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• Computationally simple Pseudo-Gaussian Distribution with varying mean and standard deviation?

  - by mstksg

  This picture from wikipedia has a nice example of the sort of functions I'd ideally like to generate http://en.wikipedia.org/wiki/File:Normal_Distribution_PDF.svg Right now I'm using the Irwin-Hall Distribution, which is more or less a Polynomial approximation of the Gaussian distribution...basically, you use uniform random number generator and iterate it x times, and take the average. The more iterations, the more like a Gaussian Distribution it is. It's pretty nice; however I'd like to be able to have one where I can vary the mean. For example, let's say I wanted a number between the range 0 and 10, but around 7. Like, the mean (if I repeated this function multiple times) would turn out to be 7, but the actual range is 0-10. Is there one I should look up, or should I work on doing some fancy maths with standard Gaussian Distributions?

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• Asymptotic runtime question

  - by 2hype

  If f(n) is T(g(n)), then the function 2^(f(n)) is always T(2^(g(n))). Is this statement true or false, and why?

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• Gaining information from nodes of tree

  - by jainp

  I am working with the tree data structure and trying to come up with a way to calculate information I can gain from the nodes of the tree. I am wondering if there are any existing techniques which can assign higher numerical importance to a node which appears less frequently at lower level (Distance from the root of the tree) than the same nodes appearance at higher level and high frequency. To give an example, I want to give more significance to node Book, at level 2 appearing once, then at level 3 appearing thrice. Will appreciate any suggestions/pointers to techniques which achieve something similar. Thanks, Prateek

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• Examples of useful or non-trival dual interfaces

  - by Scott Weinstein

  Recently Erik Meijer and others have show how IObservable/IObserver is the dual of IEnumerable/IEnumerator. The fact that they are dual means that any operation on one interface is valid on the other, thus providing a theoretical foundation for the Reactive Extentions for .Net Do other dual interfaces exist? I'm interested in any example, not just .Net based.

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• curious ill conditioned numerical problem

  - by aaa

  hello. somebody today showed me this curious ill conditioned problem (apparently pretty famous), which looks relatively simple ƒ = (333.75 - a^2)b^6 + a^2 (11a^2 b^2 - 121b^4 - 2) + 5.5b^8 + a/(2^b) where a = 77617 and b = 33096 can you determine correct answer?

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• What is an XYZ-complete problem?

  - by TheMachineCharmer

  EDIT: Diagram: http://www.cs.umass.edu/~immerman/complexity_theory.html There must be some meaning to the word "complete" its used every now and then. Look at the diagram. I tried reading previous posts about NP- My question is what does the word "COMPLETE" mean? Why is it there? What is its significance? N- Non-deterministic - makes sense' P- Polynomial - makes sense but the "COMPLETE" is still a mystery for me.

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• count of distinct acyclic paths from A[a,b] to A[c,d]?

  - by Sorush Rabiee

  I'm writing a sokoban solver for fun and practice, it uses a simple algorithm (something like BFS with a bit of difference). now i want to estimate its running time ( O and omega). but need to know how to calculate count of acyclic paths from a vertex to another in a network. actually I want an expression that calculates count of valid paths, between two vertices of a m*n matrix of vertices. a valid path: visits each vertex 0 or one times. have no circuits for example this is a valid path: but this is not: What is needed is a method to find count of all acyclic paths between the two vertices a and b. comments on solving methods and tricks are welcomed.

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• What exactly are administrative redexes after CPS conversion?

  - by eljenso

  In the context of Scheme and CPS conversion, I'm having a little trouble deciding what administrative redexes (lambdas) exactly are: all the lambda expressions that are introduced by the CPS conversion only the lambda expressions that are introduced by the CPS conversion but you wouldn't have written if you did the conversion "by hand" or through a smarter CPS-converter If possible, a good reference would be welcome.

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• Create My own language with "Functional Programming Language"

  - by esehara

  I prefer Haskell. I already know How to create my own language with Procedural Language (for example: C, Java, Python, etc). But, I know How to create my own language with Functional Language (for example Haskell, Clojure and Scala). I've already read: Internet Resources Write Yourself a Scheme in 48 Hours Real World Haskell - Chapter 16.Using Persec Writing A Lisp Interpreter In Haskell Parsec, a fast combinator parser Implementing functional languages: a tutorial Books Introduction Functional Programming Using Haskell 2nd Edition -- Haskell StackOverflow (but with procedural language) Learning to write a compiler create my own programming language Source Libraries and tools/HJS -- Haskell Are there any other good sources? I wants to get more links,or sources.

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• How does a compiler first compile itself in the same language?

  - by jdk

  I recently read the Mono C# compiler is able to compile itself using the C# language. Cool. In the past I've heard of other languages doing the same. It twists my mind - at inception seems like a chicken and egg problem: syntax vs compiler. What comes first, second and third, etc?...

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• Finding the heaviest length-constrained path in a weighted Binary Tree

  - by Hristo

  UPDATE I worked out an algorithm that I think runs in O(n*k) running time. Below is the pseudo-code: routine heaviestKPath( T, k ) // create 2D matrix with n rows and k columns with each element = -8 // we make it size k+1 because the 0th column must be all 0s for a later // function to work properly and simplicity in our algorithm matrix = new array[ T.getVertexCount() ][ k + 1 ] (-8); // set all elements in the first column of this matrix = 0 matrix[ n ][ 0 ] = 0; // fill our matrix by traversing the tree traverseToFillMatrix( T.root, k ); // consider a path that would arc over a node globalMaxWeight = -8; findArcs( T.root, k ); return globalMaxWeight end routine // node = the current node; k = the path length; node.lc = node’s left child; // node.rc = node’s right child; node.idx = node’s index (row) in the matrix; // node.lc.wt/node.rc.wt = weight of the edge to left/right child; routine traverseToFillMatrix( node, k ) if (node == null) return; traverseToFillMatrix(node.lc, k ); // recurse left traverseToFillMatrix(node.rc, k ); // recurse right // in the case that a left/right child doesn’t exist, or both, // let’s assume the code is smart enough to handle these cases matrix[ node.idx ][ 1 ] = max( node.lc.wt, node.rc.wt ); for i = 2 to k { // max returns the heavier of the 2 paths matrix[node.idx][i] = max( matrix[node.lc.idx][i-1] + node.lc.wt, matrix[node.rc.idx][i-1] + node.rc.wt); } end routine // node = the current node, k = the path length routine findArcs( node, k ) if (node == null) return; nodeMax = matrix[node.idx][k]; longPath = path[node.idx][k]; i = 1; j = k-1; while ( i+j == k AND i < k ) { left = node.lc.wt + matrix[node.lc.idx][i-1]; right = node.rc.wt + matrix[node.rc.idx][j-1]; if ( left + right > nodeMax ) { nodeMax = left + right; } i++; j--; } // if this node’s max weight is larger than the global max weight, update if ( globalMaxWeight < nodeMax ) { globalMaxWeight = nodeMax; } findArcs( node.lc, k ); // recurse left findArcs( node.rc, k ); // recurse right end routine Let me know what you think. Feedback is welcome. I think have come up with two naive algorithms that find the heaviest length-constrained path in a weighted Binary Tree. Firstly, the description of the algorithm is as follows: given an n-vertex Binary Tree with weighted edges and some value k, find the heaviest path of length k. For both algorithms, I'll need a reference to all vertices so I'll just do a simple traversal of the Tree to have a reference to all vertices, with each vertex having a reference to its left, right, and parent nodes in the tree. Algorithm 1 For this algorithm, I'm basically planning on running DFS from each node in the Tree, with consideration to the fixed path length. In addition, since the path I'm looking for has the potential of going from left subtree to root to right subtree, I will have to consider 3 choices at each node. But this will result in a O(n*3^k) algorithm and I don't like that. Algorithm 2 I'm essentially thinking about using a modified version of Dijkstra's Algorithm in order to consider a fixed path length. Since I'm looking for heaviest and Dijkstra's Algorithm finds the lightest, I'm planning on negating all edge weights before starting the traversal. Actually... this doesn't make sense since I'd have to run Dijkstra's on each node and that doesn't seem very efficient much better than the above algorithm. So I guess my main questions are several. Firstly, do the algorithms I've described above solve the problem at hand? I'm not totally certain the Dijkstra's version will work as Dijkstra's is meant for positive edge values. Now, I am sure there exist more clever/efficient algorithms for this... what is a better algorithm? I've read about "Using spine decompositions to efficiently solve the length-constrained heaviest path problem for trees" but that is really complicated and I don't understand it at all. Are there other algorithms that tackle this problem, maybe not as efficiently as spine decomposition but easier to understand? Thanks.

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• What does the q in a q-grammar stand for?

  - by Aru

  So I've been reading sites and the classic books on compilers, reading about s-grammar and q-grammars I wondered what the s and q stand for, I think the s stands for simple grammar. While the q...well, I have no idea. What does the q in a q-grammar stand for?

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• What is a data structure for quickly finding non-empty intersections of a list of sets?

  - by Andrey Fedorov

  I have a set of N items, which are sets of integers, let's assume it's ordered and call it I[1..N]. Given a candidate set, I need to find the subset of I which have non-empty intersections with the candidate. So, for example, if: I = [{1,2}, {2,3}, {4,5}] I'm looking to define valid_items(items, candidate), such that: valid_items(I, {1}) == {1} valid_items(I, {2}) == {1, 2} valid_items(I, {3,4}) == {2, 3} I'm trying to optimize for one given set I and a variable candidate sets. Currently I am doing this by caching items_containing[n] = {the sets which contain n}. In the above example, that would be: items_containing = [{}, {1}, {1,2}, {2}, {3}, {3}] That is, 0 is contained in no items, 1 is contained in item 1, 2 is contained in itmes 1 and 2, 2 is contained in item 2, 3 is contained in item 2, and 4 and 5 are contained in item 3. That way, I can define valid_items(I, candidate) = union(items_containing[n] for n in candidate). Is there any more efficient data structure (of a reasonable size) for caching the result of this union? The obvious example of space 2^N is not acceptable, but N or N*log(N) would be.

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• Git dirctet acyclic graph - children know their parents but not the other way around

  - by dayscott

  Git is implemented as a directed acyclic graph. Children know their parents but not the other way round. This makes sense because i can reach every commit only through a branch or a tag ( generally speaking through a reference). That's how i traverse the tree. What other reasons had the developers of Git to make "the children know their parents but not the other way around"?/ What are the key benefits of this?

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• Throughput measurements

  - by dotsid

  I wrote simple load testing tool for testing performance of Java modules. One problem I faced is algorithm of throughput measurements. Tests are executed in several thread (client configure how much times test should be repeated), and execution time is logged. So, when tests are finished we have following history: 4 test executions 2 threads 36ms overall time - idle * test execution 5ms 9ms 4ms 13ms T1 |-*****-*********-****-*************-| 3ms 6ms 7ms 11ms T2 |-***-******-*******-***********-----| <-----------------36ms---------------> For the moment I calculate throughput (per second) in a following way: 1000 / overallTime * threadCount. But there is problem. What if one thread will complete it's own tests more quickly (for whatever reason): 3ms 3ms 3ms 3ms T1 |-***-***-***-***----------------| 3ms 6ms 7ms 11ms T2 |-***-******-*******-***********-| <--------------32ms--------------> In this case actual throughput is much better because of measured throughput is bounded by the most slow thread. So, my question is how should I measure throughput of code execution in multithreaded environment.

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• efficacy of register allocation algorithms!

  - by aksci

  i'm trying to do a research/project on register allocation using graph coloring where i am to test the efficiency of different optimizing register allocation algorithms in different scenarios. how do i start? what are the prerequisites and the grounds with which i can test them. what all algos can i use? thank you!

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• determine if intersection of a set with conjunction of two other sets is empty

  - by koen

  For any three given sets A, B and C: is there a way to determine (programmatically) whether there is an element of A that is part of the conjunction of B and C? example: A: all numbers greater than 3 B: all numbers lesser than 7 C: all numbers that equal 5 In this case there is an element in set A, being the number 5, that fits. I'm implementing this as specifications, so this numerical range is just an example. A, B, C could be anything.

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• What is Turing Complete?

  - by david

  What does the expression Turing Complete means? Can you give a simple explanation, without going into too much theoretical details?

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• Asymptotic runtime of list-to-tree function

  - by Deestan

  I have a merge function which takes time O(log n) to combine two trees into one, and a listToTree function which converts an initial list of elements to singleton trees and repeatedly calls merge on each successive pair of trees until only one tree remains. Function signatures and relevant implementations are as follows: merge :: Tree a -> Tree a -> Tree a --// O(log n) where n is size of input trees singleton :: a -> Tree a --// O(1) empty :: Tree a --// O(1) listToTree :: [a] -> Tree a --// Supposedly O(n) listToTree = listToTreeR . (map singleton) listToTreeR :: [Tree a] -> Tree a listToTreeR [] = empty listToTreeR (x:[]) = x listToTreeR xs = listToTreeR (mergePairs xs) mergePairs :: [Tree a] -> [Tree a] mergePairs [] = [] mergePairs (x:[]) = [x] mergePairs (x:y:xs) = merge x y : mergePairs xs This is a slightly simplified version of exercise 3.3 in Purely Functional Data Structures by Chris Okasaki. According to the exercise, I shall now show that listToTree takes O(n) time. Which I can't. :-( There are trivially ceil(log n) recursive calls to listToTreeR, meaning ceil(log n) calls to mergePairs. The running time of mergePairs is dependent on the length of the list, and the sizes of the trees. The length of the list is 2^h-1, and the sizes of the trees are log(n/(2^h)), where h=log n is the first recursive step, and h=1 is the last recursive step. Each call to mergePairs thus takes time (2^h-1) * log(n/(2^h)) I'm having trouble taking this analysis any further. Can anyone give me a hint in the right direction?

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• Could a truly random number be generated using pings to psuedo-randomly selected IP addresses?

  - by _ande_turner_

  The question posed came about during a 2nd Year Comp Science lecture while discussing the impossibility of generating numbers in a deterministic computational device. This was the only suggestion which didn't depend on non-commodity-class hardware. Subsequently nobody would put their reputation on the line to argue definitively for or against it. Anyone care to make a stand for or against. If so, how about a mention as to a possible implementation?

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• The Immerman-Szelepcsenyi Theorem

  - by Daniel Lorch

  In the Immerman-Szelepcsenyi Theorem, two algorithms are specified that use non-determinisim. There is a rather lengthy algorithm using "inductive counting", which determines the number of reachable configurations for a given non-deterministic turing machine. The algorithm looks like this: Let m_{i+1}=0 For all configurations C Let b=0, r=0 For all configurations D Guess a path from I to D in at most i steps If found Let r=r+1 If D=C or D goes to C in 1 step Let b=1 If r<m_i halt and reject Let m_{i+1}=m_{i+1}+b I is the starting configuration. m_i is the number of configurations reachable from the starting configuration in i steps. This algorithm only calculates the "next step", i.e. m_i+1 from m_i. This seems pretty reasonable, but since we have nondeterminisim, why don't we just write: Let m_i = 0 For all configurations C Guess a path from I to C in at most i steps If found m_i = m_i + 1 What is wrong with this algorithm? I am using nondeterminism to guess a path from I to C, and I verify reachability I am iterating through the list of ALL configurations, so I am sure to not miss any configuration I respect space bounds I can generate a certificate (the list of reachable configs) I believe I have a misunderstanding of the "power" of non-determinisim, but I can't figure out where to look next. I am stuck on this for quite a while and I would really appreciate any help.

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• Are mathematical Algorithms protected by copyright?

  - by analogy

  I wish to implement an algorithm which i read in a journal paper in my software (commercial). I want to know if this is allowed or not. The algorithm in question is described in http://arxiv.org/abs/0709.2938 It is a very simple algorithm and a number of implementations exist in python (http://igraph.sourceforge.net/) and java. One of them is in gpl another which i got from a different researcher and had no license attached. There are significant differences in two implementations, e.g. second one uses threads and multiple cores. It is possible to rewrite/ (not translate) the algorithm. So can I use it in my software or on a server for commercial purpose. Thanks UPDATE: I am completely aware of copyright on the text of paper, it was published in phys rev E. I am concerned with use of the algorithm, in commercial software. Also the publication means that unless the patent has been already filed. The method has been disclosed publicly hence barring patent in future. Also the GPL implementation is not by authors themselves but comes from a third party. Finally i am not using the GPL implementation but creating my own using C++.

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• How to randomize a sorted list?

  - by Faken

  Here's a strange question for you guys, I have a nice sorted list that I wish to randomize. How would i go about doing that? In my application, i have a function that returns a list of points that describe the outline of a discretized object. Due to the way the problem is solved, the function returns a nice ordered list. i have a second boundary described in math and want to determine if the two objects intersect each other. I simply itterate over the points and determine if any one point is inside the mathematical boundary. The method works well but i want to increase speed by randomizing the point data. Since it is likely that that my mathematical boundary will be overlapped by a series of points that are right beside each other, i think it would make sense to check a randomized list rather than iterating over a nice sorted one (as it only takes a single hit to declare an intersection). So, any ideas on how i would go about randomizing an ordered list?

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• How do I create a good evaluation function for a new board game?

  - by A. Rex

  I write programs to play board game variants sometimes. The basic strategy is standard alpha-beta pruning or similar searches, sometimes augmented by the usual approaches to endgames or openings. I've mostly played around with chess variants, so when it comes time to pick my evaluation function, I use a basic chess evaluation function. However, now I am writing a program to play a completely new board game. How do I choose a good or even decent evaluation function? The main challenges are that the same pieces are always on the board, so a usual material function won't change based on position, and the game has been played less than a thousand times or so, so humans don't necessarily play it enough well yet to give insight. (PS. I considered a MoGo approach, but random games aren't likely to terminate.) Any ideas? Game details: The game is played on a 10-by-10 board with a fixed six pieces per side. The pieces have certain movement rules, and interact in certain ways, but no piece is ever captured. The goal of the game is to have enough of your pieces in certain special squares on the board. The goal of the computer program is to provide a player which is competitive with or better than current human players.

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• Parent Child Relationships with Fluent NHibernate?

  - by ElHaix

  I would like to create a cascading tree/list of N number of children for a given parent, where a child can also become a parent. Given the following data structure: CountryType=1; ColorType=3; StateType=5 6,7,8 = {Can, US, Mex} 10, 11, 12 = {Red, White, Blue} 20,21,22= {California, Florida, Alberta} TreeID ListTypeID ParentTreeID ListItemID 1 1 Null 6 (Canada is a Country) 2 1 Null 7 (US is a Country) 3 1 Null 8 (Mexico is a Country) 4 3 3 10 (Mexico has Red) 5 3 3 11 (Mexico has White) 6 5 1 22 (Alberta is in Canada) 7 5 7 20 (California is in US) 8 5 7 21 (Florida is in US) 9 3 6 10 (Alberta is Red) 10 3 6 12 (Alberta is Blue) 11 3 2 10 (US is Red) 12 3 2 11 (Us is Blue) How would this be represented in Fluent NHibernate classes? Some direction would be appreciated. Thanks.

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