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  • Finding the heaviest of N objects using M scales

    - by cpprulez
    We have N objects and M scales. It's up to us what the objects are, and we need to position the objects on the scales so that it is undoubtful which is the heaviest object. For example, if we have 3 objects: "a", "b", "c" and 2 scales, one possible solution is "a" "b", "b" = "c" (here "a" is the heaviest). I need an algorithm which generates such solutions given N and M. Also let's assume that "a" is always the heaviest object. I've lost a few hours figuring out how to do it, but no matter what I figure out, there's always cases which I miss. For example, another solution is: "a" + "c" = 2 * "b", "a" "c".

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  • Is OOP based on any branch of mathematics?

    - by ektrules
    I know relational databases are based on set-theory, functional programming is based on lambda calculus, logic programming is based on logic (of course :)), and now that I think of it; I'm not sure if imperative and generic programming is based on any particular branch of mathematics either.

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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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  • 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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  • optimized grid for rectangular items

    - by peterchen
    I have N rectangular items with an aspect ratio Aitem (X:Y). I have a rectangular display area with an aspect ratio Aview The items should be arranged in a table-like layout (i.e. r rows, c columns). what is the ideal grid rows x columns, so that individual items are largest? (rows * colums = N, of course - i.e. there may be "unused" grid places). A simple algorithm could iterate over rows = 1..N, calculate the required number of columns, and keep the row/column pair with the largest items. I wonder if there's a non-iterative algorithm, though (e.g. for Aitem = Aview = 1, rows / cols can be approximated by sqrt(N)).

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  • what is the best algorithm to use for this problem

    - by slim
    Equilibrium index of a sequence is an index such that the sum of elements at lower indexes is equal to the sum of elements at higher indexes. For example, in a sequence A: A[0]=-7 A[1]=1 A[2]=5 A[3]=2 A[4]=-4 A[5]=3 A[6]=0 3 is an equilibrium index, because: A[0]+A[1]+A[2]=A[4]+A[5]+A[6] 6 is also an equilibrium index, because: A[0]+A[1]+A[2]+A[3]+A[4]+A[5]=0 (sum of zero elements is zero) 7 is not an equilibrium index, because it is not a valid index of sequence A. If you still have doubts, this is a precise definition: the integer k is an equilibrium index of a sequence if and only if and . Assume the sum of zero elements is equal zero. Write a function int equi(int[] A); that given a sequence, returns its equilibrium index (any) or -1 if no equilibrium indexes exist. Assume that the sequence may be very long.

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  • Find the centroid of a polygon with weighted vertices

    - by Calle Kabo
    Hi, I know how to find the centroid (center of mass) of a regular polygon. This assumes that every part of the polygon weighs the same. But how do I calculate the centroid of a weightless polygon (made from aerogel perhaps :), where each vertex has a weight? Simplified illustration of what I mean using straight line: 5kg-----------------5kg ^center of gravity 10kg---------------5kg ^center of gravity offset du to weight of vertices Of course, I know how to calculate the center of gravity on a straight line with weighted vertices, but how do I do it on a polygon with weighted vertices? Thanks for your time!

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  • Can we find out the difference between 2 RGb colors to find out a 3rd color?

    - by AK
    2 colors are mixed together. If i have the RGB for the resultant color and RGB for one of the colors mixed, then somehow i could calculate the 2nd color? I will try to explain visually what i am trying to say. Here is a flickr link http://www.flickr.com/photos/48150615@N08/4407414157 I know that the circle in the middle has an opacity of 20% Is there any way to know the color value of the circle so that i can deduct that to get the same color value as the background color.

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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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  • C++ Compound Interest Exercise

    - by Lameste
    I'm a beginner trying to learn C++ using "C++ Primer Plus Sixth Edition". I'm on Chapter 5, going over loops. Anyways I was doing this programming exercise from the book, the problem is: Daphne invests $100 at 10% simple interest.That is, every year, the investment earns 10% of the original investment, or $10 each and every year: interest = 0.10 × original balance At the same time, Cleo invests $100 at 5% compound interest.That is, interest is 5% of the current balance, including previous additions of interest: interest = 0.05 × current balance Cleo earns 5% of $100 the first year, giving her $105.The next year she earns 5% of $105, or $5.25, and so on.Write a program that finds how many years it takes for the value of Cleo’s investment to exceed the value of Daphne’s investment and then displays the value of both investments at that time. Here is the code I have written for this exercise, I'm not getting good results though. #include <iostream> #include <array> double Daphne(int, double, double); double Chleo(double, double); int main() { using namespace std; int p = 100; //Principle double i1 = 0.1; // 10% interest rate double i2 = 0.05; // 5% interest rate double dInv = 0; //Daphnes investment double cInv = 0; // Chleos investment int t=1; //Starting at year 1 double s1 = 0; //Sum 1 for Daphne double s2 = 0; // Sum 2 for Chleo s1 = p + 10; //Initial interest (base case after year 1) for Daphne s2 = p + (i2*p); //Initial interest (base case after year 1) for Chleo /*cout << s1 << endl; cout << s2 << endl;*/ while (cInv < dInv) { dInv = Daphne(p, i1, s1); cInv = Chleo(i2, s2); t++; } cout << "The time taken for Chleos investment to exceed Daphnes was: " << t << endl; cout << "Daphnes investment at " << t << " years is: " << dInv << endl; cout << "Chleos invesment at " << t << " years is: " << cInv << endl; system("pause"); return 0; } double Daphne(int p, double i, double s1) { s1 = s1 + (p*i); return s1; } double Chleo(double i, double s2){ s2 = s2 + (s2*i); return s2; } Output from console: The time taken for Chleos investment to exceed Daphnes was: 1 Daphnes investment at 1 years is: 0 Chleos invesment at 1 years is: 0 Press any key to continue . . . Can anyone explain why I'm getting this current result? The while loop is supposed to continue executing statements until Chleo's investment exceeds Daphnes.

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  • Question about the mathematical properties of hashes

    - by levand
    Take a commonly used binary hash function - for example, SHA-256. As the name implies, it outputs a 256 bit value. Let A be the set of all possible 256 bit binary values. A is extremely large, but finite. Let B be the set of all possible binary values. B is infinite. Let C be the set of values obtained by running SHA-256 on every member of B. Obviously this can't be done in practice, but I'm guessing we can still do mathematical analysis of it. My Question: By necessity, C ? A. But does C = A?

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  • Pretty Pixel-level Picture Painting, Programatically

    - by dreeves
    My mac laptop has 1,024,000 pixels. What's the simplest way to turn my display completely black and go nuts with writing little programs to twiddle pixels to my heart's delight? To make it more concrete, say I wanted to implement the Chaos Game to draw a Sierpinski triangle, at the pixel level, with nothing else on the screen. What are ways to do that?

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  • Calculate percentage of up votes

    - by MakuraYami
    I have searched this site and Google and even though the idea is pretty simple I can't figure it out. I need to (like seen on YouTube) calculate the % of up-votes based on the amount up-votes and down-votes. I have two vars, $upvotes and $downvotes now i need to calculate $ratio For example $upvotes = 3; $downvotes = 1; The ratio here needs to be 75 (%) If you have $upvotes = 0; $downvotes = 100; It needs to be 0 (%) How do I calculate the percentage (in PHP)?

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  • Arrange points in sequence.

    - by Himadri
    I have some points in 3D which are in a single plane. I want to arrange them in clock wise or counter clockwise order. The points can create a concave or convex polygon in a single plane. Can any body give any suggestions?

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  • Efficient Multiplication of Varying-Length #s [Conceptual]

    - by Milan Patel
    Write the pseudocode of an algorithm that takes in two arbitrary length numbers (provided as strings), and computes the product of these numbers. Use an efficient procedure for multiplication of large numbers of arbitrary length. Analyze the efficiency of your algorithm. I decided to take the (semi) easy way out and use the Russian Peasant Algorithm. It works like this: a * b = a/2 * 2b if a is even a * b = (a-1)/2 * 2b + a if a is odd My pseudocode is: rpa(x, y){ if x is 1 return y if x is even return rpa(x/2, 2y) if x is odd return rpa((x-1)/2, 2y) + y } I have 3 questions: Is this efficient for arbitrary length numbers? I implemented it in C and tried varying length numbers. The run-time in was near-instant in all cases so it's hard to tell empirically... Can I apply the Master's Theorem to understand the complexity...? a = # subproblems in recursion = 1 (max 1 recursive call across all states) n / b = size of each subproblem = n / 1 - b = 1 (problem doesn't change size...?) f(n^d) = work done outside recursive calls = 1 - d = 0 (the addition when a is odd) a = 1, b^d = 1, a = b^d - complexity is in n^d*log(n) = log(n) this makes sense logically since we are halving the problem at each step, right? What might my professor mean by providing arbitrary length numbers "as strings". Why do that? Many thanks in advance

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  • Radius of multiple latitude/longitude points

    - by zekial
    I have a program that takes as input an array of lat/long points. I need to perform a check on that array to ensure that all of the points are within a certain radius. So, for example, the maximum radius I will allow is 100 miles. Given an array of lat/long (coming from a MySQL database, could be 10 points could be 10000) I need to figure out if they will all fit in a circle with radius of 100 miles. Kinda stumped on how to approach this. Any help would be greatly appreciated.

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  • How to turn this simple 10 digit hex number back into 8 digits?

    - by Babil
    The algorithm to convert input 8 digit hex number into 10 digit are following: Given that the 8 digit number is: '12 34 56 78' x1 = 1 * 16^8 * 2^3 x2 = 2 * 16^7 * 2^2 x3 = 3 * 16^6 * 2^1 x4 = 4 * 16^4 * 2^4 x5 = 5 * 16^3 * 2^3 x6 = 6 * 16^2 * 2^2 x7 = 7 * 16^1 * 2^1 x8 = 8 * 16^0 * 2^0 Final 10 digit hex is: = x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 = '08 86 42 98 E8' The problem is - how to go back to 8 digit hex from a given 10 digit hex (for example: 08 86 42 98 E8 to 12 34 56 78) Some sample input and output are following: input output 11 11 11 11 08 42 10 84 21 22 22 33 33 10 84 21 8C 63 AB CD 12 34 52 D8 D0 88 64 45 78 96 32 21 4E 84 98 62 FF FF FF FF 7B DE F7 BD EF

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