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  • Mathematically Find Max Value without Conditional Comparison

    - by Cnich
    ----------Updated ------------ codymanix and moonshadow have been a big help thus far. I was able to solve my problem using the equations and instead of using right shift I divided by 29. Because with 32bits signed 2^31 = overflows to 29. Which works! Prototype in PHP $r = $x - (($x - $y) & (($x - $y) / (29))); Actual code for LEADS (you can only do one math function PER LINE!!! AHHHH!!!) DERIVDE1 = IMAGE1 - IMAGE2; DERIVED2 = DERIVED1 / 29; DERIVED3 = DERIVED1 AND DERIVED2; MAX = IMAGE1 - DERIVED3; ----------Original Question----------- I don't think this is quite possible with my application's limitations but I figured it's worth a shot to ask. I'll try to make this simple. I need to find the max values between two numbers without being able to use a IF or any conditional statement. In order to find the the MAX values I can only perform the following functions Divide, Multiply, Subtract, Add, NOT, AND ,OR Let's say I have two numbers A = 60; B = 50; Now if A is always greater than B it would be simple to find the max value MAX = (A - B) + B; ex. 10 = (60 - 50) 10 + 50 = 60 = MAX Problem is A is not always greater than B. I cannot perform ABS, MAX, MIN or conditional checks with the scripting applicaiton I am using. Is there any way possible using the limited operation above to find a value VERY close to the max?

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  • Learning AES: the KeyBytes

    - by Tom Brito
    I got the following example from here: import java.security.Security; import javax.crypto.Cipher; import javax.crypto.spec.SecretKeySpec; public class MainClass { public static void main(String[] args) throws Exception { Security.addProvider(new org.bouncycastle.jce.provider.BouncyCastleProvider()); byte[] input = "www.java2s.com".getBytes(); byte[] keyBytes = new byte[] { 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17 }; SecretKeySpec key = new SecretKeySpec(keyBytes, "AES"); Cipher cipher = Cipher.getInstance("AES/ECB/PKCS7Padding", "BC"); System.out.println(new String(input)); // encryption pass cipher.init(Cipher.ENCRYPT_MODE, key); byte[] cipherText = new byte[cipher.getOutputSize(input.length)]; int ctLength = cipher.update(input, 0, input.length, cipherText, 0); ctLength += cipher.doFinal(cipherText, ctLength); System.out.println(new String(cipherText)); System.out.println(ctLength); // decryption pass cipher.init(Cipher.DECRYPT_MODE, key); byte[] plainText = new byte[cipher.getOutputSize(ctLength)]; int ptLength = cipher.update(cipherText, 0, ctLength, plainText, 0); ptLength += cipher.doFinal(plainText, ptLength); System.out.println(new String(plainText)); System.out.println(ptLength); } } I imagine that the byte[] keyBytes should be random generated, so I gone to test the max size before do it. When adding one more byte 0x18 to the array, the exception raised: InvalidKeyException: Key length not 128/192/256 bits. But the original 18 bytes (from 0 to 17) are not multiple of nither 128, 192 or 256. I would like to understand the math here.. can anyone explain me? Thanks!

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  • A function where small changes in input always result in large changes in output

    - by snowlord
    I would like an algorithm for a function that takes n integers and returns one integer. For small changes in the input, the resulting integer should vary greatly. Even though I've taken a number of courses in math, I have not used that knowledge very much and now I need some help... An important property of this function should be that if it is used with coordinate pairs as input and the result is plotted (as a grayscale value for example) on an image, any repeating patterns should only be visible if the image is very big. I have experimented with various algorithms for pseudo-random numbers with little success and finally it struck me that md5 almost meets my criteria, except that it is not for numbers (at least not from what I know). That resulted in something like this Python prototype (for n = 2, it could easily be changed to take a list of integers of course): import hashlib def uniqnum(x, y): return int(hashlib.md5(str(x) + ',' + str(y)).hexdigest()[-6:], 16) But obviously it feels wrong to go over strings when both input and output are integers. What would be a good replacement for this implementation (in pseudo-code, python, or whatever language)?

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  • How to create a magic square in PHP?

    - by TerranRich
    I'd like to try my hand at creating a Magic Square in PHP (i.e. a grid of numbers that all add up to the same value), but I really don't know where to start. I know of the many methods that create magic square, such as starting "1" at a fixed position, then moving in a specific direction with each iteration. But that doesn't create a truly randomized Magic Square, which is what I'm aiming for. I want to be able to generate an N-by-N Magic Square of N² numbers where each row and column adds up to N(N²+1)/2 (e.g. a 5x5 square where all rows/columns add up to 65 — the diagonals don't matter). Can anybody provide a starting point? I don't want anybody to do the work for me, I just need to know how to start such a project? I know of one generator, written in Java (http://www.dr-mikes-math-games-for-kids.com/how-to-make-a-magic-square.html) but the last Java experience I had was over 10 years ago before I quickly abandoned it. Therefore, I don't really understand what the code is actually doing. I did notice, however, that when you generate a new square, it shows the numbers 1-25 (for a 5x5 square), in order, before quickly generating a fresh randomized square.

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  • php calculate float HELP!!

    - by apis17
    help!! i have weird math calculation here. hope someone will explain. $a = 1.85/100; $b = 1.5/100; $c = 1.1/100; $d = 0.4/100; $e = 0.4/100; $f = 0.4/100; $g = 0.4/100; $h = $a + $b + $c + $d + $e + $f + $g; echo $h*100 ."<br>"; $i = $h-$a; $i = $i-$b; $i = $i-$c; $i = $i-$d; $i = $i-$e; $i = $i-$f; $i = $i-$g; echo $i; last $i value should be 0 but it returns 6.93889390391E-18

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  • Calculate total batch upload transfer percent with limited information

    - by GONeale
    Hi there, I have a system which uploads to a server file by file and displays a progress bar on file upload progress, then underneath a second progress bar which I want to indicate percentage of batch complete across all files queued to upload. Information and algorithms I can work out are: Bytes Sent / Total Bytes To Send = First progress bar (eg. 512KB of 1024KB (50%)) That works fine. However supposing I have two other files left to upload, but both file sizes are unknown (as this is only known once the file is about to commence upload, at which point it is compressed and file size is determined) how would I go about making my third progress bar? I didn't think this would be possible as I would need "Total Bytes Sent" / "Total Bytes To Send", to replicate the logic of my first progress bar on a larger scale, however I did get a version working: "Current file number we are on" / "total number of files to send" returning the percentage through the batch, however obviously will not incrementally update and it's pretty crude. So on further thinking I thought if I could incorporate the current file % with this algorithm I could perhaps get the correct progress percentage of my batch's current point. I tried this algorithm, but alas to no such avail (sorry to any math heads, it's probably quite apparent why it won't work) ("Current file number we are on" / "total number of files to send") * ("Bytes Sent" / "Total Bytes To Send") For example I thought I was on the right track when testing with this example: 2/3 (2nd of 3rd file) = 66% (this is right so far) but then when I added * 0.20 (for indicating only 20% of 2nd file has uploaded) we went back to 13%. What I need is only a little over 33%! I did try the inverse at 0.80 and a (2/3 * (2/3 * 0.2)) Can this be done without knowing entire bytes in batch to upload? Please help! Thank you!

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  • Python and a "time value of money" problem.

    - by jamieb
    (I asked this question earlier today, but I did a poor job of explaining myself. Let me try again) I have a client who is an industrial maintenance company. They sell service agreements that are prepaid 20 hour blocks of a technician's time. Some of their larger customers might burn through that agreement in two weeks while customers with fewer problems might go eight months on that same contract. I would like to use Python to help model projected sales revenue and determine how many billable hours per month that they'll be on the hook for. If each customer only ever bought a single service contract (never renewed) it would be easy to figure sales as monthly_revenue = contract_value * qty_contracts_sold. Billable hours would also be easy: billable_hrs = hrs_per_contract * qty_contracts_sold. However, how do I account for renewals? Assuming that 90% (or some other arbitrary amount) of customers renew, then their monthly revenue ought to grow geometrically. Another important variable is how long the average customer burns through a contract. How do I determine what the revenue and billable hours will be 3, 6, or 12 months from now, based on various renewal and burn rates? I assume that I'd use some type of recursive function but math was never one of my strong points. Any suggestions please? Edit: I'm thinking that the best way to approach this is to think of it as a "time value of money" problem. I've retitled the question as such. The problem is probably a lot more common if you think of "monthly sales" as something similar to annuity payments.

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  • How to determine Scale of Line Graph based on Pixels/Height?

    - by Dexter
    I have a problem due to my terrible math abilities, that I cannot figure out how to scale a graph based on the maximum and minimum values so that the whole graph will fit onto the graph-area (400x420) without parts of it being off the screen (based on a given equation by user). Let's say I have this code, and it automatically draws squares and then the line graph based on these values. What is the formula (what do I multiply) to scale it so that it fits into the small graphing area? vector<int> m_x; vector<int> m_y; // gets automatically filled by user equation or values int HeightInPixels = 420;// Graphing area size!! int WidthInPixels = 400; int best_max_y = GetMaxOfVector(m_y); int best_min_y = GetMinOfVector(m_y); m_row = 0; m_col = 0; y_magnitude = (HeightInPixels/(best_max_y+best_min_y)); // probably won't work magnitude = (WidthInPixels/(int)m_x.size()); m_col = m_row = best_max_y; // number of vertical/horizontal lines to draw ////x_magnitude = (WidthInPixels/(int)m_x.size())/2; Doesn't work well ////y_magnitude = (HeightInPixels/(int)m_y.size())/2; Doesn't work well ready = true; // we have values, graph it Invalidate(); // uses WM_PAINT

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  • Scala and Java BigDecimal

    - by geejay
    I want to switch from Java to a scripting language for the Math based modules in my app. This is due to the readability, and functional limitations of mathy Java. For e.g, in Java I have this: BigDecimal x = new BigDecimal("1.1"); BigDecimal y = new BigDecimal("1.1"); BigDecimal z = x.multiply(y.exp(new BigDecimal("2")); As you can see, without BigDecimal operator overloading, simple formulas get complicated real quick. With doubles, this looks fine, but I need the precision. I was hoping in Scala I could do this: var x = 1.1; var y = 0.1; print(x + y); And by default I would get decimal-like behaviour, alas Scala doesn't use decimal calculation by default. Then I do this in Scala: var x = BigDecimal(1.1); var y = BigDecimal(0.1); println(x + y); And I still get an imprecise result. Is there something I am not doing right in Scala? Maybe I should use Groovy to maximise readability (it uses decimals by default)?

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  • need help with Java solution /newbie

    - by Racket
    Hi, I'm new to programming in general so i'm trying to be as specific as possible in this question. There's this book that i'm doing some exercises on. I managed to do more than half of what they say, but it's just one input that I have been struggling to find out. I'll write the question and thereafter my code, "Write an application that creates and prints a random phone number of the form XXX-XXX-XXXX. Include the dashes in the output. Do not let the first three digits contain an 8 or 9 (but don't be more restrictive than that), and make sure that the second set of three digits is not greater than 742. Hint: Think through the easiest way to construct the phone number. Each diigit does not have to be determined separately." OK, the highlighted sentence is what i'm looking at. Here's my code: import java.util.Random; public class PP33 { public static void main (String[] args) { Random rand = new Random(); int num1, num2, num3; num1 = rand.nextInt(900) + 100; num2 = rand.nextInt(643) + 100; num3 = rand.nextInt(9000) + 1000; System.out.println(num1+"-"+num2+"-"+num3); } } How am I suppose to do this? I'm on chapter 3 so we have not yet discussed if statements etcetera, but Aliases, String class, Packages, Import declaration, Random Class, Math Class, Formatting output (decimal- & numberFormat), Printf, Enumeration & Wrapper classes + autoboxing. So consider answer the question based only on these assumptions, please. The code doesn't have any errors. Thank you!

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  • How can I intelligently group rows of integers for a faceted search?

    - by Alastair
    I'm not even quite sure what terms I should be using for what I want, so any advice on what I'm even asking for would be very welcome. Basically, my web site lists user-generated accommodations. Each has a rent price, which users will be able to query in our new faceted search box. Users search by city, and within each city I'd like to present a different rent grouping. That is to say that in City #1, if we have listings ranging from $200 - $1000, I'd like to present checkboxes for: less than $300 $301 - $500 $501 - $700 more than $700 However, if City #2 has values that range from $500 - $1500, I want the ranges above to change accordingly. So, if I say that I want 5 or 6 range options in each city, I think I have two options: Take the min and max values and just split the difference. I don't like this idea because one listing with a rent of $10,000 will throw the whole scale off. Intelligently calculate the ranges using means, medians etc. Number 2 is what I need help with. I'm a web developer that gets logic, but was never strong on math and statistics at school. Can anyone point me towards a guide that'll help me figure this out?

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  • Resource placement (optimal strategy)

    - by blackened
    I know that this is not exactly the right place to ask this question, but maybe a wise guy comes across and has the solution. I'm trying to write a computer game and I need an algorithm to solve this question: The game is played between 2 players. Each side has 1.000 dollars. There are three "boxes" and each player writes down the amount of money he is going to place into those boxes. Then these amounts are compared. Whoever placed more money in a box scores 1 point (if draw half point each). Whoever scores more points wins his opponents 1.000 dollars. Example game: Player A: [500, 500, 0] Player B: [333, 333, 334] Player A wins because he won Box A and Box B (but lost Box C). Question: What is the optimal strategy to place the money? I have more questions to ask (algorithm related, not math related) but I need to know the answer to this one first. Update (1): After some more research I've learned that these type of problems/games are called Colonel Blotto Games. I did my best and found few (highly technical) documents on the subject. Cutting it short, the problem I have (as described above) is called simple Blotto Game (only three battlefields with symmetric resources). The difficult ones are the ones with, say, 10+ battle fields with non-symmetric resources. All the documents I've read say that the simple Blotto game is easy to solve. The thing is, none of them actually say what that "easy" solution is.

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  • How to optimize shopping carts for minimal prices?

    - by tangens
    I have a list of items I want to buy. The items are offered by different shops and different prices. The shops have individual delivery costs. I'm looking for an optimal shopping strategy (and a java library supporting it) to purchase all of the items with a minimal total price. Example: Item1 is offered at Shop1 for $100, at Shop2 for $111. Item2 is offered at Shop1 for $90, at Shop2 for $85. Delivery cost of Shop1: $10 if total order < $150; $0 otherwise Delivery cost of Shop2: $5 if total order < $50; $0 otherwise If I buy Item1 and Item2 at Shop1 the total cost is $100 + $90 +$0 = $190. If I buy Item1 and Item2 at Shop2 the total cost is $111 + $85 +$0 = $196. If I buy Item1 at Shop1 and Item2 at Shop2 the total cost is $100 + $10 + $85 + $0 = 195. I get the minimal price if I order Item1 at Shop1 and Item2 at Shop2: $195 Question I need some hints which algorithms may help me to solve optimization problems of this kind for number of items about 100 and number of shops about 20. I already looked at apache-math and its optimization package, but I have no idea what algorithm to look for.

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  • Vector deltas and moving in unknown areas

    - by dekz
    Hi All, I was in need of a little math help that I can't seem to find the answer to, any links to documentation would be greatly appreciated. Heres my situation, I have no idea where I am in this maze, but I need to move around and find my way back to the start. I was thinking of implementing a waypoint list of places i've been offset from my start at 0,0. This is a 2D cartesian plane. I've been given 2 properties, my translation speed from 0-1 and my rotation speed from -1 to 1. -1 is very left and +1 is very right. These are speed and not angles so thats where my problem lies. If I'm given 0 as a translation speed and 0.2 I will continually turn to my right at a slow speed. How do I figure out the offsets given these 2 variables? I can store it every time I take a 'step'. I just need to figure out the offsets in x and y terms given the translations and rotation speeds. And the rotation to get to those points. Any help is appreciated.

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  • Finding the digit root of a number

    - by Jessica M.
    Study question is to find the digit root of a already provided number. The teacher provides us with the number 2638. In order to find the digit root you have to add each digit separately 2 + 6 + 3 + 8 = 19. Then you take the result 19 and add those two digits together 1 + 9 = 10. Do the same thing again 1 + 0 = 1. The digit root is 1. My first step was to use the variable total to add up the number 2638 to find the total of 19. Then I tried to use the second while loop to separate the two digits by using the % I have to try and solve the problem by using basic integer arithmetic (+, -, *, /). 1.Is it necessary and or possible to solve the problem using nested while loops? 2.Is my math correct? 3. As I wrote it here it does not run in Eclipse. Am I using the while loops correctly? import acm.program.*; public class Ch4Q7 extends ConsoleProgram { public void run(){ println("This program attempts to find the digit root of your number: "); int n = readInt("Please enter your number: "); int total = 0; int root = total; while (n > 0 ){ total = total + (n %10); n = (n / 10); } while ( total > 0 ){ root = total; total = ((total % 10) + total / 10); } println("your root should be " + root); } }

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  • Find if a user is facing a certain Location using Digital Compass by constructing a triangle and usi

    - by Aidan
    Hi Guys, I'm constructing a geolocation based application and I'm trying to figure out a way to make my application realise when a user is facing the direction of the given location (a particular long / lat co-ord). I've done some Googling and checked the SDK but can't really find anything for such a thing. Does anyone know of a way? To clarify Android knows my location, the second location and my orientation. What I want is a way for Android to recognise when my orientation is "facing" the second location (e.g within 90 Degrees or so). We're also assuming that the user is stationary and needs updates every second or so therefore getBearing(); is useless. Alright so we get it has to be math, there appears to be no simple SDK stuff we can use. I did some searching of my own and found Barycentric Co-ords http://www.blackpawn.com/texts/pointinpoly/default.html . So what I'm trying to do now is map the camera's field of view. For Example if the person is facing a certain direction the program should construct a triangle around that field of view, e.g it should make one vertices the phone's position and then go out either side for a set distance making the 2 end points vertices constructing a triangle. If I had this I could then apply Barycentric co-ords to see if the point lay within the newly constructed triangle. Idea's anyone? Example. I could get my current orientation, add 45 to it and go up X distance one side and subtact 45 and go up X distance the other side to find my 2 other points. Though, how would I make android know which way it should go "up" I guess? It would know its baring as this stage so I need it to recognise it's bearing and go out that direction.

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  • How to parse mathematical expressions involving parentheses

    - by Rob P.
    Please forgive my title, I really don't know how to phrase it better. This isn't a school assignment or anything, but I realize it's a mostly academic question. But, what I've been struggling to do is parse 'math' text and come up with an answer. For Example - I can figure out how to parse '5 + 5' or '3 * 5' - but I fail when I try to correctly chain operations together. (5 + 5) * 3 It's mostly just bugging me that I can't figure it out. If anyone can point me in a direction, I'd really appreciate it. EDIT Thanks for all of the quick responses. I'm sorry I didn't do a better job of explaining. First - I'm not using regular expressions. I also know there are already libraries available that will take, as a string, a mathematical expression and return the correct value. So, I'm mostly looking at this because, sadly, I don't "get it". Second - What I've tried doing (is probably misguided) but I was counting '(' and ')' and evaluating the deepest items first. In simple examples, this worked; but my code is not pretty and more complicated stuff crashes. When I 'calculated' the lowest level, I was modifying the string. So... (5 + 5) * 3 Would turn into 10 * 3 Which would then evaluate to 30 But it just felt 'wrong'. I hope that helps clarify things. I'll certainly check out the links provided.

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  • Calculating distance between two X,Y coordinates

    - by Umopepisdn
    I am writing a tool for a game that involves calculating the distance between two coordinates on a spherical plane 500 units across. That is, [0,0] through [499,499] are valid coordinates, and [0,0] and [499,499] are also right next to each other. Currently, in my application, I am comparing the distance between a city with an [X,Y] location respective to the user's own [X,Y] location, which they have configured in advance. To do this, I found this algorithm, which kind of works: Math.sqrt ( dx * dx + dy * dy ); Because sorting a paged list by distance is a useful thing to be able to do, I implemented this algorithm in a MySQL query and have made it available to my application using the following part of my SELECT statement: SQRT( POW( ( ".strval($sourceX)." - cityX ) , 2 ) + POW( ( ".strval($sourceY)." - cityY ) , 2 ) ) AS distance This works fine for many calculations, but does not take into account the fact that [0,0] and [499,499] are kitty-corner to one another. Is there any way I can tweak this algorithm to generate an accurate distance, given that 0 and 499 are adjacent? Thanks, -Umo

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  • Interview question : What is the fastest way to generate prime number recursively ?

    - by hilal
    Generation of prime number is simple but what is the fastest way to find it and generate( prime numbers) it recursively ? Here is my solution. However, it is not the best way. I think it is O(N*sqrt(N)). Please correct me, if I am wrong. public static boolean isPrime(int n) { if (n < 2) { return false; } else if (n % 2 == 0 & n != 2) { return false; } else { return isPrime(n, (int) Math.sqrt(n)); } } private static boolean isPrime(int n, int i) { if (i < 2) { return true; } else if (n % i == 0) { return false; } else { return isPrime(n, --i); } } public static void generatePrimes(int n){ if(n < 2) { return ; } else if(isPrime(n)) { System.out.println(n); } generatePrimes(--n); } public static void main(String[] args) { generatePrimes(200); }

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  • how to reverse an angle

    - by MissHalberd
    I am no mathematician, but I somehow got into game development as a hobby. Having never studied anything beyond basic math, I have a lot of trouble figuring out how to reverse the angle of something, facing to the opposite direction, among the X axis. One image says more than 1000 words though (specially uneducated words): http://img156.imageshack.us/i/wihwin.png/ I basically want to reverse the direction of cannon objects adhered to a robot. When the robot changes from facing right to facing left, I do (180 - angle) as everyone suggested me, but it reverses the angle...literally, making the cannons aim up when they are aiming down. So, I need to do something else, but it escapes my knowledge. Anyone would be so kind to help me with this? Oh, I use regular C by the way, in case there's something built-in specific to it. To put it in other words, I work in 2D, so I want an angle that is facing right to face left. 0 being "totally to the right", 180 "left", 90 "up" and 270 "down". I want something that is aiming with an angle of 91 to turn into 89 when reversed, literally. There's no Z axis present. EDIT: Thanks for the answers! Trying them out now. I'll post which one worked in a minute!

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  • Beginner Question ; About Prime Generation in "C" - What is wrong with my code ? -

    - by alorsoncode
    I'm a third year irregular CS student and ,i just realized that i have to start coding. I passed my coding classes with lower bound grades so that i haven't a good background in coding&programming. I'm trying to write a code that generates prime numbers between given upper and lower bounds. Not knowing C well, enforce me to write a rough code then go over it to solve. I can easily set up the logic for intended function but i probably create a wrong algorithm through several different ways. Here I share my last code, i intend to calculate that when a number gives remainder Zero , it should be it self and 1 , so that count==2; What is wrong with my implementation and with my solution generating style? I hope you will warm me up to programming world, i couldn't find enough motivation and courage to get deep into programming. Thanks in Advance :) Stdio and Math.h is Included int primegen(int down,int up) { int divisor,candidate,count=0,k; for(candidate=down;candidate<=up;candidate++) { for(divisor=1;divisor<=candidate;divisor++) { k=(candidate%divisor); } if (k==0) count++; if(count==2) { printf("%d\n", candidate); count=0; } else { continue; } } } int main() { primegen(3,15); return 0; }

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  • Value types of variable size

    - by YellPika
    I'm trying to code a small math library in C#. I wanted to create a generic vector structure where the user could define the element type (int, long, float, double, etc.) and dimensions. My first attempt was something like this... public struct Vector<T> { public readonly int Dimensions; public readonly T[] Elements; // etc... } Unfortunately, Elements, being an array, is also a reference type. Thus, doing this, Vector<int> a = ...; Vector<int> b = a; a[0] = 1; b[0] = 2; would result in both a[0] and b[0] equaling 2. My second attempt was to define an interface IVector<T>, and then use Reflection.Emit to automatically generate the appropriate type at runtime. The resulting classes would look roughly like this: public struct Int32Vector3 : IVector<T> { public int Element0; public int Element1; public int Element2; public int Dimensions { get { return 3; } } // etc... } This seemed fine until I found out that interfaces seem to act like references to the underlying object. If I passed an IVector to a function, and changes to the elements in the function would be reflected in the original vector. What I think is my problem here is that I need to be able to create classes that have a user specified number of fields. I can't use arrays, and I can't use inheritance. Does anyone have a solution? EDIT: This library is going to be used in performance critical situations, so reference types are not an option.

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  • Is there an algorithm for converting quaternion rotations to Euler angle rotations?

    - by Will Baker
    Is there an existing algorithm for converting a quaternion representation of a rotation to an Euler angle representation? The rotation order for the Euler representation is known and can be any of the six permutations (i.e. xyz, xzy, yxz, yzx, zxy, zyx). I've seen algorithms for a fixed rotation order (usually the NASA heading, bank, roll convention) but not for arbitrary rotation order. Furthermore, because there are multiple Euler angle representations of a single orientation, this result is going to be ambiguous. This is acceptable (because the orientation is still valid, it just may not be the one the user is expecting to see), however it would be even better if there was an algorithm which took rotation limits (i.e. the number of degrees of freedom and the limits on each degree of freedom) into account and yielded the 'most sensible' Euler representation given those constraints. I have a feeling this problem (or something similar) may exist in the IK or rigid body dynamics domains. Solved: I just realised that it might not be clear that I solved this problem by following Ken Shoemake's algorithms from Graphics Gems. I did answer my own question at the time, but it occurs to me it may not be clear that I did so. See the answer, below, for more detail. Just to clarify - I know how to convert from a quaternion to the so-called 'Tait-Bryan' representation - what I was calling the 'NASA' convention. This is a rotation order (assuming the convention that the 'Z' axis is up) of zxy. I need an algorithm for all rotation orders. Possibly the solution, then, is to take the zxy order conversion and derive from it five other conversions for the other rotation orders. I guess I was hoping there was a more 'overarching' solution. In any case, I am surprised that I haven't been able to find existing solutions out there. In addition, and this perhaps should be a separate question altogether, any conversion (assuming a known rotation order, of course) is going to select one Euler representation, but there are in fact many. For example, given a rotation order of yxz, the two representations (0,0,180) and (180,180,0) are equivalent (and would yield the same quaternion). Is there a way to constrain the solution using limits on the degrees of freedom? Like you do in IK and rigid body dynamics? i.e. in the example above if there were only one degree of freedom about the Z axis then the second representation can be disregarded. I have tracked down one paper which could be an algorithm in this pdf but I must confess I find the logic and math a little hard to follow. Surely there are other solutions out there? Is arbitrary rotation order really so rare? Surely every major 3D package that allows skeletal animation together with quaternion interpolation (i.e. Maya, Max, Blender, etc) must have solved exactly this problem?

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  • difference equations in MATLAB - why the need to switch signs?

    - by jefflovejapan
    Perhaps this is more of a math question than a MATLAB one, not really sure. I'm using MATLAB to compute an economic model - the New Hybrid ISLM model - and there's a confusing step where the author switches the sign of the solution. First, the author declares symbolic variables and sets up a system of difference equations. Note that the suffixes "a" and "2t" both mean "time t+1", "2a" means "time t+2" and "t" means "time t": %% --------------------------[2] MODEL proc-----------------------------%% % Define endogenous vars ('a' denotes t+1 values) syms y2a pi2a ya pia va y2t pi2t yt pit vt ; % Monetary policy rule ia = q1*ya+q2*pia; % ia = q1*(ya-yt)+q2*pia; %%option speed limit policy % Model equations IS = rho*y2a+(1-rho)yt-sigma(ia-pi2a)-ya; AS = beta*pi2a+(1-beta)*pit+alpha*ya-pia+va; dum1 = ya-y2t; dum2 = pia-pi2t; MPs = phi*vt-va; optcon = [IS ; AS ; dum1 ; dum2; MPs]; He then computes the matrix A: %% ------------------ [3] Linearization proc ------------------------%% % Differentiation xx = [y2a pi2a ya pia va y2t pi2t yt pit vt] ; % define vars jopt = jacobian(optcon,xx); % Define Linear Coefficients coef = eval(jopt); B = [ -coef(:,1:5) ] ; C = [ coef(:,6:10) ] ; % B[c(t+1) l(t+1) k(t+1) z(t+1)] = C[c(t) l(t) k(t) z(t)] A = inv(C)*B ; %(Linearized reduced form ) As far as I understand, this A is the solution to the system. It's the matrix that turns time t+1 and t+2 variables into t and t+1 variables (it's a forward-looking model). My question is essentially why is it necessary to reverse the signs of all the partial derivatives in B in order to get this solution? I'm talking about this step: B = [ -coef(:,1:5) ] ; Reversing the sign here obviously reverses the sign of every component of A, but I don't have a clear understanding of why it's necessary. My apologies if the question is unclear or if this isn't the best place to ask.

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  • JavaScript + Maths: Image zoom with CSS3 Transforms, How to set Origin? (with example)

    - by Sunday Ironfoot
    My Math skills really suck! I'm trying to implement an image zoom effect, a bit like how the Zoom works with Google Maps, but with a grid of fix position images. I've uploaded an example of what I have so far here: http://www.dominicpettifer.co.uk/Files/MosaicZoom.html (uses CSS3 transforms so only works with Firefox, Opera, Chrome or Safari) Use your mouse wheel to zoom in/out. The HTML source is basically an outer div with an inner-div, and that inner-div contains 16 images arranged using absolute position. It's going to be a Photo Mosaic basically. I've got the zoom bit working using CSS3 transforms: $(this).find('div').css('-moz-transform', 'scale(' + scale + ')'); ...however, I'm relying on the mouse X/Y position on the outer div to zoom in on where the mouse cursor is, similar to how Google Maps functions. The problem is that if you zoom right in on an image, move the cursor to the bottom/left corner and zoom again, instead of zooming to the bottom/left corner of the image, it zooms to the bottom/left of the entire mosaic. This has the effect of appearing to jump about the mosaic as you zoom in closer while moving the mouse around, even slightly. That's basically the problem, I want the zoom to work exactly like Google Maps where it zooms exactly to where your mouse cursor position is, but I can't get my head around the Maths to calculate the transform-origin: X/Y values correctly. Please help, been stuck on this for 3 days now. Here is the full code listing for the mouse wheel event: var scale = 1; $("#mosaicContainer").mousewheel(function(e, delta) { if (delta > 0) { scale += 1; } else { scale -= 1; } scale = scale < 1 ? 1 : (scale > 40 ? 40 : scale); var x = e.pageX - $(this).offset().left; var y = e.pageY - $(this).offset().top; $(this).find('div').css('-moz-transform', 'scale(' + scale + ')') .css('-moz-transform-origin', x + 'px ' + y + 'px'); return false; });

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