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  • Arbitrary-precision arithmetic Explanation

    - by TT
    I'm trying to learn C and have come across the inability to work with REALLY big numbers (i.e., 100 digits, 1000 digits, etc.). I am aware that there exist libraries to do this, but I want to attempt to implement it myself. I just want to know if anyone has or can provide a very detailed, dumbed down explanation of arbitrary-precision arithmetic. Thanks!

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  • How can I evaluate the connectedness of my nodes?

    - by Travis Leleu
    I've got a space that has nodes that are all interconnected, based on a "similarity score". I would like to determine how "connected" a node is with the others. My purpose is to find nodes that are poorly connected to make sure that the backlink from the other node is prioritized. Perhaps an example would help. I've got a web page that links to my other pages based on a similarity score. Suppose I have the pages: A, B, C, ... A has a backlink from every other page, so it's very well connected. It also has links to all my other pages (each line in the graph is essentially bidirectional). B only has 1 backlink, from A. C has a link from A and D. I would like to make sure that the A-B link is prioritized over the A-C link (even if the similarity score between C and A is higher than B and A). In short, I would like to evaluate which nodes are least and best connected, so that I can mangle the results to my means. I believe this is Graph Connectedness, but I'm at a loss to develop a (simple) algorithm that will help me here. Simply counting the backlinks to a node may be a starting point -- but then how do I take the next step, which is to properly weight the links on the original node (A, in the example above)?

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  • How to solve generic algebra using solver/library programmatically? Matlab, Mathematica, Wolfram etc?

    - by DevDevDev
    I'm trying to build an algebra trainer for students. I want to construct a representative problem, define constraints and relationships on the parameters, and then generate a bunch of Latex formatted problems from the representation. As an example: A specific question might be: If y < 0 and (x+3)(y-5) = 0, what is x? Answer (x = -3) I would like to encode this as a Latex formatted problem like. If $y<0$ and $(x+constant_1)(y+constant_2)=0$ what is the value of x? Answer = -constant_1 And plug into my problem solver constant_1 > 0, constant_1 < 60, constant_1 = INTEGER constant_2 < 0, constant_2 > -60, constant_2 = INTEGER Then it will randomly construct me pairs of (constant_1, constant_2) that I can feed into my Latex generator. Obviously this is an extremely simple example with no real "solving" but hopefully it gets the point across. Things I'm looking for ideally in priority order * Solve algebra problems * Definition of relationships relatively straight forward * Rich support for latex formatting (not just writing encoded strings) Thanks!

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  • How to write an intersects for Shapes in android

    - by Rafael T
    I have an written an Object called Shape which has a Point representing the topLeftCorner and a Dimension with represents its width and height. To get the topRightCorner I can simply add the width to the topLeftPoint.x. I use to rotate them on a certain degree around their center. The problem after the rotation is, that my intersects(Shape) method fails, because it does not honor the rotation of the Shapes. The rotation will be the same for each Shape. My current implementation looks like this inside my Shape Object: public boolean intersects(Shape s){ // functions returning a Point of shape s return intersects(s.topLeft()) || intersects(s.topRight()) || intersects(s.bottomLeft()) || intersects(s.bottomRight()) || intersects(s.leftCenter()) || intersects(s.rightCenter()) || intersects(s.center()); } public boolean intersects(Point p){ return p.x >= leftX() && p.x <= rightX() && p.y >= topY() && p.y <= bottomY(); } Basically I need functions like rotatedLeftX() or rotatedTopRight() to work properly. Also for that calculation I think it doesn't matter when the topLeft point before a rotation of ie 90 will turn into topRight... I already read this and this Question here, but do not understand it fully.

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  • Python integer incrementing with ++

    - by Znarkus
    I've always laughed to myself when I looked back at my VB6 days, "What modern language doesn't allow incrementing with double plus signs?": number++ To my surprise I can't find anything about this in the Python docs. Must I really subject myself to number = number + 1? Doesn't people use the ++/-- notation? :-(

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  • How to get colliding effect or bouncy when ball hits the track.

    - by Chandan Shetty SP
    I am using below formula to move the ball circular, where accelX and accelY are the values from accelerometer, it is working fine. But the problem in this code is mRadius (I fixed its value to 50), i need to change mRadius according to accelerometer values and also i need bouncing effect when it touches the track. Currently i am developing code by assuming only one ball is on the board. float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); Here is the snap of the game i want to develop: Updated: I am sending the updated code... mRadius = 5; mRange = NSMakeRange(0,60); -(void) updateBall: (UIAccelerationValue) accelX withY:(UIAccelerationValue)accelY { float degrees = -atan2(accelX, accelY) * 180 / 3.14159; int x = cCentrePoint.x + mRadius * cos(degreesToRadians(degrees)); int y = cCentrePoint.y + mRadius * sin(degreesToRadians(degrees)); //self.targetRect is rect of ball Object self.targetRect = CGRectMake(newX, newY, 8, 9); self.currentRect = self.targetRect; //http://books.google.co.in/books?id=WV9glgdrrrUC&pg=PA455#v=onepage&q=&f=false static NSDate *lastDrawTime; if(lastDrawTime!=nil) { NSTimeInterval secondsSinceLastDraw = -([lastDrawTime timeIntervalSinceNow]); ballXVelocity = ballXVelocity + (accelX * secondsSinceLastDraw) * [self isTouchedTrack:mRadius andRange:mRange]; ballYVelocity = ballYVelocity + -(accelY * secondsSinceLastDraw) * [self isTouchedTrack:mRadius andRange:mRange]; distXTravelled = distXTravelled + secondsSinceLastDraw * ballXVelocity * 50; distYTravelled = distYTravelled + secondsSinceLastDraw * ballYVelocity * 50; CGRect temp = self.targetRect; temp.origin.x += distXTravelled; temp.origin.y += distYTravelled; int radius = (temp.origin.x - cCentrePoint.x) / cos(degreesToRadians(degrees)); if( !NSLocationInRange(abs(radius),mRange)) { //Colided with the tracks...Need a better logic here ballXVelocity = -ballXVelocity; } else { // Need a better logic here self.targetRect = temp; } //NSLog(@"angle = %f",degrees); } [lastDrawTime release]; lastDrawTime = [ [NSDate alloc] init]; } In the above code i have initialized mRadius and mRange(indicate track) to some constant for testing, i am not getting the moving of the ball as i expected( bouncing effect when Collided with track ) with respect to accelerometer. Help me to recognize where i went wrong or send some code snippets or links which does the similar job. I am searching for better logic than my code, if you found share with me.

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  • Interpolating height for a point inside a grid based on a discrete height function.

    - by fastrack20
    Hi, I have been wracking my brain to come up with a solution to this problem. I have a lookup table that returns height values for various points (x,z) on the grid. For instance I can calculate the height at A, B, C and D in Figure 1. However, I am looking for a way to interpolate the height at P (which has a known (x,z)). The lookup table only has values at the grid intervals, and P lies between these intervals. I am trying to calculate values s and t such that: A'(s) = A + s(C-A) B'(t) = B + t(P-B) I would then use the these two equations to find the intersection point of B'(t) with A'(s) to find a point X on the line A-C. With this I can calculate the height at this point X and with that the height at point P. My issue lies in calculating the values for s and t. Any help would be greatly appreciated.

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  • Efficiency of manually written loops vs operator overloads (C++)

    - by Sagekilla
    Hi all, in the program I'm working on I have 3-element arrays, which I use as mathematical vectors for all intents and purposes. Through the course of writing my code, I was tempted to just roll my own Vector class with simple +, -, *, /, etc overloads so I can simplify statements like: for (int i = 0; i < 3; i++) r[i] = r1[i] - r2[i]; // becomes: r = r1 - r2; Which should be more or less identical in generated code. But when it comes to more complicated things, could this really impact my performance heavily? One example that I have in my code is this: Manually written version: for (int j = 0; j < 3; j++) { p.vel[j] = p.oldVel[j] + (p.oldAcc[j] + p.acc[j]) * dt2 + (p.oldJerk[j] - p.jerk[j]) * dt12; p.pos[j] = p.oldPos[j] + (p.oldVel[j] + p.vel[j]) * dt2 + (p.oldAcc[j] - p.acc[j]) * dt12; } Using a Vector class with operator overloads: p.vel = p.oldVel + (p.oldAcc + p.acc) * dt2 + (p.oldJerk - p.jerk) * dt12; p.pos = p.oldPos + (p.oldVel + p.vel) * dt2 + (p.oldAcc - p.acc) * dt12; I am compiling my code for maximum possible speed, as it's extremely important that this code runs quickly and calculates accurately. So will me relying on my Vector's for these sorts of things really affect me? For those curious, this is part of some numerical integration code which is not trivial to run in my program. Any insight would be appreciated, as would any idioms or tricks I'm unaware of.

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  • Built in raytracing?

    - by acidzombie24
    Relating to this question i was wondering if .NET has any libs (or a function) i can use to detect if one point collides with another. I am not sure what angles i should use but is there some function like this func(point src, rect target, angle, distanceOfVision, listPointOrRectOfWalls) Pretty unlikely but i dont know a formula or how to start. Its a quick and dirty prototype. I am thinking of writing the func about but dropping angle and just make line of sight a rectangle and check if any points is between src and target.

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  • How to generate correlated binary variables

    - by jonalm
    Dear All I need to generate a series of N random binary variables with a given correlation function. Let x = {x_i} be a series of binary variables (taking the value 0 or 1, i running form 1 to N). The marginal probability is given Pr(x_i = 1) = p, and the values should be correlated in the following way E[ x_i x_j ] = const * |i-j|^-alfa where alfa is a positive number. Is it possible to generate a series like this? preferably in python.

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  • IE 8 Chinese encoding characters

    - by digitalbart
    Hello, I am unable to render Chinese characters in IE 8. I have researched this and I am aware of the meta tag to force compatibility mode. I am also aware of the language pack you can install. Finally I have seen that Microsoft actually forces IE7 compatibility mode on their Chinese website. http://www.microsoft.com/zh/cn/default.aspx I am wondering if anyone has any alternatives solutions to this problem. None them seem that appealing to me. I am using utf8 as my encoding and this problem only occurs in IE8. Thanks

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  • analyzing hashes

    - by calccrypto
    Is anyone willing to devote some time to helping me analyze a (hopefully cryptographically secure) hash? I honestly have no idea what im doing, so i need someone to show me how to, to teach me. almost all of the stuff ive found online have been really long, tedious, and vague the code is in python because for some reason i dont know c/c++. all i know about the hash: 1. there are no collisions (so far) and 2. differences between two similar inputs results in wildly different differences and please dont tell me that if i dont know what im doing, i shouldnt be doing it.

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  • How to create pulsating value from 0..1..0..1..0 etc for a given duration?

    - by pollux
    Hi I'm working on some code where I have a Time object with a member time. Time.time gives me the time since my application started in seconds (float value). Now I want to create a pulsating value between 0 and 1 and then from 1 to 0 again, which continues doing thins untill the application stops. I was thinking to use sin() but don't know what to pass to it as paramters to create this pulsing value. How would I create this pulsating value? Kind regards, Pollux

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  • How are a session identifiers generated?

    - by Asaf R
    Most web applications depend on some kind of session with the user (for instance, to retain login status). The session id is kept as a cookie in the user's browser and sent with every request. To make it hard to guess the next user's session these session-ids need to be sparse and somewhat random. The also have to be unique. The question is - how to efficiently generate session ids that are sparse and unique? This question has a good answer for unique random numbers, but it seems not scalable for a large range of numbers, simply because the array will end up taking a lot of memory.

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  • How do i know if this is random enough?

    - by David
    I wrote a program in java that rolls a die and records the total number of times each value 1-6 is rolled. I rolled 6 Million times. Here's the distribution: #of 0's: 0 #of 1's: 1000068 #of 2's: 999375 #of 3's: 999525 #of 4's: 1001486 #of 5's: 1000059 #of 6's: 999487 (0 wasn't an option.) Is this distribution consistant with random dice rolls? What objective statistical tests might confirm that the dice rolls are indeed random enough?

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  • Given an even number of vertices, how to find an optimum set of pairs based on proximity?

    - by Alex Z
    The problem: We have a set of n vertices in 3D euclidean space, and there is an even number of these vertices. We want to pair them up based on their proximity. In other words, we'd like to be able to find a set of vertex pairs, where the vertices in each pair are as close as possible together. We want to minimise sacrificing the proximity between the vertices of any other pairs as much as possible in doing this. I am not looking for the most optimal solution (if it even strictly exists/can be done), just a reasonable one that can be computed relatively quickly. A relatively awful brute force approach involves choosing a vertex and looping through the rest to find its nearest neighbor and then repeating until there are none left. Of course as we near the end of the list the closest vertex could be very far away, but it is the only choice, therefore this can fail badly on the third point above.

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  • is it possible to write a program which prints its own source code utilizing a "sequence-generating-

    - by guest
    is it possible to write a program which prints its own source code utilizing a "sequence-generating-function"? what i call a sequence-generating-function is simply a function which returns a value out of a specific interval (i.e. printable ascii-charecters (32-126)). the point now is, that this generated sequence should be the programs own source-code. as you see, implementing a function which returns an arbitrary sequence is really trivial, but since the returned sequence must contain the implementation of the function itself it is a highly non-trivial task. this is how such a program (and its corresponding output) could look like #include <stdio.h> int fun(int x) { ins1; ins2; ins3; . . . return y; } int main(void) { int i; for ( i=0; i<size of the program; i++ ) { printf("%c", fun(i)); } return 0; } i personally think it is not possible, but since i don't know very much about the underlying matter i posted my thoughts here. i'm really looking forward to hear some opinions!

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  • How to get points that intersect the treadline?

    - by chutsu
    Basically I did the Cavendish experiment, and I have a damped sinusoidal wave plotted on Excel. With Position (mm) against Time (s). My problem is that I have added a tread line through the wave function, and wish to calculate the points of which the wave function intersects the tread line. From this I will then be able to calculate the time period. At the moment I'm just having difficulty getting the intersects.. Thanks

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  • Calculate minimum moves to solve a puzzle

    - by Luke
    I'm in the process of creating a game where the user will be presented with 2 sets of colored tiles. In order to ensure that the puzzle is solvable, I start with one set, copy it to a second set, then swap tiles from one set to another. Currently, (and this is where my issue lies) the number of swaps is determined by the level the user is playing - 1 swap for level 1, 2 swaps for level 2, etc. This same number of swaps is used as a goal in the game. The user must complete the puzzle by swapping a tile from one set to the other to make the 2 sets match (by color). The order of the tiles in the (user) solved puzzle doesn't matter as long as the 2 sets match. The problem I have is that as the number of swaps I used to generate the puzzle approaches the number of tiles in each set, the puzzle becomes easier to solve. Basically, you can just drag from one set in whatever order you need for the second set and solve the puzzle with plenty of moves left. What I am looking to do is after I finish building the puzzle, calculate the minimum number of moves required to solve the puzzle. Again, this is almost always less than the number of swaps used to create the puzzle, especially as the number of swaps approaches the number of tiles in each set. My goal is to calculate the best case scenario and then give the user a "fudge factor" (i.e. 1.2 times the minimum number of moves). Solving the puzzle in under this number of moves will result in passing the level. A little background as to how I currently have the game configured: Levels 1 to 10: 9 tiles in each set. 5 different color tiles. Levels 11 to 20: 12 tiles in each set. 7 different color tiles. Levels 21 to 25: 15 tiles in each set. 10 different color tiles. Swapping within a set is not allowed. For each level, there will be at least 2 tiles of a given color (one for each set in the solved puzzle). Is there any type of algorithm anyone could recommend to calculate the minimum number of moves to solve a given puzzle?

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