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  • Algorithm for a dice problem

    - by vivekeviv
    I was thinking what should be the best algorithm for finding all the solutions of this puzzle. http://1cup1coffee.com/puzzle/endice/ Could backtracking be the an approach for solving this or can you suggest any other approach? Thanks

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  • An algorithm for pavement usage calculation

    - by student
    Given an area of specific size I need to find out how many pavement stones to use to completely pave the area. Suppose that I have an empty floor of 100 metre squares and stones with 20x10 cm and 30x10 cm sizes. I must pave the area with minimum usage of stones of both sizes. Anyone knows of an algorithm that calculates this? (Sorry if my English is bad) C# is preferred.

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  • Algorithm for deciding price ranges.

    - by Paul Knopf
    I am looking for code that will take a huge list of numbers, and calculate price ranges correctly. There must be some algorithm that will choose the proper ranges, no? I am looking for this code in c#, but any language will do (I can convert). Thanks in advance!

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  • Reducing Integer Fractions Algorithm - Solution Explanation?

    - by Andrew Tomazos - Fathomling
    This is a followup to this problem: Reducing Integer Fractions Algorithm Following is a solution to the problem from a grandmaster: #include <cstdio> #include <algorithm> #include <functional> using namespace std; const int MAXN = 100100; const int MAXP = 10001000; int p[MAXP]; void init() { for (int i = 2; i < MAXP; ++i) { if (p[i] == 0) { for (int j = i; j < MAXP; j += i) { p[j] = i; } } } } void f(int n, vector<int>& a, vector<int>& x) { a.resize(n); vector<int>(MAXP, 0).swap(x); for (int i = 0; i < n; ++i) { scanf("%d", &a[i]); for (int j = a[i]; j > 1; j /= p[j]) { ++x[p[j]]; } } } void g(const vector<int>& v, vector<int> w) { for (int i: v) { for (int j = i; j > 1; j /= p[j]) { if (w[p[j]] > 0) { --w[p[j]]; i /= p[j]; } } printf("%d ", i); } puts(""); } int main() { int n, m; vector<int> a, b, x, y, z; init(); scanf("%d%d", &n, &m); f(n, a, x); f(m, b, y); printf("%d %d\n", n, m); transform(x.begin(), x.end(), y.begin(), insert_iterator<vector<int> >(z, z.end()), [](int a, int b) { return min(a, b); }); g(a, z); g(b, z); return 0; } It isn't clear to me how it works. Can anyone explain it? The equivilance is as follows: a is the numerator vector of length n b is the denominator vector of length m

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  • random, Graphics point ,searching- algorithm, via dual for loop set

    - by LoneXcoder
    hello and thanks for joining me in my journey to the custom made algorithm for "guess where the pixel is" this for Loop set (over Point.X, Point.Y), is formed in consecutive/linear form: //Original\initial Location Point initPoint = new Point(150, 100); // No' of pixels to search left off X , and above Y int preXsrchDepth, preYsrchDepth; // No' of pixels to search to the right of X, And Above Y int postXsrchDepth, postYsrchDepth; preXsrchDepth = 10; // will start search at 10 pixels to the left from original X preYsrchDepth = 10; // will start search at 10 pixels above the original Y postXsrchDepth = 10; // will stop search at 10 pixels to the right from X postYsrchDepth = 10; // will stop search at 10 pixels below Y int StopXsearch = initPoint.X + postXsrchDepth; //stops X Loop itarations at initial pointX + depth requested to serch right of it int StopYsearch = initPoint.Y + postYsrchDepth; //stops Y Loop itarations at initial pointY + depth requested below original location int CountDownX, CountDownY; // Optional not requierd for loop but will reports the count down how many iterations left (unless break; triggerd ..uppon success) Point SearchFromPoint = Point.Empty; //the point will be used for (int StartX = initPoint.X - preXsrchDepth; StartX < StopXsearch; StartX++) { SearchFromPoint.X = StartX; for (int StartY = initPoint.Y - preYsrchDepth; StartY < StpY; StartY++) { CountDownX = (initPoint.X - StartX); CountDownY=(initPoint.Y - StartY); SearchFromPoint.Y = StartY; if (SearchSuccess) { same = true; AAdToAppLog("Search Report For: " + imgName + "Search Completed Successfully On Try " + CountDownX + ":" + CountDownY); break; } } } <-10 ---- -5--- -1 X +1--- +5---- +10 what i would like to do is try a way of instead is have a little more clever approach <+8---+5-- -8 -5 -- +2 +10 X -2 - -10 -8-- -6 ---1- -3 | +8 | -10 Y +1 -6 | | +9 .... I do know there's a wheel already invented in this field (even a full-trailer truck amount of wheels (: ) but as a new programmer, I really wanted to start of with a simple way and also related to my field of interest in my project. can anybody show an idea of his, he learnt along the way to Professionalism in algorithm /programming having tests to do on few approaches (kind'a random cleverness...) will absolutely make the day and perhaps help some others viewing this page in the future to come it will be much easier for me to understand if you could use as much as possible similar naming to variables i used or implenet your code example ...it will be Greatly appreciated if used with my code sample, unless my metod is a realy flavorless. p.s i think that(atleast as human being) the tricky part is when throwing inconsecutive numbers you loose track of what you didn't yet use, how do u take care of this too . thanks allot in advance looking forward to your participation !

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  • Latex: Listing all figures (tables, algorithm) once again at the end of the document

    - by Zlatko
    Hi all, I have been writhing a rather large document with latex. Now I would like to list all the figures / tables / algortihms once again at the end of the file so that I can check if they all look the same. For example, if every algorithm has the same notation. How can I do this? I know about \listofalgorithms and \listoffigures but they only list the names of the algorithms or figures and the pages where they are. Thanks.

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  • Al Zimmermann's Son of Darts

    - by polygenelubricants
    There's about 2 months left in Al Zimmermann's Son of Darts programming contest, and I'd like to improve my standing (currently in the 60s) to something more respectable. I'd like to get some ideas from the great community of stackoverflow on how best to approach this problem. The contest problem is known as the Global Postage Stamp Problem in literatures. I don't have much experience with optimization algorithms (I know of hillclimbing and simulated annealing in concept only from college), and in fact the program that I have right now is basically sheer brute force, which of course isn't feasible for the larger search spaces. Here are some papers on the subject: A Postage Stamp Problem (Alter & Barnett, 1980) Algorithms for Computing the h-Range of the Postage Stamp Problem (Mossige, 1981) A Postage Stamp Problem (Lunnon, 1986) Two New Techniques for Computing Extremal h-bases Ak (Challis, 1992) Any hints and suggestions are welcome. Also, feel free to direct me to the proper site if stackoverflow isn't it.

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  • Performance in backpropagation algorithm

    - by Taban
    I've written a matlab program for standard backpropagation algorithm, it is my homework and I should not use matlab toolbox, so I write the entire code by myself. This link helped me for backpropagation algorithm. I have a data set of 40 random number and initial weights randomly. As output, I want to see a diagram that shows the performance. I used mse and plot function to see performance for 20 epochs but the result is this: I heard that performance should go up through backpropagation, so I want to know is there any problem with my code or this result is normal because local minimums. This is my code: Hidden_node=inputdlg('Enter the number of Hidden nodes'); a=0.5;%initialize learning rate hiddenn=str2num(Hidden_node{1,1}); randn('seed',0); %creating data set s=2; N=10; m=[5 -5 5 5;-5 -5 5 -5]; S = s*eye(2); [l,c] = size(m); x = []; % Creating the training set for i = 1:c x = [x mvnrnd(m(:,i)',S,N)']; end % target value toutput=[ones(1,N) zeros(1,N) ones(1,N) zeros(1,N)]; for epoch=1:20; %number of epochs for kk=1:40; %number of patterns %initial weights of hidden layer for ii=1 : 2; for jj=1 :hiddenn; whidden{ii,jj}=rand(1); end end initial the wights of output layer for ii=1 : hiddenn; woutput{ii,1}=rand(1); end for ii=1:hiddenn; x1=x(1,kk); x2=x(2,kk); w1=whidden{1,ii}; w2=whidden{2,ii}; activation{1,ii}=(x1(1,1)*w1(1,1))+(x2(1,1)*w2(1,1)); end %calculate output of hidden nodes for ii=1:hiddenn; hidden_to_out{1,ii}=logsig(activation{1,ii}); end activation_O{1,1}=0; for jj=1:hiddenn; activation_O{1,1} = activation_O{1,1}+(hidden_to_out{1,jj}*woutput{jj,1}); end %calculate output out{1,1}=logsig(activation_O{1,1}); out_for_plot(1,kk)= out{1,ii}; %calculate error for output node delta_out{1,1}=(toutput(1,kk)-out{1,1}); %update weight of output node for ii=1:hiddenn; woutput{ii,jj}=woutput{ii,jj}+delta_out{1,jj}*hidden_to_out{1,ii}*dlogsig(activation_O{1,jj},logsig(activation_O{1,jj}))*a; end %calculate error of hidden nodes for ii=1:hiddenn; delta_hidden{1,ii}=woutput{ii,1}*delta_out{1,1}; end %update weight of hidden nodes for ii=1:hiddenn; for jj=1:2; whidden{jj,ii}= whidden{jj,ii}+(delta_hidden{1,ii}*dlogsig(activation{1,ii},logsig(activation{1,ii}))*x(jj,kk)*a); end end a=a/(1.1);%decrease learning rate end %calculate performance e=toutput(1,kk)-out_for_plot(1,1); perf(1,epoch)=mse(e); end plot(perf); Thanks a lot.

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  • Allocation algorithm help, using Python.

    - by Az
    Hi there, I've been working on this general allocation algorithm for students. The pseudocode for it (a Python implementation) is: for a student in a dictionary of students: for student's preference in a set of preferences (ordered from 1 to 10): let temp_project be the first preferred project check if temp_project is available if so, allocate it to them and make the project UNavailable to others Quite simply this will try to allocate projects by starting from their most preferred. The way it works, out of a set of say 100 projects, you list 10 you would want to do. So the 10th project wouldn't be the "least preferred overall" but rather the least preferred in their chosen set, which isn't so bad. Obviously if it can't allocate a project, a student just reverts to the base case which is an allocation of None, with a rank of 11. What I'm doing is calculating the allocation "quality" based on a weighted sum of the ranks. So the lower the numbers (i.e. more highly preferred projects), the better the allocation quality (i.e. more students have highly preferred projects). That's basically what I've currently got. Simple and it works. Now I'm working on this algorithm that tries to minimise the allocation weight locally (this pseudocode is a bit messy, sorry). The only reason this will probably work is because my "search space" as it is, isn't particularly large (just a very general, anecdotal observation, mind you). Since the project is only specific to my Department, we have their own limits imposed. So the number of students can't exceed 100 and the number of preferences won't exceed 10. for student in a dictionary/list/whatever of students: where i = 0 take the (i)st student, (i+1)nd student for their ranks: allocate the projects and set local_weighting to be sum(student_i.alloc_proj_rank, student_i+1.alloc_proj_rank) these are the cases: if local_weighting is 2 (i.e. both ranks are 1): then i += 1 and and continue above if local weighting is = N>2 (i.e. one or more ranks are greater than 1): let temp_local_weighting be N: pick student with lowest rank and then move him to his next rank and pick the other student and reallocate his project after this if temp_local_weighting is < N: then allocate those projects to the students move student with lowest rank to the next rank and reallocate other if temp_local_weighting < previous_temp_allocation: let these be the new allocated projects try moving for the lowest rank and reallocate other else: if this weighting => previous_weighting let these be the allocated projects i += 1 and move on for the rest of the students So, questions: This is sort of a modification of simulated annealing, but any sort of comments on this would be appreciated. How would I keep track of which student is (i) and which student is (i+1) If my overall list of students is 100, then the thing would mess up on (i+1) = 101 since there is none. How can I circumvent that? Any immediate flaws that can be spotted? Extra info: My students dictionary is designed as such: students[student_id] = Student(student_id, student_name, alloc_proj, alloc_proj_rank, preferences) where preferences is in the form of a dictionary such that preferences[rank] = {project_id}

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  • image processing algorithm in MATLAB

    - by user261002
    I am trying to reconstruct an algorithm belong to this paper: Decomposition of biospeckle images in temporary spectral bands Here is an explanation of the algorithm: We recorded a sequence of N successive speckle images with a sampling frequency fs. In this way it was possible to observe how a pixel evolves through the N images. That evolution can be treated as a time series and can be processed in the following way: Each signal corresponding to the evolution of every pixel was used as input to a bank of filters. The intensity values were previously divided by their temporal mean value to minimize local differences in reflectivity or illumination of the object. The maximum frequency that can be adequately analyzed is determined by the sampling theorem and s half of sampling frequency fs. The latter is set by the CCD camera, the size of the image, and the frame grabber. The bank of filters is outlined in Fig. 1. In our case, ten 5° order Butterworth11 filters were used, but this number can be varied according to the required discrimination. The bank was implemented in a computer using MATLAB software. We chose the Butter-worth filter because, in addition to its simplicity, it is maximally flat. Other filters, an infinite impulse response, or a finite impulse response could be used. By means of this bank of filters, ten corresponding signals of each filter of each temporary pixel evolution were obtained as output. Average energy Eb in each signal was then calculated: where pb(n) is the intensity of the filtered pixel in the nth image for filter b divided by its mean value and N is the total number of images. In this way, en values of energy for each pixel were obtained, each of hem belonging to one of the frequency bands in Fig. 1. With these values it is possible to build ten images of the active object, each one of which shows how much energy of time-varying speckle there is in a certain frequency band. False color assignment to the gray levels in the results would help in discrimination. and here is my MATLAB code base on that : clear all for i=0:39 str = num2str(i); str1 = strcat(str,'.mat'); load(str1); D{i+1}=A; end new_max = max(max(A)); new_min = min(min(A)); for i=20:180 for j=20:140 ts = []; for k=1:40 ts = [ts D{k}(i,j)]; %%% kth image pixel i,j --- ts is time series end ts = double(ts); temp = mean(ts); ts = ts-temp; ts = ts/temp; N = 5; % filter order W = [0.00001 0.05;0.05 0.1;0.1 0.15;0.15 0.20;0.20 0.25;0.25 0.30;0.30 0.35;0.35 0.40;0.40 0.45;0.45 0.50]; N1 = 5; for ind = 1:10 Wn = W(ind,:); [B,A] = butter(N1,Wn); ts_f(ind,:) = filter(B,A,ts); end for ind=1:10 imag_test1{ind}(i,j) =sum((ts_f(ind,:)./mean(ts_f(ind,:))).^2); end end end for i=1:10 temp_imag = imag_test1{i}(:,:); x=isnan(temp_imag); temp_imag(x)=0; temp_imag=medfilt2(temp_imag); t_max = max(max(temp_imag)); t_min = min(min(temp_imag)); temp_imag = (temp_imag-t_min).*(double(new_max-new_min)/double(t_max-t_min))+double(new_min); imag_test2{i}(:,:) = temp_imag; end for i=1:10 A=imag_test2{i}(:,:); B=A/max(max(A)); B=histeq(B); figure,imshow(B) colorbar end but I am not getting the same result as paper. has anybody has aby idea why? or where I have gone wrong? Refrence Link to the paper

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  • C optimization breaks algorithm

    - by Halpo
    I am programming an algorithm that contains 4 nested for loops. The problem is at at each level a pointer is updated. The innermost loop only uses 1 of the pointers. The algorithm does a complicated count. When I include a debugging statement that logs the combination of the indexes and the results of the count I get the correct answer. When the debugging statement is omitted, the count is incorrect. The program is compiled with the -O3 option on gcc. Why would this happen?

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  • optimized grid for rectangular items

    - by peterchen
    I have N rectangular items with an aspect ratio Aitem (X:Y). I have a rectangular display area with an aspect ratio Aview The items should be arranged in a table-like layout (i.e. r rows, c columns). what is the ideal grid rows x columns, so that individual items are largest? (rows * colums = N, of course - i.e. there may be "unused" grid places). A simple algorithm could iterate over rows = 1..N, calculate the required number of columns, and keep the row/column pair with the largest items. I wonder if there's a non-iterative algorithm, though (e.g. for Aitem = Aview = 1, rows / cols can be approximated by sqrt(N)).

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  • WebSphere Application Server EJB Optimization

    - by Chris Aldrich
    We are working on developing a Java EE based application. Our application is Java 1.5 compatible and will be deployed to WAS ND 6.1.0.21 with EBJ 3.0 and Web Services feature packs. The configuration is currently one cell with two clusters. Each cluster will have two nodes. Our application, or our system, as I should rather say, comes in two or three parts. Part 1: An ear deployed to one cluster that contains 3rd party vendor code combined with customization code. Their code is EJB 2.0 compliant and has a lot of Remote Home interfaces. Part 2: An ear deployed to the same cluster as the first ear. This ear contains EBJ 3's that make calls into the EJB 2's supplied by the vendor and the custom code. These EJB 3's are used by the JSF UI also packaged with the EAR, and some of them are also exposed as web services (JAX-WS 2.0 with SOAP 1.2 compliance) for other clients. Part 3: There may be other services that do not depend on our vendor/custom code app. These services will be EJB 3.0's and web services that are deployed to the other cluster. Per a recommendation from some IBM staff on site here, communication between nodes in a cluster can be EJB RMI. But if we are going across clusters and/or other cells, then the communication should be web services. That said, some of us are wondering about performance and optimizing communication for speed of our applications that will use our web services and EJB's. Right now most EJB's are exposed as remote. (and our vendor set theirs up that way, rather than also exposing local home interfaces). We are wondering if WAS does any optimizations between apps in the same node/cluster node space. If two apps are installed in the same area and they call each other via remote home interface, is WAS smart enough to make it a local home interface call? Are their other optimization techniques? Should we consider them? Should we not? What are the costs/benefits? Here is the question from one of our team members as sent in their email: The question is: Supposing we develop our EJBs as remote EJBs, where our UI controller code is talking to our EXT java services via EJB3...what are our options for performance optimization when both the EJB server and client are running in the same container? As one point of reference, google has given me some oooooold websphere performance tuning documentation from 2000 that explains a tuning configuration you can set to enable Call By Reference for EJB communication when they're in the same application server JVM. It states the following: Because EJBs are inherently location independent, they use a remote programming model. Method parameters and return values are serialized over RMI-IIOP and returned by value. This is the intrinsic RMI "Call By Value" model. WebSphere provides the "No Local Copies" performance optimization for running EJBs and clients (typically servlets) in the same application server JVM. The "No Local Copies" option uses "Call By Reference" and does not create local proxies for called objects when both the client and the remote object are in the same process. Depending on your workload, this can result in a significant overhead savings. Configure "No Local Copies" by adding the following two command line parameters to the application server JVM: * -Djavax.rmi.CORBA.UtilClass=com.ibm.CORBA.iiop.Util * -Dcom.ibm.CORBA.iiop.noLocalCopies=true CAUTION: The "No Local Copies" configuration option improves performance by changing "Call By Value" to "Call By Reference" for clients and EJBs in the same JVM. One side effect of this is that the Java object derived (non-primitive) method parameters can actually be changed by the called enterprise bean. Consider Figure 16a: Also, we will also be using Process Server 6.2 and WESB 6.2 as well in the future. Any ideas? recommendations? Thanks

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  • Effective optimization strategies on modern C++ compilers

    - by user168715
    I'm working on scientific code that is very performance-critical. An initial version of the code has been written and tested, and now, with profiler in hand, it's time to start shaving cycles from the hot spots. It's well-known that some optimizations, e.g. loop unrolling, are handled these days much more effectively by the compiler than by a programmer meddling by hand. Which techniques are still worthwhile? Obviously, I'll run everything I try through a profiler, but if there's conventional wisdom as to what tends to work and what doesn't, it would save me significant time. I know that optimization is very compiler- and architecture- dependent. I'm using Intel's C++ compiler targeting the Core 2 Duo, but I'm also interested in what works well for gcc, or for "any modern compiler." Here are some concrete ideas I'm considering: Is there any benefit to replacing STL containers/algorithms with hand-rolled ones? In particular, my program includes a very large priority queue (currently a std::priority_queue) whose manipulation is taking a lot of total time. Is this something worth looking into, or is the STL implementation already likely the fastest possible? Along similar lines, for std::vectors whose needed sizes are unknown but have a reasonably small upper bound, is it profitable to replace them with statically-allocated arrays? I've found that dynamic memory allocation is often a severe bottleneck, and that eliminating it can lead to significant speedups. As a consequence I'm interesting in the performance tradeoffs of returning large temporary data structures by value vs. returning by pointer vs. passing the result in by reference. Is there a way to reliably determine whether or not the compiler will use RVO for a given method (assuming the caller doesn't need to modify the result, of course)? How cache-aware do compilers tend to be? For example, is it worth looking into reordering nested loops? Given the scientific nature of the program, floating-point numbers are used everywhere. A significant bottleneck in my code used to be conversions from floating point to integers: the compiler would emit code to save the current rounding mode, change it, perform the conversion, then restore the old rounding mode --- even though nothing in the program ever changed the rounding mode! Disabling this behavior significantly sped up my code. Are there any similar floating-point-related gotchas I should be aware of? One consequence of C++ being compiled and linked separately is that the compiler is unable to do what would seem to be very simple optimizations, such as move method calls like strlen() out of the termination conditions of loop. Are there any optimization like this one that I should look out for because they can't be done by the compiler and must be done by hand? On the flip side, are there any techniques I should avoid because they are likely to interfere with the compiler's ability to automatically optimize code? Lastly, to nip certain kinds of answers in the bud: I understand that optimization has a cost in terms of complexity, reliability, and maintainability. For this particular application, increased performance is worth these costs. I understand that the best optimizations are often to improve the high-level algorithms, and this has already been done.

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  • How to document and teach others "optimized beyond recognition" computationally intensive code?

    - by rwong
    Occasionally there is the 1% of code that is computationally intensive enough that needs the heaviest kind of low-level optimization. Examples are video processing, image processing, and all kinds of signal processing, in general. The goals are to document, and to teach the optimization techniques, so that the code does not become unmaintainable and prone to removal by newer developers. (*) (*) Notwithstanding the possibility that the particular optimization is completely useless in some unforeseeable future CPUs, such that the code will be deleted anyway. Considering that software offerings (commercial or open-source) retain their competitive advantage by having the fastest code and making use of the newest CPU architecture, software writers often need to tweak their code to make it run faster while getting the same output for a certain task, whlist tolerating a small amount of rounding errors. Typically, a software writer can keep many versions of a function as a documentation of each optimization / algorithm rewrite that takes place. How does one make these versions available for others to study their optimization techniques?

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  • Good book for THINKING in terms of algorithms?

    - by chrisgoyal
    Before you mark this is a duplicate, let me explain why this is different. Most of the books on algorithms are more of a reference. You basically have a list of algorithms at your disposal. But what happens when you need to create a new algorithm for something? These books don't teach how to think in terms of algorithms. So I'm looking for books that will teach me the thinking-process of creating algorithms. Any good suggestions?

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  • I need to choose a compression algorithm

    - by chiz
    I need to choose a compression algorithm to compress some data. I don't know the type of data I'll be compressing in advance (think of it as kinda like the WinRAR program). I've heard of the following algorithms but I don't know which one I should use. Can anyone post a short list of pros and cons? For my application the first priority is decompression speed; the second priority is space saved. Compression (not decompression) speed is irrelevant. Deflate Implode Plain Huffman bzip2 lzma

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  • Algorithm - find the minimal time

    - by exTyn
    I've found this problem somewhere on the internet, but I'm not sure about the proper solution. I think, that it has to be done by greedy algorithm, however I haven't spend much time thinking about that. I suppose, You may enjoy solving this problem, and I will get my answer. Win-win situation :). Problem N people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. Because it's night, the torch has to be used when crossing the bridge. Every person can cross the bridge in some (given) time (person n1 can cross the bridge in t1 time, person n2 in t2 time etc.). When two people cross the bridge together, they must move at the slower person's pace. What is the mimimal time for the whole grup to cross the bridge?

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  • Interval tree algorithm that supports merging of intervals with no overlap

    - by Dave Griffiths
    I'm looking for an interval tree algorithm similar to the red-black interval tree in CLR but that supports merging of intervals by default so that there are never any overlapping intervals. In other words if you had a tree containing two intervals [2,3] and [5,6] and you added the interval [4,4], the result would be a tree containing just one interval [2,6]. Thanks Update: the use case I'm considering is calculating transitive closure. Interval sets are used to store the successor sets because they have been found to be quite compact. But if you represent interval sets just as a linked list I have found that in some situations they can become quite large and hence so does the time required to find the insertion point. Hence my interest in interval trees. Also there may be quite a lot of merging one tree with another (i.e. a set OR operation) - if both trees are large then it may be better to create a new tree using inorder walks of both trees rather than repeated insertions of each interval.

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  • Properties of bad fibonacci algorithm

    - by John Smith
    I was looking at the canonical bad fibonacci algorithm the other day: public static int fib(int n) { // Base Case if (n < 2) return 1; else return fib(n-1) + fib(n-2); } I made the interesting observation. When you call fib(n), then for k between 1 and n fib(k) is called precisely fib(n-k+1) times (or fib(n-k) depending on your definition of fib(0) ). Also, fib(0) is called fib(n-k-1) times. This then allows me to find that in fib(100) there are exactly 708449696358523830149 calls to the fib function. Are there other interesting observations on this function you know of?

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  • Algorithm to generate numerical concept hierarchy

    - by Christophe Herreman
    I have a couple of numerical datasets that I need to create a concept hierarchy for. For now, I have been doing this manually by observing the data (and a corresponding linechart). Based on my intuition, I created some acceptable hierarchies. This seems like a task that can be automated. Does anyone know if there is an algorithm to generate a concept hierarchy for numerical data? To give an example, I have the following dataset: Bangladesh 521 Brazil 8295 Burma 446 China 3259 Congo 2952 Egypt 2162 Ethiopia 333 France 46037 Germany 44729 India 1017 Indonesia 2239 Iran 4600 Italy 38996 Japan 38457 Mexico 10200 Nigeria 1401 Pakistan 1022 Philippines 1845 Russia 11807 South Africa 5685 Thailand 4116 Turkey 10479 UK 43734 US 47440 Vietnam 1042 for which I created the following hierarchy: LOWEST ( < 1000) LOW (1000 - 2500) MEDIUM (2501 - 7500) HIGH (7501 - 30000) HIGHEST ( 30000)

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  • Time complexity of Sieve of Eratosthenes algorithm

    - by eSKay
    From Wikipedia: The complexity of the algorithm is O(n(logn)(loglogn)) bit operations. How do you arrive at that? That the complexity includes the loglogn term tells me that there is a sqrt(n) somewhere. Suppose I am running the sieve on the first 100 numbers (n = 100), assuming that marking the numbers as composite takes constant time (array implementation), the number of times we use mark_composite() would be something like n/2 + n/3 + n/5 + n/7 + ... + n/97 = O(n) And to find the next prime number (for example to jump to 7 after crossing out all the numbers that are multiples of 5), the number of operations would be O(n). So, the complexity would be O(n^2). Do you agree?

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