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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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  • 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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  • 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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  • 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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  • What data stucture should I use for BigInt class

    - by user1086004
    I would like to implement a BigInt class which will be able to handle really big numbers. I want only to add and multiply numbers, however the class should also handle negative numbers. I wanted to represent the number as a string, but there is a big overhead with converting string to int and back for adding. I want to implement addition as on the high school, add corresponding order and if the result is bigger than 10, add the carry to next order. Then I thought that it would be better to handle it as a array of unsigned long long int and keep the sign separated by bool. With this I'm afraid of size of the int, as C++ standard as far as I know guarantees only that int < float < double. Correct me if I'm wrong. So when I reach some number I should move in array forward and start adding number to the next array position. Is there any data structure that is appropriate or better for this? Thanks in advance.

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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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  • 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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  • 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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  • 6^x = 5 equation, how to solve it?

    - by Tom
    If it would be 6^x = 1 or 6^x = 6 or 6^x = 36 it would be extremely easy, but how to solve this equation: 6^x = 5 I don't need an answer, I want to find out how to solve equations like this one, I need solution. Thanks.

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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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  • 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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  • simple rank formula

    - by Graham
    I'm looking for a mathmatical ranking formula. Sample is 2008 2009 2010 A 5 6 4 B 6 7 5 C 7 8 2 I want to add a rank column for each period code field rank 2008 2009 2010 2008 2009 2010 B 6 7 5 2 1 1 A 5 6 4 3 2 2 C 7 2 2 1 3 3 please do not reply with methods that loop thru the rows and columns, incrementing the rank value as it goes, that's easy. I'm looking for a formula much like finding the percent total (item / total). I know i've seen this before but an havning a tough time locating it. Thanks in advance!

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  • Why isnt int pow(int base, int exponent) in the standard C++ libraries?

    - by Dan O
    I feel like I must just be unable to find it. Is there any reason that the c++ pow function does not implement the "power" function for anything except floats and doubles? I know the implementation is trivial, I just feel like I'm doing work that should be in a standard library. A robust power function (ie handles overflow in some consistent, explicit way) is not fun to write.

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  • getting the value of a filter at an arbitrary time

    - by Andiih
    Context: I'm trying to improve the values returned by the iPhone CLLocationManager, although this is a more generally applicable problem. The key is that CLLocationManger returns data on current velocity as and when it feels like it, rather than at a fixed sample rate. I'd like to use a feedback equation to improve accuracy v=(k*v)+(1-k)*currentVelocity where currentVelocity is the speed returned by didUpdateToLocation:fromLocation: and v is the output velocity (and also used for the feedback element). Because of the "as and when" nature of didUpdateToLocation:fromLocation: I could calculate the time interval since it was last called, and do something like for (i=0;i<timeintervalsincelastcalled;i++) v=(k*v)+(1-k)*currentVelocity which would work, but is wasteful of cycles. Especially as I probably want timeintervalsincelastcalled to be measured as 10ths of a second. Is there a way to solve this without the loop ? i.e. rework (integrate?) the formula so I put an interval into the equation and get the same answer as I would have by iteration ?

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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 implement a grapher in C#

    - by iansinke
    So I'm writing a graphing calculator. So far I have a semi-functional grapher, however, I'm having a hard time getting a good balance between accurate graphs and smooth looking curves. The current implementation (semi-pseudo-code) looks something like this: for (float i = GraphXMin; i <= GraphXMax; i++) { PointF P = new PointF(i, EvaluateFunction(Function, i) ListOfPoints.Add(P) } Graphics.DrawCurve(ListOfPoints) The problem with this is since it only adds a point at every integer value, graphs end up distorted when their turning points don't fall on integers (e.g. sin(x)^2). I tried incrementing i by something smaller (like 0.1), which works, but the graph looks very rough. I am using C# and GDI+. I have SmoothingMethod set to AntiAlias, so that's not the problem, as you can see from the first graph. Is there some sort of issue with drawing curves with a lot of points? Should the points perhaps be positioned exactly on pixels? I'm sure some of you have worked on something very similar before, so any suggestions? While you're at it, do you have any suggestions for graphing functions with asymptotes? e.g. 1/x^2 P.S. I'm not looking for a library that does all this - I want to write it myself.

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