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• I need help with 2D collision response (of stacking rotating polygons, with friction and gravity, for a game)

  - by Register Sole

  Hi I am looking for suggestions on how to write a collision response for game programming purpose (so not a scientific simulation). I am dealing with 2D polygons that are rotating, and I want them to be able to stack. I also want friction and gravity. I have a detection mechanism that returns the separating axis, how long the polygons are overlapping, and up to 2 points of contact. For the response, I am currently using an impulse-based response, which main idea is: find the separating axis, length of overlap, and the point of contact (if there are two, pick a random point between to simulate averaged force. i believe there are better ways than this) separate the object (modifying their positions, taking into account of their masses. i do not separate them completely though, to keep track that they are colliding to reduce jitter) calculate normal force based on the coefficient of restitution as if there is no friction. calculate friction, as if there is no normal force. I also assume that the direction of the friction is the same throughout the collision. apply the two forces (which result in a rather inaccurate result, since each force is calculated as if the other is not present. for non-rotating bodies though, this method is exact) I am aware that this method requires the coefficient of friction to be sufficiently small due to the assumption that the direction of friction stays the same in a collision. Also, the result is visually satisfying if gravity is not present. However, when there is gravity, objects on ground jitter and drift (even with zero coefficient of restitution)! It also happens for stacking objects. Larger coefficient of restitution and gravity increase the jittering. I hope you can help me with this. Some things i would like to know more about is how to handle collision with two point of contacts (how to end up having an object sitting still on the ground?), how to reduce, and prevent if possible, jitter and drift (do people use the most accurate method possible, or is there a trick to overcome this?), and how to handle multiple objects collision (for example, in the case of stacking objects, how do I check collisions between all of them and keep them all stable at every frame so they don't jitter?). A total reformulation of my algorithm is also welcomed, as long as it works. Another thing to note is that I am not making a Physics game, so I only need a visually satisfying response (though a realistic response is preferable, if it is not performance-heavy). But surely jittering and drifting objects on flat ground are not at all acceptable. In addition, I am a Physics student, so feel free to talk about impulse and whatever needed. Finally, I'm sorry for the long post. I tried to be as concise as I can. Thank you for reading it! EDIT It seems what I didn't manage to come up all this time is to separate resting contact as a class of its own and how to solve them. Currently reading the paper suggested by Jedediah. More suggestions on the topic are welcome :) CASE CLOSED After reading various papers referenced in the paper, successfully implemented simultaneous impulse method (referring to the original paper by Erin Catto, [Catt05]). Thanks maaaan!! The paper is wonderful. The current system is visibly much better than the previous. Still haven't separated resting contact as a class of its own though, which brings me to my next question. Love you all! Haha (sorry, I'm just so happy thanks to you).

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• Access to bound data in IMultiValueConverter.ConvertBack() in C#/WPF

  - by absence

  I have a problem with a multibinding: <Canvas> <local:SPoint x:Name="sp" Width="10" Height="10"> <Canvas.Left><!-- irrelevant binding here --></Canvas.Left> <Canvas.Top> <MultiBinding Converter="{StaticResource myConverter}" Mode="TwoWay"> <Binding ElementName="cp1" Path="(Canvas.Top)"/> <Binding ElementName="cp1" Path="Height"/> <Binding ElementName="cp2" Path="(Canvas.Top)"/> <Binding ElementName="cp2" Path="Height"/> <Binding ElementName="sp" Path="Height"/> <Binding ElementName="sp" Path="Slope" Mode="TwoWay"/> </MultiBinding> </Canvas.Top> </local:SPoint> <local:CPoint x:Name="cp1" Width="10" Height="10" Canvas.Left="20" Canvas.Top="150"/> <local:CPoint x:Name="cp2" Width="10" Height="10" Canvas.Left="100" Canvas.Top="20"/> </Canvas> In order to calculate the Canvas.Top value, myConverter needs all the bound values. This works great in Convert(). Going the other way, myConverter should ideally calculate the Slope value (Binding.DoNothing for the rest), but it needs the other values in addition to the Canvas.Top one passed to ConvertBack(). What is the right way to solve this? I have tried making the binding OneWay and create an additional multibinding for local:SPoint.Slope, but that causes infinite recursion and stack overflow. I was thinking the ConverterParameter could be used, but it seems like it's not possible to bind to it.

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• C# average function for large numbers without overflow exception

  - by Ron Klein

  .NET Framework 3.5. I'm trying to calculate the average of some pretty large numbers. For instance: using System; using System.Linq; class Program { static void Main(string[] args) { var items = new long[] { long.MaxValue - 100, long.MaxValue - 200, long.MaxValue - 300 }; try { var avg = items.Average(); Console.WriteLine(avg); } catch (OverflowException ex) { Console.WriteLine("can't calculate that!"); } Console.ReadLine(); } } Obviously, the mathematical result is 9223372036854775607 (long.MaxValue - 200), but I get an exception there. This is because the implementation (on my machine) to the Average extension method, as inspected by .NET Reflector is: public static double Average(this IEnumerable<long> source) { if (source == null) { throw Error.ArgumentNull("source"); } long num = 0L; long num2 = 0L; foreach (long num3 in source) { num += num3; num2 += 1L; } if (num2 <= 0L) { throw Error.NoElements(); } return (((double) num) / ((double) num2)); } I know I can use a BigInt library (yes, I know that it is included in .NET Framework 4.0, but I'm tied to 3.5). But I still wonder if there's a pretty straight forward implementation of calculating the average of integers without an external library. Do you happen to know about such implementation? Thanks!!

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• C# average function without overflow exception

  - by Ron Klein

  .NET Framework 3.5. I'm trying to calculate the average of some pretty large numbers. For instance: using System; using System.Linq; class Program { static void Main(string[] args) { var items = new long[] { long.MaxValue - 100, long.MaxValue - 200, long.MaxValue - 300 }; try { var avg = items.Average(); Console.WriteLine(avg); } catch (OverflowException ex) { Console.WriteLine("can't calculate that!"); } Console.ReadLine(); } } Obviously, the mathematical result is 9223372036854775607 (long.MaxValue - 200), but I get an exception there. This is because the implementation (on my machine) to the Average extension method, as inspected by .NET Reflector is: public static double Average(this IEnumerable<long> source) { if (source == null) { throw Error.ArgumentNull("source"); } long num = 0L; long num2 = 0L; foreach (long num3 in source) { num += num3; num2 += 1L; } if (num2 <= 0L) { throw Error.NoElements(); } return (((double) num) / ((double) num2)); } I know I can use a BigInt library (yes, I know that it is included in .NET Framework 4.0, but I'm tied to 3.5). But I still wonder if there's a pretty straight forward implementation of calculating the average of integers without an external library. Do you happen to know about such implementation? Thanks!! UPDATE: The previous example, of three large integers, was just an example to illustrate the overflow issue. The question is about calculating an average of any set of numbers which might sum to a large number that exceeds the type's max value. Sorry about this confusion. I also changed the question's title to avoid additional confusion. Thanks all!!

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• Map/Reduce on an array of hashes in CouchDB

  - by sebastiangeiger

  Hello everyone, I am looking for a map/reduce function to calculate the status in a Design Document. Below you can see an example document from my current database. { "_id": "0238f1414f2f95a47266ca43709a6591", "_rev": "22-24a741981b4de71f33cc70c7e5744442", "status": "retrieved image urls", "term": "Lucas Winter", "urls": [ { "status": "retrieved", "url": "http://...." }, { "status": "retrieved", "url": "http://..." } ], "search_depth": 1, "possible_labels": { "gender": "male" }, "couchrest-type": "SearchTerm" } I'd like to get rid of the status key and rather calculate it from the statuses of the urls. My current by_status view looks like the following: function(doc) { if (doc['status']) { emit(doc['status'], null); } } I tried some things but nothing actually works. Right now my Map Function looks like this: function(doc) { if(doc.urls){ emit(doc._id, doc.urls) } } And my Reduce Function function(key, value, rereduce){ var reduced_status = "retrieved" for(var url in value){ if(url.status=="new"){ reduced_status = "new"; } } return reduced_status; } The result is that I get retrieved everywhere which is definitely not right. I tried to narrow down the problem and it seems to be that value is no array, when I use the following Reduce Function I get length 1 everywhere, which is impossible because I have 12 documents in my database, each containing between 20 to 200 urls function(key, value, rereduce){ return value.length; } What am I doing wrong? (I know I want you to write code for me and I'm feeling guilty, but right now I do the calculation of the statuses in ruby after getting the data from the database. It would be nice to already get the right data from the database)

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• C# - closures over class fields inside an initializer?

  - by Richard Berg

  Consider the following code: using System; namespace ConsoleApplication2 { class Program { static void Main(string[] args) { var square = new Square(4); Console.WriteLine(square.Calculate()); } } class MathOp { protected MathOp(Func<int> calc) { _calc = calc; } public int Calculate() { return _calc(); } private Func<int> _calc; } class Square : MathOp { public Square(int operand) : base(() => _operand * _operand) // runtime exception { _operand = operand; } private int _operand; } } (ignore the class design; I'm not actually writing a calculator! this code merely represents a minimal repro for a much bigger problem that took awhile to narrow down) I would expect it to either: print "16", OR throw a compile time error if closing over a member field is not allowed in this scenario Instead I get a nonsensical exception thrown at the indicated line. On the 3.0 CLR it's a NullReferenceException; on the Silverlight CLR it's the infamous Operation could destabilize the runtime.

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• Implementing Naïve Bayes algorithm in Java - Need some guidance

  - by techventure

  hello stackflow people As a School assignment i'm required to implement Naïve Bayes algorithm which i am intending to do in Java. In trying to understand how its done, i've read the book "Data Mining - Practical Machine Learning Tools and Techniques" which has a section on this topic but am still unsure on some primary points that are blocking my progress. Since i'm seeking guidance not solution in here, i'll tell you guys what i thinking in my head, what i think is the correct approach and in return ask for correction/guidance which will very much be appreciated. please note that i am an absolute beginner on Naïve Bayes algorithm, Data mining and in general programming so you might see stupid comments/calculations below: The training data set i'm given has 4 attributes/features that are numeric and normalized(in range[0 1]) using Weka (no missing values)and one nominal class(yes/no) 1) The data coming from a csv file is numeric HENCE * Given the attributes are numeric i use PDF (probability density function) formula. + To calculate the PDF in java i first separate the attributes based on whether they're in class yes or class no and hold them into different array (array class yes and array class no) + Then calculate the mean(sum of the values in row / number of values in that row) and standard divination for each of the 4 attributes (columns) of each class + Now to find PDF of a given value(n) i do (n-mean)^2/(2*SD^2), + Then to find P( yes | E) and P( no | E) i multiply the PDF value of all 4 given attributes and compare which is larger, which indicates the class it belongs to In temrs of Java, i'm using ArrayList of ArrayList and Double to store the attribute values. lastly i'm unsure how to to get new data? Should i ask for input file (like csv) or command prompt and ask for 4 values? I'll stop here for now (do have more questions) but I'm worried this won't get any responses given how long its got. I will really appreciate for those that give their time reading my problems and comment.

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• Double type returns -1.#IND/NaN error when calculating pi iteratively

  - by Draak

  I am working through a problem for my MCTS certification. The program has to calculate pi until the user presses a key, at which point the thread is aborted, the result returned to the main thread and printed in the console. Simple enough, right? This exercise is really meant to be about threading, but I'm running into another problem. The procedure that calculates pi returns -1.#IND. I've read some of the material on the web about this error, but I'm still not sure how to fix it. When I change double to Decimal type, I unsurprisingly get Overflow Exception very quickly. So, the question is how do I store the numbers correctly? Do I have to create a class to somehow store parts of the number when it gets too big to be contained in a Decimal? Class PiCalculator Dim a As Double = 1 Dim b As Double = 1 / Math.Sqrt(2) Dim t As Double = 1 / 4 Dim p As Double = 1 Dim pi As Double Dim callback As DelegateResult Sub New(ByVal _callback As DelegateResult) callback = _callback End Sub Sub Calculate() Try Do While True Dim a1 = (a + b) / 2 Dim b1 = Math.Sqrt(a * b) Dim t1 = t - p * (a - a1) ^ 2 Dim p1 = 2 * p a = a1 b = b1 t = t1 p = p1 pi = ((a + b) ^ 2) / (4 * t) Loop Catch ex As ThreadAbortException Finally callback(pi) End Try End Sub End Class

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• Python: speed up removal of every n-th element from list.

  - by ChristopheD

  I'm trying to solve this programming riddle and althought the solution (see code below) works correct, it is too slow for succesful submission. Any pointers as how to make this run faster? (removal of every n-th element from a list)? Or suggestions for a better algorithm to calculate the same; seems I can't think of anything else then brute-force for now... Basically the task at hand is: GIVEN: L = [2,3,4,5,6,7,8,9,10,11,........] 1. Take the first remaining item in list L (in the general case 'n'). Move it to the 'lucky number list'. Then drop every 'n-th' item from the list. 2. Repeat 1 TASK: Calculate the n-th number from the 'lucky number list' ( 1 <= n <= 3000) My current code (it calculates the 3000 first lucky numbers in about a second on my machine - but unfortunately too slow): """ SPOJ Problem Set (classical) 1798. Assistance Required URL: http://www.spoj.pl/problems/ASSIST/ """ sieve = range(3, 33900, 2) luckynumbers = [2] while True: wanted_n = input() if wanted_n == 0: break while len(luckynumbers) < wanted_n: item = sieve[0] luckynumbers.append(item) items_to_delete = set(sieve[::item]) sieve = filter(lambda x: x not in items_to_delete, sieve) print luckynumbers[wanted_n-1]

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• Average function without overflow exception

  - by Ron Klein

  .NET Framework 3.5. I'm trying to calculate the average of some pretty large numbers. For instance: using System; using System.Linq; class Program { static void Main(string[] args) { var items = new long[] { long.MinValue + 100, long.MinValue + 200, long.MinValue + 300 }; try { var avg = items.Average(); Console.WriteLine(avg); } catch (OverflowException ex) { Console.WriteLine("can't calculate that!"); } Console.ReadLine(); } } Obviously, the mathematical result is 9223372036854775607 (long.MaxValue - 200), but I get an exception there. This is because the implementation (on my machine) to the Average extension method, as inspected by .NET Reflector is: public static double Average(this IEnumerable<long> source) { if (source == null) { throw Error.ArgumentNull("source"); } long num = 0L; long num2 = 0L; foreach (long num3 in source) { num += num3; num2 += 1L; } if (num2 <= 0L) { throw Error.NoElements(); } return (((double) num) / ((double) num2)); } I know I can use a BigInt library (yes, I know that it is included in .NET Framework 4.0, but I'm tied to 3.5). But I still wonder if there's a pretty straight forward implementation of calculating the average of integers without an external library. Do you happen to know about such implementation? Thanks!! UPDATE: The previous example, of three large integers, was just an example to illustrate the overflow issue. The question is about calculating an average of any set of numbers which might sum to a large number that exceeds the type's max value. Sorry about this confusion. I also changed the question's title to avoid additional confusion. Thanks all!!

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• Concurrent cartesian product algorithm in Clojure

  - by jqno

  Is there a good algorithm to calculate the cartesian product of three seqs concurrently in Clojure? I'm working on a small hobby project in Clojure, mainly as a means to learn the language, and its concurrency features. In my project, I need to calculate the cartesian product of three seqs (and do something with the results). I found the cartesian-product function in clojure.contrib.combinatorics, which works pretty well. However, the calculation of the cartesian product turns out to be the bottleneck of the program. Therefore, I'd like to perform the calculation concurrently. Now, for the map function, there's a convenient pmap alternative that magically makes the thing concurrent. Which is cool :). Unfortunately, such a thing doesn't exist for cartesian-product. I've looked at the source code, but I can't find an easy way to make it concurrent myself. Also, I've tried to implement an algorithm myself using map, but I guess my algorithmic skills aren't what they used to be. I managed to come up with something ugly for two seqs, but three was definitely a bridge too far. So, does anyone know of an algorithm that's already concurrent, or one that I can parallelize myself?

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• IBasic Accumulator

  - by Tara

  I am trying to do an accumulator in IBasic for a college assignment and I have the general stuff down but I cannot get it to accumulate. The code is below. My question is how do I get it to accumulate and pass to the different module. I'm trying to calculate how many right answers the user gets. Also, i need to calculate the percentage of right answers. so if the user gets 9 out of 10 right theyed answer 90% right. 'October 15, 2009 ' 'Lab 7.5 Programming Challenge 1 - Average Test Scores ' 'This is a dice game ' declare main() declare inputName(name:string) declare getAnswer(num1:int, num2:int) declare getResult(num1:int, num2:int, answer:int) declare avgRight(getRight:int) declare printInfo(name:string, getRight:int, averege:float) openconsole main() do:until inkey$<>"" closeconsole end sub main() def name:string def num1, num2, answer, total, getRight:int def averege:float inputName (name) getRight = 0 For counter = 1 to 10 getRight = getAnswer(num1, num2) getRight = getRight + 1 next counter average = avgRight (getRight) printInfo(Name, getRight, average) end sub inputName (name) Input "Please enter your name: " ,name return sub getAnswer(num1, num2) def answer, getRight:int num1 = rnd (10) + 1 num2 = rnd (10) + 1 Print num1, "+ " ,num2 Input "What is the answer to the equation? " ,answer getRight = getResult(num1, num2, answer) return getRight sub getResult(num1, num2, answer) def getRight:int if answer = num1 + num2 getRight = 1 else getRight = 0 endif return getRight sub avgRight(getRight) def average:float average = getRight / 10 return average sub printInfo(name, getRight, averege) Print "The students name is: " ,name Print "The number right is: " ,getRight Print Using ("&##.#&", "The average right is " ,averege * 100, "%") return

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• What is the most platform- and Python-version-independent way to make a fast loop for use in Python?

  - by Statto

  I'm writing a scientific application in Python with a very processor-intensive loop at its core. I would like to optimise this as far as possible, at minimum inconvenience to end users, who will probably use it as an uncompiled collection of Python scripts, and will be using Windows, Mac, and (mainly Ubuntu) Linux. It is currently written in Python with a dash of NumPy, and I've included the code below. Is there a solution which would be reasonably fast which would not require compilation? This would seem to be the easiest way to maintain platform-independence. If using something like Pyrex, which does require compilation, is there an easy way to bundle many modules and have Python choose between them depending on detected OS and Python version? Is there an easy way to build the collection of modules without needing access to every system with every version of Python? Does one method lend itself particularly to multi-processor optimisation? (If you're interested, the loop is to calculate the magnetic field at a given point inside a crystal by adding together the contributions of a large number of nearby magnetic ions, treated as tiny bar magnets. Basically, a massive sum of these.) # calculate_dipole # ------------------------- # calculate_dipole works out the dipole field at a given point within the crystal unit cell # --- # INPUT # mu = position at which to calculate the dipole field # r_i = array of atomic positions # mom_i = corresponding array of magnetic moments # --- # OUTPUT # B = the B-field at this point def calculate_dipole(mu, r_i, mom_i): relative = mu - r_i r_unit = unit_vectors(relative) #4pi / mu0 (at the front of the dipole eqn) A = 1e-7 #initalise dipole field B = zeros(3,float) for i in range(len(relative)): #work out the dipole field and add it to the estimate so far B += A*(3*dot(mom_i[i],r_unit[i])*r_unit[i] - mom_i[i]) / sqrt(dot(relative[i],relative[i]))**3 return B

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• Required Working Precision for the BBP Algorithm?

  - by brainfsck

  Hello, I'm looking to compute the nth digit of Pi in a low-memory environment. As I don't have decimals available to me, this integer-only BBP algorithm in Python has been a great starting point. I only need to calculate one digit of Pi at a time. How can I determine the lowest I can set D, the "number of digits of working precision"? D=4 gives me many correct digits, but a few digits will be off by one. For example, computing digit 393 with precision of 4 gives me 0xafda, from which I extract the digit 0xa. However, the correct digit is 0xb. No matter how high I set D, it seems that testing a sufficient number of digits finds an one where the formula returns an incorrect value. I've tried upping the precision when the digit is "close" to another, e.g. 0x3fff or 0x1000, but cannot find any good definition of "close"; for instance, calculating at digit 9798 gives me 0xcde6 , which is not very close to 0xd000, but the correct digit is 0xd. Can anyone help me figure out how much working precision is needed to calculate a given digit using this algorithm? Thank you,

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• How do you efficiently implement a document similarity search system?

  - by Björn Lindqvist

  How do you implement a "similar items" system for items described by a set of tags? In my database, I have three tables, Article, ArticleTag and Tag. Each Article is related to a number of Tags via a many-to-many relationship. For each Article i want to find the five most similar articles to implement a "if you like this article you will like these too" system. I am familiar with Cosine similarity and using that algorithm works very well. But it is way to slow. For each article, I need to iterate over all articles, calculate the cosine similarity for the article pair and then select the five articles with the highest similarity rating. With 200k articles and 30k tags, it takes me half a minute to calculate the similar articles for a single article. So I need another algorithm that produces roughly as good results as cosine similarity but that can be run in realtime and which does not require me to iterate over the whole document corpus each time. Maybe someone can suggest an off-the-shelf solution for this? Most of the search engines I looked at does not enable document similarity searching.

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• Detecting Asymptotes in a Graph

  - by nasufara

  I am creating a graphing calculator in Java as a project for my programming class. There are two main components to this calculator: the graph itself, which draws the line(s), and the equation evaluator, which takes in an equation as a String and... well, evaluates it. To create the line, I create a Path2D.Double instance, and loop through the points on the line. To do this, I calculate as many points as the graph is wide (e.g. if the graph itself is 500px wide, I calculate 500 points), and then scale it to the window of the graph. Now, this works perfectly for most any line. However, it does not when dealing with asymptotes. If, when calculating points, the graph encounters a domain error (such as 1/0), the graph closes the shape in the Path2D.Double instance and starts a new line, so that the line looks mathematically correct. Example: However, because of the way it scales, sometimes it is rendered correctly, sometimes it isn't. When it isn't, the actual asymptotic line is shown, because within those 500 points, it skipped over x = 2.0 in the equation 1 / (x-2), and only did x = 1.98 and x = 2.04, which are perfectly valid in that equation. Example: In that case, I increased the window on the left and right one unit each. My question is: Is there a way to deal with asymptotes using this method of scaling so that the resulting line looks mathematically correct? I myself have thought of implementing a binary search-esque method, where, if it finds that it calculates one point, and then the next point is wildly far away from the last point, it searches in between those points for a domain error. I had trouble figuring out how to make it work in practice, however. Thank you for any help you may give!

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• Calculating odds distribution with 6-sided dice

  - by Stephen

  I'm trying to calculate the odds distribution of a changing number of 6-sided die rolls. For example, 3d6 ranges from 3 to 18 as follows: 3:1, 4:3, 5:6, 6:10, 7:15, 8:21, 9:25, 10:27, 11:27, 12:25, 13:21, 14:15, 15:10, 16:6, 17:3, 18:1 I wrote this php program to calculate it: function distributionCalc($numberDice,$sides=6) { for ( $i=0; $i<pow($sides,$numberDice); $i++) { $sum=0; for ($j=0; $j<$numberDice; $j++) { $sum+=(1+(floor($i/pow($sides,$j))) % $sides); } $distribution[$sum]++; } return $distribution; } The inner $j for-loop uses the magic of the floor and modulus functions to create a base-6 counting sequence with the number of digits being the number of dice, so 3d6 would count as: 111,112,113,114,115,116,121,122,123,124,125,126,131,etc. The function takes the sum of each, so it would read as: 3,4,5,6,7,8,4,5,6,7,8,9,5,etc. It plows through all 3^6 possible results and adds 1 to the corresponding slot in the $distribution array between 3 and 18. Pretty straightforward. However, it only works until about 8d6, afterward i get server time-outs because it's now doing billions of calculations. But I don't think it's necessary because die probability follows a sweet bell-curve distribution. I'm wondering if there's a way to skip the number crunching and go straight to the curve itself. Is there a way to do this, so, for example, with 80d6 (80-480)? Can the distribution be projected without doing 6^80 calculations? I'm not a professional coder and probability is still new to me, so thanks for all the help! Stephen

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• Finding text orientation in image (angle for rotation)

  - by maximus

  There is an image captured by camera, and I need to find the angle of the text in order to rotate it to make the image better for OCR results. So I know that the fourier transform can be used for that purpose, My question is, does it really gives good results or may be it is better to use something different than that? Can you tell me if there is a good method for this purpose? I am afraid that not every image containing the text will give me a good result after using fourier transform method. Actually, if I make like it is written here: link text (see the part related with an example of text image) calculating the logarithm of the magnitude of the Fourier transform of image with text and then thresholding it, I get that points and I can calculate the line approximately passing through them, and after getting the line calculate the angle, and then make an affine transform, But, what if I do not get a good result every time using this method , and make a false transform? Any ideas please to judge wether the result is correct or not, or may be another method is better? The binary image can contain noise, even if there are not so much of them, the angle found as a result can be not accurate.

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• Average performance of binary search algorithm?

  - by Passionate Learner

  http://en.wikipedia.org/wiki/Binary_search_algorithm#Average_performance BinarySearch(int A[], int value, int low, int high) { int mid; if (high < low) return -1; mid = (low + high) / 2; if (A[mid] > value) return BinarySearch(A, value, low, mid-1); else if (A[mid] < value) return BinarySearch(A, value, mid+1, high); else return mid; } If the integer I'm trying to find is always in the array, can anyone help me write a program that can calculate the average performance of binary search algorithm? I know I can do this by actually running the program and counting the number of calls, but what I'm trying to do here is to do it without calling the function. I'm not asking for a time complexity, I'm trying to calculate the average number of calls. For example, the average number of calls to find a integer in A[2], it would be 1.67 (5/3).

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• Abstract Methods in "Product" - Factory Method C#

  - by Regina Foo

  I have a simple class library (COM+ service) written in C# to consume 5 web services: Add, Minus, Divide, Multiply and Compare. I've created the abstract product and abstract factory classes. The abstract product named WS's code: public abstract class WS { public abstract double Calculate(double a, double b); public abstract string Compare(double a, double b); } As you see, when one of the subclasses inherits WS, both methods must be overridden which might not be useful in some subclasses. E.g. Compare doesn't need Calculate() method. To instantiate a new CompareWS object, the client class will call the CreateWS() method which returns a WS object type. public class CompareWSFactory : WSFactory { public override WS CreateWS() { return new CompareWS(); } } But if Compare() is not defined as abstract in WS, the Compare() method cannot be invoked. This is only an example with two methods, but what if there are more methods? Is it stupid to define all the methods as abstract in the WS class? My question is: I want to define abstract methods that are common to all subclasses of WS whereas when the factory creates a WS object type, all the methods of the subclasses can be invoked (overridden methods of WS and also the methods in subclasses). How should I do this?

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• Temperature anomaly calculation of time series data

  - by neel

  I have a time series like following: Data <- structure(list(Year = c(1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1991L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L, 1992L), Month = c(8L, 9L, 9L, 9L, 10L, 10L, 10L, 11L, 11L, 11L, 12L, 12L, 12L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 5L, 5L, 5L, 6L, 6L, 6L, 7L, 7L, 7L, 8L, 8L, 8L, 9L, 9L, 9L, 10L, 10L, 10L, 11L, 11L, 11L, 12L, 12L, 12L), Day = c(30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 28L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L, 10L, 20L, 30L), Hour = c(0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L), temperature = c(72.5, 64, 62.5, 64, 64, 53, 52, 52, 45.5, 49, 50, 50, 59, 63.5, 69.5, 61, 61, NaN, NaN, 39.5, 37, 45.5, 45, 39, 43.5, 52, 53, 56, 64, 66, 66.5, 73.5, 81, 85, 89.5, 87.5, 88.5, 83, 84.5, 74, 60.5, 59, 53, 60.5, 62.5, 64.5, 63, 62, 65.5)), .Names = c("Year", "Month", "Day", "Hour", "temperature"), class = "data.frame", row.names = c(NA, -49L)) and I have to calculate standardized anomaly. The steps to calculate the anomalies are following: Monthly premature departures from the long-term (1991-2007) average are obtained. Then standardized by dividing by the standard deviation of monthly temperature. The standardized monthly anomalies are then weighted by multiplying by the fraction of the average temperature for the given month. These weighted anomalies are then summed over 3 month time period. Can you please help me?

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• Memcache key generation strategy

  - by Maxim Veksler

  Given function f1 which receives n String arguments, would be considered better random key generation strategy for memcache for the scenario described below ? Our Memcache client does internal md5sum hashing on the keys it gets public class MemcacheClient { public Object get(String key) { String md5 = Md5sum.md5(key) // Talk to memcached to get the Serialization... return memcached(md5); } } First option public static String f1(String s1, String s2, String s3, String s4) { String key = s1 + s2 + s3 + s4; return get(key); } Second option /** * Calculate hash from Strings * * @param objects vararg list of String's * * @return calculated md5sum hash */ public static String stringHash(Object... strings) { if(strings == null) throw new NullPointerException("D'oh! Can't calculate hash for null"); MD5 md5sum = new MD5(); // if(prevHash != null) // md5sum.Update(prevHash); for(int i = 0; i < strings.length; i++) { if(strings[i] != null) { md5sum.Update("_" + strings[i] + "_"); // Convert to String... } else { // If object is null, allow minimum entropy by hashing it's position md5sum.Update("_" + i + "_"); } } return md5sum.asHex(); } public static String f1(String s1, String s2, String s3, String s4) { String key = stringHash(s1, s2, s3, s4); return get(key); } Note that the possible problem with the second option is that we are doing second md5sum (in the memcache client) on an already md5sum'ed digest result. Thanks for reading, Maxim.

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• How to recalculate all-pairs shorthest paths on-line if nodes are getting removed?

  - by Pavel Shved

  Latest news about underground bombing made me curious about the following problem. Assume we have a weighted undirected graph, nodes of which are sometimes removed. The problem is to re-calculate shortest paths between all pairs of nodes fast after such removals. With a simple modification of Floyd-Warshall algorithm we can calculate shortest paths between all pairs. These paths may be stored in a table, where shortest[i][j] contains the index of the next node on the shortest path between i and j (or NULL value if there's no path). The algorithm requires O(n³) time to build the table, and eacho query shortest(i,j) takes O(1). Unfortunately, we should re-run this algorithm after each removal. The other alternative is to run graph search on each query. This way each removal takes zero time to update an auxiliary structure (because there's none), but each query takes O(E) time. What algorithm can be used to "balance" the query and update time for all-pairs shortest-paths problem when nodes of the graph are being removed?

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• Detecting Singularities in a Graph

  - by nasufara

  I am creating a graphing calculator in Java as a project for my programming class. There are two main components to this calculator: the graph itself, which draws the line(s), and the equation evaluator, which takes in an equation as a String and... well, evaluates it. To create the line, I create a Path2D.Double instance, and loop through the points on the line. To do this, I calculate as many points as the graph is wide (e.g. if the graph itself is 500px wide, I calculate 500 points), and then scale it to the window of the graph. Now, this works perfectly for most any line. However, it does not when dealing with singularities. If, when calculating points, the graph encounters a domain error (such as 1/0), the graph closes the shape in the Path2D.Double instance and starts a new line, so that the line looks mathematically correct. Example: However, because of the way it scales, sometimes it is rendered correctly, sometimes it isn't. When it isn't, the actual asymptotic line is shown, because within those 500 points, it skipped over x = 2.0 in the equation 1 / (x-2), and only did x = 1.98 and x = 2.04, which are perfectly valid in that equation. Example: In that case, I increased the window on the left and right one unit each. My question is: Is there a way to deal with singularities using this method of scaling so that the resulting line looks mathematically correct? I myself have thought of implementing a binary search-esque method, where, if it finds that it calculates one point, and then the next point is wildly far away from the last point, it searches in between those points for a domain error. I had trouble figuring out how to make it work in practice, however. Thank you for any help you may give!

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• Algorithm To Select Most Popular Places from Database

  - by Russell C.

  We have a website that contains a database of places. For each place our users are able to take one of the follow actions which we record: VIEW - View it's profile RATING - Rate it on a scale of 1-5 stars REVIEW - Review it COMPLETED - Mark that they've been there WISH LIST - Mark that they want to go there FAVORITE - Mark that it's one of their favorites In our database table of places each place contains a count of the number of times each action above was taken as well as the average rating given by users. views ratings avg_rating completed wishlist favorite What we want to be able to do is generate lists of the top places using the above information. Ideally, we would want to be able to generate this list using a relatively simple SQL query without needing to do any legwork to calculate additional fields or stack rank places against one another. That being said, since we only have about 50,000 places we could run a nightly cron job to calculate some fields such as rankings on different categories if it would make a meaningful difference in the overall results of our top places. I'd appreciate if you could make some suggestions on how we should think about bubbling the best places to the top, which criteria we should weight more heavily, and given that information - suggest what the MySQL query would need to look like in order to select the top 10 places. One thing to note is that at this time we are less concerned with the recency of a place being popular - meaning that looking at the aggregate information is fine and that more recent data doesn't need to be weighted more heavily. Thanks in advance for your help & advice!

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