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  • Intersection of line and rectangle with maximum segment length

    - by Aarkan
    I have a vector represented by the slope m. Then there is rectangle (assume axis aligned), which is represented by top-left and bottom-right corner. Of course, there may be many lines with slope m and intersecting the given rectangle. The problem is to find out the line whose length of line intercept inside the rectangle is maximum among all such lines. i.e., if the line intersects rectangle at P1 and P2, then the problem is to find the equation of line for which length of P1P2 is maximum. I proceeded like this. Let the line is: y = m*x + c. Then find out the intersection with each side of rectangle and finding out the maxima for distance function between each pair of points. But it will only give me the length of line segment and there seem to be many corner cases to handle. Could anyone please suggest a better way to do this. Thanks in advance.

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  • Basic C++ code for multiplication of 2 matrix or vectors (C++ beginner)

    - by Ice
    I am a new C++ user and I am also doing a major in Maths so thought I would try implement a simple calculator. I got some code off the internet and now I just need help to multiply elements of 2 matrices or vectors. Matrixf multiply(Matrixf const& left, Matrixf const& right) { // error check if (left.ncols() != right.nrows()) { throw std::runtime_error("Unable to multiply: matrix dimensions not agree."); } /* I have all the other part of the code for matrix*/ /** Now I am not sure how to implement multiplication of vector or matrix.**/ Matrixf ret(1, 1); return ret; }

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  • Can a real number "cover" all integers within its range?

    - by macias
    Is there a guarantee that a real number (float, double, etc) can "cover" all integers within its range? By cover I mean, that for every integer within its range there is such real number that this equality holds: real == int Or in another example, let's say I have the biggest real number which is smaller than given integer. When I add "epsilon" will I get this number equal to given integer or bigger than integer? (I know that among real numbers you should not write comparisons as == for equality, I am simply asking for better understanding subject, not for coding comparisons.)

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  • 3D points to quaternions

    - by Hubrus
    For the simplicity, we'll consider two 3D points, that moves one relatively to other, in time. Let's say: at moment t0, we have P1(0,0,0) and P2(0,2,0) at moment t1, P1 is still (0,0,0) but P2 changed to (0,2,2). From what I've understood reading about quaternions, is that, at moment t0, Q1 (representing P1) and Q2 (representing P2) will be both (0, 0, 0, 0). But at the moment t1, Q2 will become something else (w, x, y, z). How do I calculate the Q2 at t1 moment? I've googled a lot on this subject, but I was able to find only rotation between quaternions. I will appreciate any guidance. Thanks!

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  • Shortest distance between points on a toroidally wrapped (x- and y- wrapping) map?

    - by mstksg
    I have a toroidal-ish Euclidean-ish map. That is the surface is a flat, Euclidean rectangle, but when a point moves to the right boundary, it will appear at the left boundary (at the same y value), given by x_new = x_old % width Basically, points are plotted based on: (x_new, y_new) = ( x_old % width, y_old % height) Think Pac Man -- walking off one edge of the screen will make you appear on the opposite edge. What's the best way to calculate the shortest distance between two points? The typical implementation suggests a large distance for points on opposite corners of the map, when in reality, the real wrapped distance is very close. The best way I can think of is calculating Classical Delta X and Wrapped Delta X, and Classical Delta Y and Wrapped Delta Y, and using the lower of each pair in the Sqrt(x^2+y^2) distance formula. But that would involve many checks, calculations, operations -- some that I feel might be unnecessary. Is there a better way?

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  • java random percentages

    - by erw
    I need to generate n percentages (integers between 0 and 100) such that the sum of all n numbers adds up to 100. If I just do nextInt() n times, each time ensuring that the parameter is 100 minus the previously accumulated sum, then my percentages are biased (i.e. the first generated number will usually be largest etc.). How do I do this in an unbiased way?

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  • Is there an easily available implementation of erf() for Python?

    - by rog
    I can implement the error function, erf, myself, but I'd prefer not to. Is there a python package with no external dependencies that contains an implementation of this function? I have found http://pylab.sourceforge.net/packages/included_functions.htmlthis but this seems to be part of some much larger package (and it's not even clear which one!). I'm sorry if this is a naive question - I'm totally new to Python.

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  • License key pattern detection?

    - by Ricket
    This is not a real situation; please ignore legal issues that you might think apply, because they don't. Let's say I have a set of 200 known valid license keys for a hypothetical piece of software's licensing algorithm, and a license key consists of 5 sets of 5 alphanumeric case-insensitive (all uppercase) characters. Example: HXDY6-R3DD7-Y8FRT-UNPVT-JSKON Is it possible (or likely) to extrapolate other possible keys for the system? What if the set was known to be consecutive; how do the methods change for this situation, and what kind of advantage does this give? I have heard of "keygens" before, but I believe they are probably made by decompiling the licensing software rather than examining known valid keys. In this case, I am only given the set of keys and I must determine the algorithm. I'm also told it is an industry standard algorithm, so it's probably not something basic, though the chance is always there I suppose. If you think this doesn't belong in Stack Overflow, please at least suggest an alternate place for me to look or ask the question. I honestly don't know where to begin with a problem like this. I don't even know the terminology for this kind of problem.

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  • Double # showing 0 on android

    - by Dave
    I'm embarrassed to ask this question, but after 45 minutes of not finding a solution I will resort to public humiliation. I have a number that is being divided by another number and I'm storing that number in a double variable. The numbers are randomly generated, but debugging the app shows that both numbers are in fact being generated. Lets just say the numbers are 476 & 733. I then take the numbers and divide them to get the percentage 476/733 = .64 I then print out the variable and it's always set to 0. I've tried using DecimalFormat and NumberFormat. No matter what I try though it always says the variable is 0. I know there is something simple that I'm missing, I just can't find it =/.

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  • Function to convert a z-score into a percentage

    - by Daniel
    Google doesn't want to help! I'm able to calculate z-scores, and we are trying to produce a function that given a z-score gives us a percent of the population in a normal distribution that would be under that z-score. All I can find are references to z-score to percentage tables. Any pointers?

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  • Wpf. Chart optimization. More than million points

    - by Evgeny
    I have custom control - chart with size, for example, 300x300 pixels and more than one million points (maybe less) in it. And its clear that now he works very slowly. I am searching for algoritm which will show only few points with minimal visual difference. I have link to component which have functionallity exactly what i need (2 million points demo): http://www.mindscape.co.nz/demo/SilverlightElements/demopage.html#/ChartOverviewPage I will be grateful for any matherials, links or thoughts how to realize such functionallity.

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  • How to calculate the state of a graph?

    - by zcb
    Given a graph G=(V,E), each node i is associated with 'Ci' number of objects. At each step, for every node i, the Ci objects will be taken away by the neighbors of i equally. After K steps, output the number of objects of the top five nodes which has the most objects. Some Constrains: |V|<10^5, |E|<2*10^5, K<10^7, Ci<1000 My current idea is: represent the transformation in each step with a matrix. This problem is converted to the calculation of the power of matrix. But this solution is much too slow considering |V| can be 10^5. Is there any faster way to do it?

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  • Dilemma with two types and operator +

    - by user35443
    I have small problem with operators. I have this code: public class A { public string Name { get; set; } public A() { } public A(string Name) { this.Name = Name; } public static implicit operator B(A a) { return new B(a.Name); } public static A operator+(A a, A b) { return new A(a.Name + " " + b.Name); } } public class B { public string Name { get; set; } public B() { } public B(string Name) { this.Name = Name; } public static implicit operator A(B b) { return new A(b.Name); } public static B operator +(B b, B a) { return new B(b.Name + " " + a.Name); } } Now I want to know, which's conversion operator will be called and which's addition operator will be called in this operation: new A("a") + new B("b"); Will it be operator of A, or of B? (Or both?) Thanks....

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  • Scaling range of values with negative numbers

    - by Pradeep Kumar
    How can I scale a set of values to fit a new range if they include negative numbers? For example, I have a set of numbers (-10, -9, 1, 4, 10) which have to scaled to a range [0 1], such that -10 maps to 0, and 10 maps to 1. The regular method for an arbitrary number 'x' would be: (x - from_min) * (to_max - to_min) / (from_max - from_min) + to_min but this does not work for negative numbers. Any help is appreciated. Thanks!!

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  • need help with some basic java.

    - by Racket
    Hi, I'm doing the first chapter exercises on my Java book and I have been stuck for a problem for a while now. I'll print the question, prompt/read a double value representing a monetary amount. Then determine the fewest number of each bill and coin needed to represent that amount, starting with the highest (assume that a ten dollar bill is the maximum size needed). For example, if the value entered is 47,63 (forty-seven dollars and sixty-three cents), and the program should print the equivalent amount as: 4 ten dollar bills 1 five dollar bills 2 one dollar bills 2 quarters 1 dimes 0 nickels 3 pennies" etc. I'm doing an example exactly as they said in order to get an idea, as you will see in the code. Nevertheless, I managed to print 4 dollars, and I can't figure out how to get "1 five dollar", only 7 dollars (see code). Please, don't do the whole code for me. I just need some advice in regards to what I said. Thank you. import java.util.Scanner; public class PP29 { public static void main (String[] args) { Scanner sc = new Scanner (System.in); int amount; double value; double test1; double quarter; System.out.println("Enter \"double\" value: "); value = sc.nextDouble(); amount = (int) value / 10; // 47,63 / 10 = 4. int amount2 = (int) value % 10; // 47 - 40 = 7 quarter = value * 100; // 47,63 * 100 = 4736 int sum = (int) quarter % 100; // 4763 / 100 => 4763-4700 = 63. System.out.println(amount); System.out.println(amount2); } }

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  • Replace for loop with formula

    - by hamax
    I have this loop that runs in O(end - start) and I would like to replace it with something O(1). If "width" wouldn't be decreasing, it would be pretty simple. for (int i = start; i <= end; i++, width--) if (i % 3 > 0) // 1 or 2, but not 0 z += width; start, end and width have positive values

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  • division problems

    - by David
    This line of code: System.out.println ("aray[j], "+aray[j]+", divided by sum, "+sum+", equals: aray[j]/sum: "+ aray[j]/sum) ; is yeilding this line of text: aray[j], 21, divided by sum, 100, equals: aray[j]/sum: 0 why is it doing this? (everything is right eccept that the answer should be .21)

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  • Recursively determine average value

    - by theva
    I have to calculate an average value of my simulation. The simulation is ongoing and I want (for each iteration) to print the current average value. How do I do that? I tried the code below (in the loop), but I do not think that the right value is calculated... int average = 0; int newValue; // Continuously updated value. if(average == 0) { average = newValue; } average = (average + newValue)/2; I also taught about store each newValue in an array and for each iteration summarize the whole array and do the calculation. However, I don't think that's a good solution, because the loop is an infinity loop so I can't really determine the size of the array. There is also a possibility that I am thinking too much and that the code above is actually correct, but I don't think so...

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  • Fastest method to define whether a number is a triangular number

    - by psihodelia
    A triangular number is the sum of the n natural numbers from 1 to n. What is the fastest method to find whether a given positive integer number is a triangular one? I suppose, there must be a hidden pattern in a binary representation of such numbers (like if you need to find whether a number is even/odd you check its least significant bit). Here is a cut of the first 1200th up to 1300th triangular numbers, you can easily see a bit-pattern here (if not, try to zoom out): (720600, '10101111111011011000') (721801, '10110000001110001001') (723003, '10110000100000111011') (724206, '10110000110011101110') (725410, '10110001000110100010') (726615, '10110001011001010111') (727821, '10110001101100001101') (729028, '10110001111111000100') (730236, '10110010010001111100') (731445, '10110010100100110101') (732655, '10110010110111101111') (733866, '10110011001010101010') (735078, '10110011011101100110') (736291, '10110011110000100011') (737505, '10110100000011100001') (738720, '10110100010110100000') (739936, '10110100101001100000') (741153, '10110100111100100001') (742371, '10110101001111100011') (743590, '10110101100010100110') (744810, '10110101110101101010') (746031, '10110110001000101111') (747253, '10110110011011110101') (748476, '10110110101110111100') (749700, '10110111000010000100') (750925, '10110111010101001101') (752151, '10110111101000010111') (753378, '10110111111011100010') (754606, '10111000001110101110') (755835, '10111000100001111011') (757065, '10111000110101001001') (758296, '10111001001000011000') (759528, '10111001011011101000') (760761, '10111001101110111001') (761995, '10111010000010001011') (763230, '10111010010101011110') (764466, '10111010101000110010') (765703, '10111010111100000111') (766941, '10111011001111011101') (768180, '10111011100010110100') (769420, '10111011110110001100') (770661, '10111100001001100101') (771903, '10111100011100111111') (773146, '10111100110000011010') (774390, '10111101000011110110') (775635, '10111101010111010011') (776881, '10111101101010110001') (778128, '10111101111110010000') (779376, '10111110010001110000') (780625, '10111110100101010001') (781875, '10111110111000110011') (783126, '10111111001100010110') (784378, '10111111011111111010') (785631, '10111111110011011111') (786885, '11000000000111000101') (788140, '11000000011010101100') (789396, '11000000101110010100') (790653, '11000001000001111101') (791911, '11000001010101100111') (793170, '11000001101001010010') (794430, '11000001111100111110') (795691, '11000010010000101011') (796953, '11000010100100011001') (798216, '11000010111000001000') (799480, '11000011001011111000') (800745, '11000011011111101001') (802011, '11000011110011011011') (803278, '11000100000111001110') (804546, '11000100011011000010') (805815, '11000100101110110111') (807085, '11000101000010101101') (808356, '11000101010110100100') (809628, '11000101101010011100') (810901, '11000101111110010101') (812175, '11000110010010001111') (813450, '11000110100110001010') (814726, '11000110111010000110') (816003, '11000111001110000011') (817281, '11000111100010000001') (818560, '11000111110110000000') (819840, '11001000001010000000') (821121, '11001000011110000001') (822403, '11001000110010000011') (823686, '11001001000110000110') (824970, '11001001011010001010') (826255, '11001001101110001111') (827541, '11001010000010010101') (828828, '11001010010110011100') (830116, '11001010101010100100') (831405, '11001010111110101101') (832695, '11001011010010110111') (833986, '11001011100111000010') (835278, '11001011111011001110') (836571, '11001100001111011011') (837865, '11001100100011101001') (839160, '11001100110111111000') (840456, '11001101001100001000') (841753, '11001101100000011001') (843051, '11001101110100101011') (844350, '11001110001000111110') For example, can you also see a rotated normal distribution curve, represented by zeros between 807085 and 831405?

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