  • Chess algorithm

    - by Ockonal
    Hi guys, I want to create chess application without AI. I just need in checking available ways for chosen chess-object and checkmate for the king. What is the best way to implement this?

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  • Sparse O(1) array with indices being consecutive products

    - by Kos
    Hello, I'd like to pre-calculate an array of values of some unary function f. I know that I'll only need the values for f(x) where x is of the form of a*b, where both a and b are integers in range 0..N. The obvious time-optimized choice is just to make an array of size N*N and just pre-calculate just the elements which I'm going to read later. For f(a*b), I'd just check and set tab[a*b]. This is the fastest method possible - however, this is going to take a lot of space as there are lots of indices in this array (starting with N+1) which will never by touched. Another solution is to make a simple tree map... but this slows down the lookup itself very heavily by introducing lots of branches. No. I wonder - is there any solution to make such an array less sparse and smaller, but still quick branchless O(1) in lookup?

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  • How to use Boost 1.41.0 graph layout algorithmes

    - by daniil-k
    Hi I have problem using boost graph layout algorithmes. boost verision 1_41_0 mingw g++ 4.4.0. So there are issues I have encountered Can you suggest me with them? The function fruchterman_reingold_force_directed_layout isn't compiled. The kamada_kawai_spring_layout compiled but program crashed. Boost documentation to layout algorithms is wrong, sample to fruchterman_reingold_force_directed_layout isn't compiled. This is my example. To use function just uncomment one. String 60, 61, 63. #include <boost/config.hpp> #include <boost/graph/adjacency_list.hpp> #include <boost/graph/graph_utility.hpp> #include <boost/graph/simple_point.hpp> #include <boost/property_map/property_map.hpp> #include <boost/graph/circle_layout.hpp> #include <boost/graph/fruchterman_reingold.hpp> #include <boost/graph/kamada_kawai_spring_layout.hpp> #include <iostream> //typedef boost::square_topology<>::point_difference_type Point; typedef boost::square_topology<>::point_type Point; struct VertexProperties { std::size_t index; Point point; }; struct EdgeProperty { EdgeProperty(const std::size_t &w):weight(w) {} double weight; }; typedef boost::adjacency_list<boost::listS, boost::listS, boost::undirectedS, VertexProperties, EdgeProperty > Graph; typedef boost::property_map<Graph, std::size_t VertexProperties::*>::type VertexIndexPropertyMap; typedef boost::property_map<Graph, Point VertexProperties::*>::type PositionMap; typedef boost::property_map<Graph, double EdgeProperty::*>::type WeightPropertyMap; typedef boost::graph_traits<Graph>::vertex_descriptor VirtexDescriptor; int main() { Graph graph; VertexIndexPropertyMap vertexIdPropertyMap = boost::get(&VertexProperties::index, graph); for (int i = 0; i < 3; ++i) { VirtexDescriptor vd = boost::add_vertex(graph); vertexIdPropertyMap[vd] = i + 2; } boost::add_edge(boost::vertex(1, graph), boost::vertex(0, graph), EdgeProperty(5), graph); boost::add_edge(boost::vertex(2, graph), boost::vertex(0, graph), EdgeProperty(5), graph); std::cout << "Vertices\n"; boost::print_vertices(graph, vertexIdPropertyMap); std::cout << "Edges\n"; boost::print_edges(graph, vertexIdPropertyMap); PositionMap positionMap = boost::get(&VertexProperties::point, graph); WeightPropertyMap weightPropertyMap = boost::get(&EdgeProperty::weight, graph); boost::circle_graph_layout(graph, positionMap, 100); // boost::fruchterman_reingold_force_directed_layout(graph, positionMap, boost::square_topology<>()); boost::kamada_kawai_spring_layout(graph, positionMap, weightPropertyMap, boost::square_topology<>(), boost::side_length<double>(10), boost::layout_tolerance<>(), 1, vertexIdPropertyMap); std::cout << "Coordinates\n"; boost::graph_traits<Graph>::vertex_iterator i, end; for (boost::tie(i, end) = boost::vertices(graph); i != end; ++i) { std::cout << "ID: (" << vertexIdPropertyMap[*i] << ") x: " << positionMap[*i][0] << " y: " << positionMap[*i][1] << "\n"; } return 0; }

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  • fast sphere-grid intersection

    - by Mat
    hi! given a 3D grid, a 3d point as sphere center and a radius, i'd like to quickly calculate all cells contained or intersected by the sphere. Currently i take the the (gridaligned) boundingbox of the sphere and calculate the two cells for the min anx max point of this boundingbox. then, for each cell between those two cells, i do a box-sphere intersection test. would be great if there was something more efficient thanks!

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  • calculating the potential effect of inaccurate triangle vertex positions on the triangle edge lenght

    - by stingrey
    i'm not sure how to solve the following problem: i have a triangle with each of the three known vertex positions A,B,C being inaccurate, meaning they can each deviate up to certain known radii rA, rB, rC into arbitrary directions. given such a triangle, i want to calculate how much the difference of two specific edge lengths (for instance the difference between lengths of edge a and edge b) of the triangle may change in the worst case. is there any elegant mathematical solution to this problem? the naive way i thought of is calculating all 360^3 angle combinations and measuring the edge differences for each case, which is a rather high overhead.

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  • Permutatation algorithm without recursion? Java

    - by Andreas Hornig
    Hi, I would like to get all combination of a number without any repetation. Like 0.1.2, 0.2.1, 1.2.0, 1.0.2, 2.0.1, 2.1.0. I tried to find an easy scheme but couldn't find so I drawed a graph/tree for it and this screams to use recursion. But I would like to do it without, if this is possible. So could anyone please help mw how to do that? Thank you in advance, Andreas

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  • Latent Dirichlet Allocation, pitfalls, tips and programs

    - by Gregg Lind
    I'm experimenting with Latent Dirichlet Allocation for topic disambiguation and assignment, and I'm looking for advice. Which program is the "best", where best is some combination of easiest to use, best prior estimation, fast How do I incorporate my intuitions about topicality. Let's say I think I know that some items in the corpus are really in the same category, like all articles by the same author. Can I add that into the analysis? Any unexpected pitfalls or tips I should know before embarking? I'd prefer is there are R or Python front ends for whatever program, but I expect (and accept) that I'll be dealing with C.

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  • What is validating a binary search tree?

    - by dotnetdev
    I read on here of an exercise in interviews known as validating a binary search tree. How exactly does this work? What would one be looking for in validating a binary search tree? I have written a basic search tree, but never heard of this concept. Thanks

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  • Maximum bipartite graph (1,n) "matching"

    - by Imre Kelényi
    I have a bipartite graph. I am looking for a maximum (1,n) "matching", which means that each vertex from partitation A has n associated vertices from partition B. The following figure shows a maximum (1,3) matching in a graph. Edges selected for the matching are red and unselected edges are black. This differs from the standard bipartite matching problem where each vertex is associate with only one other vertex, which could be called (1,1) matching with this notation. If the matching cardinality (n) is not enforced but is an upper bound (vertices from A can have 0 < x <= n associated vertices from B), then the maximum matching can be found easily by transforming the graph to a flow network and finding the max flow. However, this does not guarantee that the maximum number of vertices from A will have n associated pairs from B.

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