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• Plotting a graph with GD

  - by Nayena

  Here it goes. I have been thinking about this for a long time, and havent really been able to put up a proper way to do it yet. I havent implemented anything yet, as im still designing the thing. The idea is that i crawl a website for internal links, i got this settled, its easy, but after the crawling, i end up with an array with lots of links, and how many times those particular link appears on the site that i crawled (and how they're connected). With this huge array, i want to draw a graph somehow. Assuming i can handle the data correctly, the real question here is how i can draw this in a image by the use of the GD library. I figured if theres less than 12 elements, i can align them up on a unit circle spacing them up as a circle and then connecting them accordingly, so anything up to 12 elements shouldn't be a problem, but if theres more than 12, it could be awesome getting them lined up like this Or well, thats just a rough drawing, but i guess its just to prove a point. So i'm here looking for guidance or tips towards getting the math down to getting the stuff lined up in a good way. I have previously made bar-graphs, so i have little experience doing math with GD. If possible, id prefer not using some plotter-library - in the end, it gives me a better understanding on how things are supposed to be.

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• Algorithm and data structure learning resources for dynamic programming

  - by Pranav

  Im learning dynamic programming now, and while I know the theory well, designing DP algorithms for new problems is still difficult. This is what i would really like now- A book or a website, which poses a problem which can be solved by dynamic programming. Also there is the solution with an explanation available, which i would like to see if i cant solve the problem even after butting my head at it for a few hours. Is there some resource that provides this sort of a thing for several categories of algorithms- like graph algorithms, dynamic programming, etc? P.S. I considered Topcoder, but the solutions there are not really appropriate for learning to implement efficient solutions.

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• Techniques and algorithms for precise and efficient graph plotting

  - by Viet

  I'd like to plot mathematical functions and I'm looking for techniques and algorithms for precise and efficient plotting. 2D plotting should suffice. I focus on techniques and algorithms, not libraries or languages. Thanks in advance!

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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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• Optimizing WordWrap Algorithm

  - by Milo

  I have a word-wrap algorithm that basically generates lines of text that fit the width of the text. Unfortunately, it gets slow when I add too much text. I was wondering if I oversaw any major optimizations that could be made. Also, if anyone has a design that would still allow strings of lines or string pointers of lines that is better I'd be open to rewriting the algorithm. Thanks void AguiTextBox::makeLinesFromWordWrap() { textRows.clear(); textRows.push_back(""); std::string curStr; std::string curWord; int curWordWidth = 0; int curLetterWidth = 0; int curLineWidth = 0; bool isVscroll = isVScrollNeeded(); int voffset = 0; if(isVscroll) { voffset = pChildVScroll->getWidth(); } int AdjWidthMinusVoffset = getAdjustedWidth() - voffset; int len = getTextLength(); int bytesSkipped = 0; int letterLength = 0; size_t ind = 0; for(int i = 0; i < len; ++i) { //get the unicode character letterLength = _unicodeFunctions.bringToNextUnichar(ind,getText()); curStr = getText().substr(bytesSkipped,letterLength); bytesSkipped += letterLength; curLetterWidth = getFont().getTextWidth(curStr); //push a new line if(curStr[0] == '\n') { textRows.back() += curWord; curWord = ""; curLetterWidth = 0; curWordWidth = 0; curLineWidth = 0; textRows.push_back(""); continue; } //ensure word is not longer than the width if(curWordWidth + curLetterWidth >= AdjWidthMinusVoffset && curWord.length() >= 1) { textRows.back() += curWord; textRows.push_back(""); curWord = ""; curWordWidth = 0; curLineWidth = 0; } //add letter to word curWord += curStr; curWordWidth += curLetterWidth; //if we need a Vscroll bar start over if(!isVscroll && isVScrollNeeded()) { isVscroll = true; voffset = pChildVScroll->getWidth(); AdjWidthMinusVoffset = getAdjustedWidth() - voffset; i = -1; curWord = ""; curStr = ""; textRows.clear(); textRows.push_back(""); ind = 0; curWordWidth = 0; curLetterWidth = 0; curLineWidth = 0; bytesSkipped = 0; continue; } if(curLineWidth + curWordWidth >= AdjWidthMinusVoffset && textRows.back().length() >= 1) { textRows.push_back(""); curLineWidth = 0; } if(curStr[0] == ' ' || curStr[0] == '-') { textRows.back() += curWord; curLineWidth += curWordWidth; curWord = ""; curWordWidth = 0; } } if(curWord != "") { textRows.back() += curWord; } updateWidestLine(); }

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• Sum of path products in DAG

  - by Jules

  Suppose we have a DAG with edges labeled with numbers. Define the value of a path as the product of the labels. For each (source,sink)-pair I want to find the sum of the values of all the paths from source to sink. You can do this in polynomial time with dynamic programming, but there are still some choices that can be made in how you decompose the problem. In my case I have one DAG that has to be evaluated repeatedly with different labelings. My question is: for a given DAG, how can we pre-compute a good strategy for computing these values for different labelings repeatedly. It would be nice if there was an algorithm that finds an optimal way, for example a way that minimizes the number of multiplications. But perhaps this is too much to ask, I would be very happy with an algorithm that just gives a good decomposition.

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• A graph problem

  - by copperhead

  I am struggling to solve the following problem http://uva.onlinejudge.org/external/1/193.html However Im not able to get a fast solution. And as seen by the times of others, there should be a solution of maximum n^2 complexity http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=3&page=show_problem&problemid=129&page=problem_stats Can I get some help?

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• All minimum spanning trees implementation

  - by russtbarnacle

  I've been looking for an implementation (I'm using networkx library.) that will find all the minimum spanning trees (MST) of an undirected weighted graph. I can only find implementations for Kruskal's Algorithm and Prim's Algorithm both of which will only return a single MST. I've seen papers that address this problem (such as http://fano.ics.uci.edu/cites/Publication/Epp-TR-95-50.html) but my head tends to explode someway through trying to think how to translate it to code. In fact i've not been able to find an implementation in any language!

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• What Math topics & resources to consider as beginner to indulge the book - Introduction to Algorithm

  - by sector7

  I'm a programmer who's beginning to appreciate the knowledge & usability of Algorithms in my work as I move forward with my skill-set. I don't want to take the short path by learning how to apply algorithms "as-is" but would rather like to know the foundation and fundamentals behind them. For that I need Math, at which I'm pretty "basic". I'm considering getting tuition's for that. What I would like is to have a concise syllabus/set of topics/book which I could hand over to my math tutor to get started. HIGHLY DESIRED: one book. the silver bullet. (fingers crossed!) PS: I've got some leads but want to hear you guys/gurus out: Discrete Math, Combinatorics, Graph theory, Calculus, Linear Algebra, and Number Theory. Looking forward to your answers. Thanks!

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• PHP OCI8 and Oracle 11g DRCP Connection Pooling in Pictures

  - by christopher.jones

  Here is a screen shot from a PHP OCI8 connection pooling demo that I like to run. It graphically shows how little database host memory is needed when using DRCP connection pooling with Oracle Database 11g. Migrating to DRCP can be as simple as starting the pool and changing the connection string in your PHP application. The script that generated the data for this graph was a simple "Parts" query application being run under various simulated user loads. I was running the database on a small Oracle Linux server with just 2G of memory. I used PHP OCI8 1.4. Apache is in pre-fork mode, as needed for PHP. Each graph has time on the horizontal access in arbitrary 'tick' time units. Click the image to see it full sized. Pooled connections Beginning with the top left graph, At tick time 65 I used Apache's 'ab' tool to start 100 concurrent 'users' running the application. These users connected to the database using DRCP: $c = oci_pconnect('phpdemo', 'welcome', 'myhost/orcl:pooled'); A second hundred DRCP users were added to the system at tick 80 and a final hundred users added at tick 100. At about tick 110 I stopped the test and restarted Apache. This closed all the connections. The bottom left graph shows the number of statements being executed by the database per second, with some spikes for background database activity and some variability for this small test. Each extra batch of users adds another 'step' of load to the system. Looking at the top right Server Process graph shows the database server processes doing the query work for each web user. As user load is added, the DRCP server pool increases (in green). The pool is initially at its default size 4 and quickly ramps up to about (I'm guessing) 35. At tick time 100 the pool increases to my configured maximum of 40 processes. Those 40 processes are doing the query work for all 300 web users. When I stopped the test at tick 110, the pooled processes remained open waiting for more users to connect. If I had left the test quiet for the DRCP 'inactivity_timeout' period (300 seconds by default), the pool would have shrunk back to 4 processes. Looking at the bottom right, you can see the amount of memory being consumed by the database. During the initial quiet period about 500M of memory was in use. The absolute number is just an indication of my particular DB configuration. As the number of pooled processes increases, each process needs more memory. You can see the shape of the memory graph echoes the Server Process graph above it. Each of the 300 web users will also need a few kilobytes but this is almost too small to see on the graph. Non-pooled connections Compare the DRCP case with using 'dedicated server' processes. At tick 140 I started 100 web users who did not use pooled connections: $c = oci_pconnect('phpdemo', 'welcome', 'myhost/orcl'); This connection string change is the only difference between the two tests. At ticks 155 and 165 I started two more batches of 100 simulated users each. At about tick 195 I stopped the user load but left Apache running. Apache then gradually returned to its quiescent state, killing idle httpd processes and producing the downward slope at the right of the graphs as the persistent database connection in each Apache process was closed. The Executions per Second graph on the bottom left shows the same step increases as for the earlier DRCP case. The database is handling this load. But look at the number of Server processes on the top right graph. There is now a one-to-one correspondence between Apache/PHP processes and DB server processes. Each PHP processes has one DB server processes dedicated to it. Hence the term 'dedicated server'. The memory required on the database is proportional to all those database server processes started. Almost all my system's memory was consumed. I doubt it would have coped with any more user load. Summary Oracle Database 11g DRCP connection pooling significantly reduces database host memory requirements allow more system memory to be allocated for the SGA and allowing the system to scale to handled thousands of concurrent PHP users. Even for small systems, using DRCP allows more web users to be active. More information about PHP and DRCP can be found in the PHP Scalability and High Availability chapter of The Underground PHP and Oracle Manual.

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• How does I/O work for large graph databases?

  - by tjb1982

  I should preface this by saying that I'm mostly a front end web developer, trained as a musician, but over the past few years I've been getting more and more into computer science. So one idea I have as a fun toy project to learn about data structures and C programming was to design and implement my own very simple database that would manage an adjacency list of posts. I don't want SQL (maybe I'll do my own query language? I'm just having fun). It should support ACID. It should be capable of storing 1TB let's say. So with that, I was trying to think of how a database even stores data, without regard to data structures necessarily. I'm working on linux, and I've read that in that world "everything is a file," including hardware (like /dev/*), so I think that that obviously has to apply to a database, too, and it clearly does--whether it's MySQL or PostgreSQL or Neo4j, the database itself is a collection of files you can see in the filesystem. That said, there would come a point in scale where loading the entire database into primary memory just wouldn't work, so it doesn't make sense to design it with that mindset (I assume). However, reading from secondary memory would be much slower and regardless some portion of the database has to be in primary memory in order for you to be able to do anything with it. I read this post: Why use a database instead of just saving your data to disk? And I found it difficult to understand how other databases, like SQLite or Neo4j, read and write from secondary memory and are still very fast (faster, it would seem, than simply writing files to the filesystem as the above question suggests). It seems the key is indexing. But even indexes need to be stored in secondary memory. They are inherently smaller than the database itself, but indexes in a very large database might be prohibitively large, too. So my question is how is I/O generally done with large databases like the one I described above that would be at least 1TB storing a big adjacency list? If indexing is more or less the answer, how exactly does indexing work--what data structures should be involved?

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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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• Algorithm for analyzing text of words

  - by Click Upvote

  I want an algorithm which would create all possible phrases in a block of text. For example, in the text: "My username is click upvote. I have 4k rep on stackoverflow" It would create the following combinations: "My username" "My Username is" "username is click" "is click" "is click upvote" "click upvote" "i have" "i have 4k" "have 4k" .. You get the idea. Basically the point is to get all possible combinations of 'phrases' out of a sentence. Any thoughts for how to best implement this?

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• Robust and fast checksum algorithm?

  - by bene

  Which checksum algorithm can you recommend in the following use case? I want to generate checksums of small JPEG files (~8 kB each) to check if the content changed. Using the filesystem's date modified is unfortunately not an option. The checksum need not be cryptographically strong but it should robustly indicate changes of any size. The second criterion is speed since it should be possible to process at least hundreds of images per second (on a modern CPU). The calculation will be done on a server with several clients. The clients send the images over Gigabit TCP to the server. So there's no disk I/O as bottleneck.

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• Modifying Bresenham's line algorithm

  - by sphennings

  I'm trying to use Bresenham's line algorithm to compute Field of View on a grid. The code I'm using calculates the lines without a problem but I'm having problems getting it to always return the line running from start point to endpoint. What do I need to do so that all lines returned run from (x0,y0) to (x1,y1) def bresenham_line(self, x0, y0, x1, y1): steep = abs(y1 - y0) > abs(x1 - x0) if steep: x0, y0 = y0, x0 x1, y1 = y1, x1 if x0 > x1: x0, x1 = x1, x0 y0, y1 = y1, y0 if y0 < y1: ystep = 1 else: ystep = -1 deltax = x1 - x0 deltay = abs(y1 - y0) error = -deltax / 2 y = y0 line = [] for x in range(x0, x1 + 1): if steep: line.append((y,x)) else: line.append((x,y)) error = error + deltay if error > 0: y = y + ystep error = error - deltax return line

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• How to generate a unique hash for a URL ?

  - by Jacques René Mesrine

  Given these two images from twitter. http://a3.twimg.com/profile_images/130500759/lowres_profilepic.jpg http://a1.twimg.com/profile_images/58079916/lowres_profilepic.jpg I want to download them to local filesystem & store them in a single directory. How shall I overcome name conflicts ? In the example above, I cannot store them as *lowres_profilepic.jpg*. My design idea is treat the URLs as opaque strings except for the last segment. What algorithms (implemented as f) can I use to hash the prefixes into unique strings. f( "http://a3.twimg.com/profile_images/130500759/" ) = 6tgjsdjfjdhgf f( "http://a1.twimg.com/profile_images/58079916/" ) = iuhd87ysdfhdk That way, I can save the files as:- 6tgjsdjfjdhgf_lowres_profilepic.jpg iuhd87ysdfhdk_lowres_profilepic.jpg I don't want a cryptographic algorithm as it this needs to be a performant operation.

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• which is best algorithm?

  - by Lopa

  Consider two algorithms A and B which solve the same problem, and have time complexities (in terms of the number of elementary operations they perform) given respectively by a(n) = 9n+6 b(n) = 2(n^2)+1 (i) Which algorithm is the best asymptotically? (ii) Which is the best for small input sizes n, and for what values of n is this the case? (You may assume where necessary that n0.) i think its 9n+6. guys could you please help me with whether its right or wrong?? and whats the answer for part b. what exactly do they want?

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