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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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  • 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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  • summing functions handles in matlab

    - by user552231
    Hi I am trying to sum two function handles, but it doesn't work. for example: y1=@(x)(x*x); y2=@(x)(x*x+3*x); y3=y1+y2 The error I receive is "??? Undefined function or method 'plus' for input arguments of type 'function_handle'." This is just a small example, in reality I actually need to iteratively sum about 500 functions that are dependent on each other. EDIT The solution by Clement J. indeed works but I couldn't manage to generalize this into a loop and ran into a problem. I have the function s=@(x,y,z)((1-exp(-x*y)-z)*exp(-x*y)); And I have a vector v that contains 536 data points and another vector w that also contains 536 data points. My goal is to sum up s(v(i),y,w(i)) for i=1...536 Thus getting one function in the variable y which is the sum of 536 functions. The syntax I tried in order to do this is: sum=@(y)(s(v(1),y,z2(1))); for i=2:536 sum=@(y)(sum+s(v(i),y,z2(i))) end

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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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  • 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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  • 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 find the largest square in the number (Java)

    - by Ypsilon IV
    Hello everyone, I want to find the largest square in the number, but I am stuck at some point. I would really appreciate some suggestions. This is what I've done so far: I take the number on the input, factorize into prime numbers, and put the sequence of prime numbers to ArrayList. Numbers are sorted, in a sense, thus the numbers in the sequence are increasing. For example, 996 is 2 2 3 83 1000 is 2 2 2 5 5 5 100000 is 2 2 2 2 2 5 5 5 5 5 My idea now is to count number of occurrences of each elements in the sequence, so if the number of occurrences is divisible by two, then this is the square. In this way, I can get another sequence, where the right most element divisible by two is the largest square. What is the most efficient way to count occurrences in the ArrayList? Or is there any better way to find the largest square? Many thanks in advance!

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  • Subdividing 3D mesh into arbitrarily sized pieces

    - by Groky
    I have a mesh defined by 4 points in 3D space. I need an algorithm which will subdivide that mesh into subdivisions of an arbitrary horizontal and vertical size. If the subdivision size isn't an exact divisor of the mesh size, the edge pieces will be smaller. All of the subdivision algorithms I've found only subdivide meshes into exact powers of 2. Does anyone know of one that can do what I want? Failing that, my thoughts about a possible implementation is to rotate the mesh so that it is flat on the Z axis, subdivide in 2D and then translate back into 3D. That's because my mind finds 3D hard ;) Any better suggestions? Using C# if that makes any difference.

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  • Code Golf: All +-*/ Combinations for 3 integers

    - by Flash84x
    Write a program that takes 3 integers separated by spaces and perform every single combination of addition, subtraction, multiplication and division operations possible and display the result with the operation combination used. Example: $./solution 1 2 3 Results in the following output 1+2+3 = 6 1-2-3 = -4 1*2*3 = 6 1/2/3 = 0 (integer answers only, round up at .5) 1*2-3 = -1 3*1+2 = 5 etc... Order of operation rules apply, assume there will be no parenthesis used i.e. (3-1)*2 = 4 is not a combination, although you could implement this for "extra credit" For results where a divide by 0 occurs simply return NaN

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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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  • 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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  • Drawing Directed Acyclic Graphs: Using DAG property to improve layout/edge routing?

    - by Robert Fraser
    Hi, Laying out the verticies in a DAG in a tree form (i.e. verticies with no in-edges on top, verticies dependent only on those on the next level, etc.) is rather simple. However, is there a simple algorithm to do this that minimizes edge crossing? (For some graphs, it may be impossible to completely eliminate edge crossing.) A picture says a thousand words, so is there an algorithm that would suggest: instead of:

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  • How to detect if a certain range resides (partly) within an other range?

    - by Tom
    Lets say I've got two squares and I know their positions, a red and blue square: redTopX; redTopY; redBotX; redBotY; blueTopX; blueTopY; blueBotX; blueBotY; Now, I want to check if square blue resides (partly) within (or around) square red. This can happen in a lot of situations, as you can see in this image I created to illustrate my situation better: Note that there's always only one blue and one red square, I just added multiple so I didn't have to redraw 18 times. My original logic was simple, I'd check all corners of square blue and see if any of them are inside square red: if ( ((redTopX >= blueTopX) && (redTopY >= blueTopY) && (redTopX <= blueBotX) && (redTopY <= blueBotY)) || //top left ((redBotX >= blueTopX) && (redTopY >= blueTopY) && (redBotX <= blueBotX) && (redTopY <= blueBotY)) || //top right ((redTopX >= blueTopX) && (redBotY >= blueTopY) && (redTopX <= blueBotX) && (redBotY <= blueBotY)) || //bottom left ((redBotX >= blueTopX) && (redBotY >= blueTopY) && (redBotX <= blueBotX) && (redBotY <= blueBotY)) //bottom right ) { //blue resides in red } Unfortunately, there are a couple of flaws in this logic. For example, what if red surrounds blue (like in situation 1)? I thought this would be pretty easy but am having trouble coming up with a good way of covering all these situations.. can anyone help me out here? Regards, Tom

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  • Faster way to compare two sets of points in N-dimensional space?

    - by Amit
    List1 contains a high number (~7^10) of N-dimensional points (N <=10), List2 contains the same or fewer number of N-dimensional points (N <=10). My task is this: I want to check which point in List2 is closest (euclidean distance) to a point in List1 for every point in List1 and subsequently perform some operation on it. I have been doing it the simple- the nested loop way when I didn't have more than 50 points in List1, but with 7^10 points, this obviously takes up a lot of time. What is the fastest way to do this? Any concepts from Computational Geometry might help?

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  • troubles with integration on matlab

    - by user648666
    I'd like some help please I really need to solve this problem. Well before anything thank you for your time... My problem: I have a matrix (826x826 double) and I want to integrate this matrix with respect to a vector of (826x1 double) I don't have the functions of any of this. Is there a command or an algorithm to take the integral of a matrix with respect to a vector? Please I really need help, I'm such a newbie at matlab. Sincerely. George

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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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  • All non-prime factorings

    - by Tony Veijalainen
    Let's say we have numbers factors, for example 1260: >>> factors(1260) [2, 2, 3, 3, 5, 7] Which would be best way to do in Python combinations with every subproduct possible from these numbers, ie all factorings, not only prime factoring, with sum of factors less than max_sum? If I do combinations from the prime factors, I have to refactor remaining part of the product as I do not know the remaining part not in combination. Example results would be: [4, 3, 3, 5, 7] (one replacement) [3, 6, 14, 5] (two replacements)

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  • How to fix this 7% where 6% , 5% works great.

    - by Stackfan
    Case 1 (discount 6%): Subtotal: 750.00 Discount: 45.00 Handling cost: 24.32 21% VAT: 0.00 Total (this is the amount you will deposit): 729.32 Case 2 (discount 7%): Subtotal: 1250.00 Discount: 87.50 Handling cost: 39.88 21% VAT: 0.00 Total (this is the amount you will deposit): 1202.38 Where i am applying this formula: (729.32 - 0.35) / 1.034/ 0.94 = 750.00 (<<--- CORRECT ) ? (1202.38 - 0.35) / 1.034/ 0.93 = 1250.01 (<<--- My problem why not 1250.00) ? How to correct the 7% formula to get exactly 1250.00 ? Instead of fraction error.

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  • Fastest way to find the rotation of a vector

    - by kriss
    I have two 2D vectors, say u and v, defined by cartesian coordinates. Imagine that vectors are needles of a clock. I'm looking for the fastest way to find out, using python, if v is after or before u (or in other words find out in wich half plane is v, regarding to position of u). For the purpose of the problem if vectors are aligned answer should be before. It seems easy using some trigonometry, but I believe there should be a faster way using coordinates only. My test case: def after(u, v): """code here""" after((4,2), (6, 1)) : True after((4,2), (3, 3)) : False after((4,2), (2, 1)) : False after((4,2), (3, -3)) : True after((4,2), (-2, -5)) : True after((4,2), (-4, -2)) : False

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