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• Things to do with supercomputer.

  - by BigBoss

  HI, Guys I wanted to create SuperComputer out of my 3 old pcs soon. There are bunch of techniquies available on net for doing this and I will be using one of them. What I would like to get suggestion is what is next !! Many of them suggest some mathematical calculation or some graphic image rendering, which still is to me so boring and not inspiring at all. Please try to suggest something out of box. I would post results of it when I am done. Cheers !

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• what is order notation f(n)=O(g(n))?

  - by Lopa

  2 questions: question 1: under what circumstances would this[O(f(n))=O(k.f(n))] be the most appropriate form of time-complexity analysis? question 2: working from mathematical definition of O notation, show that O(f(n))=O(k.f(n)), for positive constant k.? My view: For the first one I think it is average case and worst case form of time-complexity. am i right? and what else do i write in that? for the second one I think we need to define the function mathematically, so is the answer something like because the multiplication by a constant just corresponds to a readjustment of value of the arbitrary constant 'k' in definition of O.

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• How do I programmatically determine the current zoom level of a browser window?

  - by Mihai Fonoage

  Hi, I want to find out the zoom level of what is being displayed in a browser window based on the javascripts' window object properties (http://www.javascriptkit.com/jsref/window.shtml) to which I have access. I just can't seem to find the right mathematical formula for the zoom based on the inner width, page offset, etc. I found a solution, but that uses the document.body.getBoundingClientRect call which does not return anything in my case and for which I can't tell if there's a suitable replacement from the window properties. I am using Safari. Thank you, Mihai

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• Check if BigDecimal is integer value

  - by Adamski

  Can anyone recommend an efficient way of determining whether a BigDecimal is an integer value in the mathematical sense? At present I have the following code: private boolean isIntegerValue(BigDecimal bd) { boolean ret; try { bd.toBigIntegerExact(); ret = true; } catch (ArithmeticException ex) { ret = false; } return ret; } ... but would like to avoid the object creation overhead if necessary. Previously I was using bd.longValueExact() which would avoid creating an object if the BigDecimal was using its compact representation internally, but obviously would fail if the value was too big to fit into a long. Any help appreciated.

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• How to create a container that holds different types of function pointers in C++?

  - by Alex

  I'm doing a linear genetic programming project, where programs are bred and evolved by means of natural evolution mechanisms. Their "DNA" is basically a container (I've used arrays and vectors successfully) which contain function pointers to a set of functions available. Now, for simple problems, such as mathematical problems, I could use one type-defined function pointer which could point to functions that all return a double and all take as parameters two doubles. Unfortunately this is not very practical. I need to be able to have a container which can have different sorts of function pointers, say a function pointer to a function which takes no arguments, or a function which takes one argument, or a function which returns something, etc (you get the idea)... Is there any way to do this using any kind of container ? Could I do that using a container which contains polymorphic classes, which in their turn have various kinds of function pointers? I hope someone can direct me towards a solution because redesigning everything I've done so far is going to be painful.

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• Ruby RegEx not matching valid expression

  - by Matthew Carriere

  I have the following expression: ^\w(\s(+|-|\/|*)\s\w)*$ This simply looks to match a mathematical expression, where a user is prompted for terms separated by basic operators (ex: price + tax) The user may enter more than just 2 terms and one operator (ex: price + tax + moretax) I tested this expression in Rubular http://rubular.com/ With the terms: a + a (MATCH) a + a + a (MATCH) a + a + a + a a a + a a Everything works, but when I use it in Ruby it does not work! expression =~ /^\w(\s(+|-|\/|*)\s\w)*$/ I started picking the expression apart and noticed that if I remove the start of line caret it finds matches but isn't correct. a + a (MATCH) a a (MATCH) <-- this is not correct Why is this expression not working in Ruby code? (I am using Ruby 1.8.7 p174)

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• Inaccurate Logarithm in Python

  - by Avihu Turzion

  I work daily with Python 2.4 at my company. I used the versatile logarithm function 'log' from the standard math library, and when I entered log(2**31, 2) it returned 31.000000000000004, which struck me as a bit odd. I did the same thing with other powers of 2, and it worked perfectly. I ran 'log10(2**31) / log10(2)' and I got a round 31.0 I tried running the same original function in Python 3.0.1, assuming that it was fixed in a more advanced version. Why does this happen? Is it possible that there are some inaccuracies in mathematical functions in Python?

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• Code golf: Reverse Polish notation (postfix) evaluator

  - by Dario

  After having had code-golf contests on ordinary mathematical expressions, I just thought it would also be quite interesting how short an evaluation function for postfix notation (RPN) can be. Examples for RPN: 1 2 + == 3 1 2 + 3 * == 9 0 1 2 3 + + - 2 6 * + 3 / 1 - == 1 3 2 / 2.0 + == 3.5 To make things shorter, only +, -, * and /, all just in their binary version, must be supported. Operators/Operands are delimited by one space, divsions by zero don't have to be handled. The resulting code should be a function that takes the postfix string as input and returns the resulting number.

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• posmax: like argmax but gives the position(s) of the element x for which f[x] is maximal

  - by dreeves

  Mathematica has a built-in function ArgMax for functions over infinite domains, based on the standard mathematical definition. The analog for finite domains is a handy utility function. Given a function and a list (call it the domain of the function), return the element(s) of the list that maximize the function. Here's an example of finite argmax in action: http://stackoverflow.com/questions/471029/canonicalize-nfl-team-names/472213#472213 And here's my implementation of it (along with argmin for good measure): (* argmax[f, domain] returns the element of domain for which f of that element is maximal -- breaks ties in favor of first occurrence. *) SetAttributes[{argmax, argmin}, HoldFirst]; argmax[f_, dom_List] := Fold[If[f[#1]>=f[#2], #1, #2]&, First[dom], Rest[dom]] argmin[f_, dom_List] := argmax[-f[#]&, dom] First, is that the most efficient way to implement argmax? What if you want the list of all maximal elements instead of just the first one? Second, how about the related function posmax that, instead of returning the maximal element(s), returns the position(s) of the maximal elements?

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• Choice of programming language for learning data structures and algorithms

  - by bguiz

  Which programming language would you recommend to learn about data structures and algorithms in? Considering the follwing: Personal experience Language features (pointers, OO, etc) Suitability for learning DS & A concepts I ask because there are some books out there that are programming language-agnostic (written from a Mathematical perspective, and use pseudocode). If I learn from one of these I would like to work out the algorithms in a chosen language. Then, there are other books which introduce DS & A concepts with examples in a particular programming laguage - and I would follow these examples as well. Either way, I have to choose a language, and I would like to stick to one throughout. Which one best fits the bill.

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• maths: motion depending on time

  - by clamp

  hello, i have a mathematical problem: i have a function where the only parameter is the current time. the return should be a position which is used to place an object on a certain place. int position(int time) { int x = 0; //TODO implement x depending on time return x; } so basically the function is called every frame to put the object in motion. the motion should look like this (this is the actual question): a linear motion for time A, the object moves at constant speed no motion for time B, the object is stopped repeat at 1. thanks!

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• Statement hierarchy in programming languages

  - by sudo

  I quickly wrote an interpreter for some sort of experimental programing language i came up with, in PHP (yes, in PHP). The language itself doesn't have anything really special, I just wanted to give it a try. I got the basic things working (Hello World, input to output, string manipulation, arithmetics) but I'm getting stuck with the management of blocks and grouped statements. What I mean is: PHP and most other languages let you do this: ((2+2)*(8+2)+2), of course not only with mathematical computations. My program structure currently consists of a multidimensional array built like this: ID => Type (Identifier, String, Int, Newline, EOF, Comma, ...) Contents (If identifier, int or string) How could I allow statements to be executed in a defined order like in the PHP example above?

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• Math/numerical formula every computer programmer should know

  - by aaa

  This is a follow-up question to What should every programmer know and Is mathematics necessary. So the question is, as a computer programmer, what is the most important/useful mathematical or numerical formula that you use? By Formula I mean anything that involves less obvious manipulations, whenever binomial coefficients or bit hacks. I work with multidimensional arrays and various matrix representations. So for me most commonly used formulas are: A(i,j,k,..) = a[i + j*Dim0 + k*Dim0*Dim1 + ... to map indexes to one dimension ( which is basic address calculation which many people do not seem to know). And triangular number T(i) = (i*i + i)/2 which is related to binomial coefficients, used to calculate address in triangular matrixes and many other things. What is your workhorse formula that you think programmer should know?

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• TypeError: 'NoneType' object does not support item assignment

  - by R S John

  I am trying to do some mathematical calculation according to the values at particular index of a NumPy array with the following code X = np.arange(9).reshape(3,3) temp = X.copy().fill(5.446361E-01) ind = np.where(X < 4.0) temp[ind] = 0.5*X[ind]**2 - 1.0 ind = np.where(X >= 4.0 and X < 9.0) temp[ind] = (5.699327E-1*(X[ind]-1)**4)/(X[ind]**4) print temp But I am getting the following error Traceback (most recent call last): File "test.py", line 7, in <module> temp[ind] = 0.5*X[ind]**2 - 1.0 TypeError: 'NoneType' object does not support item assignment Would you please help me in solving this? Thanks

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• Flipping issue when interpolating Rotations using Quaternions

  - by uhuu

  I use slerp to interpolate between two quaternions representing rotations. The resulting rotation is then extracted as Euler angles to be fed into a graphics lib. This kind of works, but I have the following problem; when rotating around two (one works just fine) axes in the direction of the green arrow as shown in the left frame here the rotation soon jumps around to rotate from the opposite site to the opposite visual direction, as indicated by the red arrow in the right frame. This may be logical from a mathematical perspective (although not to me), but it is undesired. How could I achieve an interpolation with no visual flipping and changing of directions when rotating around more than one axis, following the green arrow at all times until the interpolation is complete? Thanks in advance.

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• DataType for storing a long serial number (10 bytes)

  - by CrimsonX

  We have a device which has a 10 byte serial number which must be read into our application and stored into a .net datatype. In the device it is stored as an unsigned 10-byte (80-bit) number. I don't expect we will be performing any mathematical operations on this number, but only displaying it to the user. The .NET framework doesn't have a built in UNIT128 to store this datatype. My suggestion for storing this datatype is to create a 10 element byte array and read in the data into this array. Are there any better solutions to this problem? Note: I have seen in this question that a GUID is a 128 byte signed integer, but it seems like a bad idea to use a GUID in this fashion. Any other suggestions?

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• Is there a list of language only character regions for UTF-8 somewhere?

  - by Brehtt

  I'm trying to analyze some UTF-8 encoded documents in a way that recognizes different language characters. For my approach to work I need to ignore non-language characters, such as control characters, mathematical symbols etc. Just trying to dissect the basic Latin section of the UTF standard has resulted in multiple regions, with characters like the division symbol being right in the middle of a range of valid Latin characters. Is there a list somewhere that identifies these regions? Or better yet, a Regex that defines the regions or something in C# that can identify the different characters?

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• set / line intersection solution

  - by Xavier

  I have two lists in python and I want to know if they intersect at the same index. Is there a mathematical way of solving this? For example if I have [9,8,7,6,5] and [3,4,5,6,7] I'd like a simple and efficient formula/algorithm that finds that at index 3 they intersect. I know I could do a search just wondering if there is a better way. I know there is a formula to solve two lines in y = mx + b form by subtracting them from each other but my "line" isn't truly a line because its limited to the items in the list and it may have curves. Any help is appreciated.

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• What application domains are CPU bound and will tend to benefit from multi-core technologies?

  - by Glomek

  I hear a lot of people talking about the revolution that is coming in programming due to multi-core processors and parallelism, but I can't shake the feeling that for most of us, CPU cycles aren't the bottleneck. Pretty much all of my programs have been I/O bound in one way or another (database, filesystem, network, user interaction, etc.) for a very long time. Now I can think of a few areas where CPU cycles are a limiting factor, like code breaking, graphics, sound, some forms of simulation (weather, physics, etc.), and some forms of mathematical research, but they all seem like fairly specialized application domains. My general impression is that most programs are still I/O bound and that for most of our industry CPUs have been plenty fast for quite a while now. Am I off my rocker? What other application domains are CPU bound today? Do any of them include a large portion of the programming population? In essence, I'm wondering whether the multi-core CPUs will impact very many of us, and if so, how?

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• Learning how to program real things.

  - by Sean

  How would you guys recommend I actually learn to program real things? I mean, I know how to do basic academic things. I can implement a templated stack/queue/map/etc. data structure in C++ or Java or whatever. I can make a text-based hangman game or whatever. Etc etc. But how can I learn to program something real, something useful? I've done project Euler up to question 100 or so, and I feel like that's given me more mathematical maturity but not programming maturity. Should I buy a book and follow exercises, struggle through interesting projects, etc, ? In short, how did you guys transition from academic exercises to real, fun and/or useful programs?

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• Django Asynchronous Processing

  - by freyrs

  Hello all, I have a bunch of Django requests which executes some mathematical computations ( written in C and executed via a Cython module ) which may take an indeterminate amount ( on the order of 1 second ) of time to execute. Also the requests don't need to access the database. Right now everything is synchronous ( using Gunicorn with sync worker types ) but I'd like to make this asynchronous and nonblocking. I am very new to asynchronous Django, and so my question is what is the best stack for doing this. Is this sort of process something a task queue is well suited for? Would anyone recommend Tornado + Celery + RabbitMQ, or perhaps something else? Thanks in advance!

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• 2d parabolic projectile

  - by ndg

  I'm looking to create a basic Javascript implementation of a projectile that follows a parabolic arc (or something close to one) to arrive at a specific point. I'm not particularly well versed when it comes to complex mathematics and have spent days reading material on the problem. Unfortunately, seeing mathematical solutions is fairly useless to me. I'm ideally looking for pseudo code (or even existing example code) to try to get my head around it. Everything I find seems to only offer partial solutions to the problem. In practical terms, I'm looking to simulate the flight of an arrow from one location (the location of the bow) to another. It strikes me there are two distinct problems here: determining the position of interception between the projectile and a (moving) target, and then calculating the trajectory of the projectile. Any help would be greatly appreciated.

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• How do we know the correct moves of Tower of Hanoi?

  - by Saqib

  We know that: In case of iterative solution: Alternating between the smallest and the next-smallest disks, follow the steps for the appropriate case: For an even number of disks: make the legal move between pegs A and B make the legal move between pegs A and C make the legal move between pegs B and C repeat until complete For an odd number of disks: make the legal move between pegs A and C make the legal move between pegs A and B make the legal move between pegs B and C repeat until complete In case of recursive solution: To move n discs from peg A to peg C: move n-1 discs from A to B. This leaves disc n alone on peg A move disc n from A to C move n-1 discs from B to C so they sit on disc n Now the questions are: How did we get this two solutions? Only by intuition? Or by logical/mathematical computation? If computation, how?

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• Prims vs Polys: what are the pros and cons of each?

  - by Richard Inglis

  I've noticed that most 3d gaming/rendering environments represent solids as a mesh of (usually triangular) 3d polygons. However some examples, such as Second Life, or PovRay use solids built from a set of 3d primitives (cube, sphere, cone, torus etc) on which various operations can be performed to create more complex shapes. So my question is: why choose one method over the other for representing 3d data? I can see there might be benefits for complex ray-tracing operations to be able to describe a surface as a single mathematical function (like PovRay does), but SL surely isn't attempting anything so ambitious with their rendering engine. Equally, I can imagine it might be more bandwidth-efficient to serve descriptions of generalised solids instead of arbitrary meshes, but is it really worth the downside that SL suffers from (ie modelling stuff is really hard, and usually the results are ugly) - was this just a bad decision made early in SL's development that they're now stuck with? Or is it an artefact of what's easiest to implement in OpenGL?

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• Any better algorithm possible here?

  - by Cupidvogel

  I am trying to solve this problem in Python. Noting that only the first kiss requires the alternation, any kiss that is not a part of the chain due to the first kiss can very well have a hug on the 2nd next person, this is the code I have come up with. This is just a simple mathematical calculation, no looping, no iteration, nothing. But still I am getting a timed-out message. Any means to optimize it? import psyco psyco.full() testcase = int(raw_input()) for i in xrange(0,testcase): n = int(raw_input()) if n%2: m = n/2; ans = 2 + 4*(2**m-1); ans = ans%1000000007; print ans else: m = n/2 - 1 ans = 2 + 2**(n/2) + 4*(2**m-1); ans = ans%1000000007 print ans

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