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• Fitting maximum amount of shapes on a surface

  - by Fuu

  In industry, there is often a problem where you need to calculate the most efficient use of material, be it fabric, wood, metal etc. So the starting point is X amount of shapes of given dimensions, made out of polygons and/or curved lines, and target is another polygon of given dimensions. I assume many of the current CAM suites implement this, but having no experience using them or of their internals, what kind of computational algorithm is used to find the most efficient use of space? Can someone point me to a book or other reference that discusses this subject?

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• How to implement square root and exponentiation on arbitrary length numbers?

  - by tomp

  I'm working on new data type for arbitrary length numbers (only non-negative integers) and I got stuck at implementing square root and exponentiation functions (only for natural exponents). Please help. I store the arbitrary length number as a string, so all operations are made char by char. Please don't include advices to use different (existing) library or other way to store the number than string. It's meant to be a programming exercise, not a real-world application, so optimization and performance are not so necessary. If you include code in your answer, I would prefer it to be in either pseudo-code or in C++. The important thing is the algorithm, not the implementation itself. Thanks for the help.

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• Compute column widths in a HTML-like manner (based on cell contents)

  - by cipak

  Hi, I have a grid of data that I want to export to RTF, PDF etc. using various (and not perfect) PHP converters/generators. What I am missing most is the HTML table automatic adjustment of column widths based on the lengths of strings in the cells (strings contain line breaks which complicate things a bit, as they should be preserved). I need an algorithm that, given the contents of the cells (plain text), a total width of the table and an average width of a character, would return a width for each column. I wouldn't want to reinvent the wheel if something is already available. Of course it can't be perfect if the font is variable width, but an approximation would do just fine. Or maybe it could have a configurable table with widths for each character. Any hint would be appreciated. Thank you.

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• Anyone Know a Great Sparse One Dimensional Array Library in Python?

  - by TheJacobTaylor

  I am working on an algorithm in Python that uses arrays heavily. The arrays are typically sparse and are read from and written to constantly. I am currently using relatively large native arrays and the performance is good but the memory usage is high (as expected). I would like to be able to have the array implementation not waste space for values that are not used and allow an index offset other than zero. As an example, if my numbers start at 1,000,000 I would like to be able to index my array starting at 1,000,000 and not be required to waste memory with a million unused values. Array reads and writes needs to be fast. Expanding into new territory can be a small delay but reads and writes should be O(1) if possible. Does anybody know of a library that can do it? Thanks!

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• How do I generate a random string of up to a certain length?

  - by slavy13

  I would like to generate a random string (or a series of random strings, repetitions allowed) of length between 1 and n characters from some (finite) alphabet. Each string should be equally likely (in other words, the strings should be uniformly distributed). The uniformity requirement means that an algorithm like this doesn't work: alphabet = "abcdefghijklmnopqrstuvwxyz" len = rand(1, n) s = "" for(i = 0; i < len; ++i) s = s + alphabet[rand(0, 25)] (pseudo code, rand(a, b) returns a integer between a and b, inclusively, each integer equally likely) It doesn't work because shorter lengths are as likely as longer ones, meaning it's more likely to generate a shorter string than a longer one, so the result is not uniform.

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• Extend MySQL implementation of PiP Algorithm?

  - by Mike

  I need to make a point in polygon MySQL query. I already found these two great solutions: http://forums.mysql.com/read.php?23,286574,286574 MySQL implementation of ray-casting Algorithm? But these functions can only check if one point is inside a poly. I have a query where the PiP part should only be one part of the query and check for x points inside a polygon. Something like this: $points = list/array/whatever of points in language of favour SELECT d.name FROM data AS d WHERE d.name LIKE %red% // just bla bla // how to do this ? AND $points INSIDE d.polygon AND myWithin( $points, d.polygo ) // or UPDATE I tried it with MBR functions like this: SET @g1 = GeomFromText('Polygon((13.43971 52.55757,13.41293 52.49825,13.53378 52.49574, 13.43971 52.55757))'); SET @g2 = GeomFromText('Point(13.497834 52.540489)'); SELECT MBRContains(@g1,@g2); G2 should NOT be inside G1 but MBR says it is.

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• Getting plane slices from array data

  - by umanga

  Greetings all, I read 3d grid data (from multiple TIF images) into a structure as follows : typedef struct VolumeData{ int nx; int ny; int nz; unsigned char *data; // size is nx*ny*nz } Now I want to get the plane slices from this 1-D grid data: eg: unsigned char* getXYPlaneStack(VolumeData *vol,int z); I could implement above function because the *data array stores image stack. But i am having difficult time implement along the other axes: unsigned char* getYZPlaneStack(VolumeData *vol,int x); and unsigned char* getXZPlaneStack(VolumeData *vol,int y); any easy algorithm for this? 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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• A programming language for teaching data structures and algorithms with? [closed]

  - by Andreas Grech

  Possible Duplicate: Choice of programming language for learning data structures and algorithms Teachers have different opinions on what programming language they would choose to teach data structures and algorithms with. Some would prefer a lower level language such as C because it allows the student to learn more about what goes on beyond the abstractions in terms of memory allocation and deallocation and pointers and pointer arithmetic. On the other hand, others would say that they would prefer a higher level language like Java because it allows the student to learn more about the concepts of the structures and the algorithm design rather than 'waste time' and fiddle around with memory segmentation faults and all the blunders that come with languages where memory management is manual. What is your take on this issue? And also, please post any references you may know of that also discuss this argument.

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• 0/1 Knapsack with irrational weights

  - by user356106

  Consider the 0/1 knapsack problem. The standard Dynamic Programming algorithm applies only when the capacity as well as the weights to fill the knapsack with are integers/ rational numbers. What do you do when the capacity/weights are irrational? The issue is that we can't memoize like we do for integer weights because we may need potentially infinite decimal places for irrational weights - leading to an infinitely large number of columns for the Dynamic Programming Table . Is there any standard method for solving this? Any comments on the complexity of this problem? Any heuristics? What about associated recurrences like (for example): f(x)=1, for x< sqrt(2) f(x)=f(x-sqrt(2))+sqrt(3)

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• Best way to search for a saturation value in a sorted list

  - by AB Kolan

  A question from Math Battle. This particular question was also asked to me in one of my job interviews. " A monkey has two coconuts. It is fooling around by throwing coconut down from the balconies of M-storey building. The monkey wants to know the lowest floor when coconut is broken. What is the minimal number of attempts needed to establish that fact? " Conditions: if a coconut is broken, you cannot reuse the same. You are left with only with the other coconut Possible approaches/strategies I can think of are Binary break ups & once you find the floor on which the coconut breaks use upcounting from the last found Binary break up lower index. Window/Slices of smaller sets of floors & use binary break up within the Window/Slice (but on the down side this would require a Slicing algorithm of it's own.) Wondering if there are any other way to do this.

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• Given two lines on a plane, how to find integer points closest to their intersection?

  - by Lukasz Lew

  I can't solve it: You are given 8 integers: A, B, C representing a line on a plane with equation A*x + B*y = C a, b, c representing another line x, y representing a point on a plane The two lines are not parallel therefore divide plane into 4 pieces. Point (x, y) lies inside of one these pieces. Problem: Write a fast algorithm that will find a point with integer coordinates in the same piece as (x,y) that is closest to the cross point of the two given lines. Note: This is not a homework, this is old Euler-type task that I have absolutely no idea how to approach. Update: You can assume that the 8 numbers on input are 32-bit signed integers. But you cannot assume that the solution will be 32 bit.

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• Implementing a "flag as spam/offensive" system

  - by UltraVi01

  I am looking for a community moderated way of managing/eliminating spam and offensive content. Functionality similar to StackOverflow and many other sites seems like a good way to go. Although I'm sure this could greatly vary based on specific needs, I am curious about the backend mechanism/algorithm --that is, has anyone had success using something like "3 strikes and you're out" -- the flagged post is automatically closed/deleted after 3 reports by users with the required credentials. Would something like this likely be effective or would it require a more complex solution to ensure honesty and effectiveness. Any thoughts / experiences would be great

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• I need to do a BASICE For Loop algorithm for a java Pyramid

  - by user1665119

  Question 2. USE THE FOR LOOP. Design and write an algorithm that will read a single positive number from the keyboard and will then print a pyramid out on the screen. The pyramid will need to be of a height equal in lines to the number inputted by the operator. Your program is not to test for negative numbers, nor is it to cater for them. For your test, use the number 7. If you would like to take the problem further, try 18 and watch what happens. Example input: 4 Example output: 1 121 12321 1234321

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• How to search for closest value in a lookup table?

  - by CSharperWithJava

  I have a simple one dimmensional array of integer values that represent a physical set of part values I have to work with. I then calculate and ideal value mathematically. How could I write an efficient search algorithm that will find the smallest abosulte difference from my ideal value in the array? The array is predetermined and constant, so it can be sorted however I need. Example Lookup array: 100, 152, 256, 282, 300 Searching for an ideal value of 125 would find 100 in the array, whereas 127 would find 152. The actual lookup array will be about 250 items long and never change.

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• Nested loop with dependent bounds trip count

  - by aaa

  hello. just out of curiosity I tried to do the following, which turned out to be not so obvious to me; Suppose I have nested loops with runtime bounds, for example: t = 0 // trip count for l in 0:N for k in 0:N for j in max(l,k):N for i in k:j+1 t += 1 t is loop trip count is there a general algorithm/way (better than N^4 obviously) to calculate loop trip count? I am working on the assumption that the iteration bounds depend only on constant or previous loop variables.

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• Horizontally Flip a One Bit Bitmap Line

  - by roygbiv

  I'm looking for an algorithm to flip a 1 Bit Bitmap line horizontally. Remember these lines are DWORD aligned! I'm currently unencoding an RLE stream to an 8 bit-per-pixel buffer, then re-encoding to a 1 bit line, however, I would like to try and keep it all in the 1 bit space in an effort to increase its speed. Profiling indicates this portion of the program to be relatively slow compared to the rest. Example line (Before Flip): FF FF FF FF 77 AE F0 00 Example line (After Flip): F7 5E EF FF FF FF F0 00

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• question about missing element in array

  - by davit-datuashvili

  i have following problem from book introduction algorithm second edition by MIT university problem is following An array A[1 . . n] contains all the integers from 0 to n except one. It would be easy to determine the missing integer in O(n) time by using an auxiliary array B[0 . . n] to record which numbers appear in A. In this problem, however, we cannot access an entire integer in A with a single operation. The elements of A are represented in binary, and the only operation we can use to access them is “fetch the j th bit of A[i],” which takes constant time. Show that if we use only this operation, we can still determine the missing inte- ger in O(n) time please help

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• Color generation based on random number

  - by Mikulas Dite

  I would like to create a color generator based on random numbers, which might differ just slightly, but I need colors to be easily recognizable from each other. I was thinking about generation then in a rgb format which would be probably easiest. I'm afraid simply multiplying given arguments wouldn't do very well. What algorithm do you suggest using? Also, second generated color should not be the same as previous one, but I don't want to store them - nor multiplying with (micro)time would do well since the scripts' parts are usually faster.

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• Partition a rectangle into near-squares of given areas

  - by Marko Dumic

  I have a set of N positive numbers, and a rectangle of dimensions X and Y that I need to partition it in N smaller rectangles such that: the surface area of each smaller rectangle is proportional to it's corresponding number in given set all space of big rectangle is occupied and there is no leftover space between smaller rectangles each small rectangle should be shaped as close to square as feasible the execution time should be reasonably small I need directions on this. Do you know of such algorithm described on the web? Do you have any ideas (pseudo-code is fine)? Thanks.

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• Do "if" statements affect in the time complexity analysis?

  - by FranXh

  According to my analysis, the running time of this algorithm should be N2, because each of the loops goes once through all the elements. I am not sure whether the presence of the if statement changes the time complexity? for(int i=0; i<N; i++){ for(int j=1; j<N; j++){ System.out.println("Yayyyy"); if(i<=j){ System.out.println("Yayyy not"); } } }

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• Is it faster to loop through a Python set of number or a set of letters?

  - by Scott Bartell

  Is it faster to loop through a Python set of numbers or a Python set of letters given that each set is the exact same length and each item within each set is the same length? Why? I would think that there would be a difference because letters have more possible characters [a-zA-Z] than numbers [0-9] and therefor would be more 'random' and likely affect the hashing to some extent. numbers = set([00000,00001,00002,00003,00004,00005, ... 99999]) letters = set(['aaaaa','aaaab','aaaac','aaaad', ... 'aaabZZ']) # this is just an example, it does not actually end here for item in numbers: do_something() for item in letters: do_something() where len(numbers) == len(letters) Update: I am interested in Python's specific hashing algorithm and what happens behind the scenes with this implementation.

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• Simple prime number program - Weird issue with threads C#

  - by Para

  Hi! This is my code: using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading; namespace FirePrime { class Program { static bool[] ThreadsFinished; static bool[] nums; static bool AllThreadsFinished() { bool allThreadsFinished = false; foreach (var threadFinished in ThreadsFinished) { allThreadsFinished &= threadFinished; } return allThreadsFinished; } static bool isPrime(int n) { if (n < 2) { return false; } if (n == 2) { return true; } if (n % 2 == 0) { return false; } int d = 3; while (d * d <= n) { if (n % d == 0) { return false; } d += 2; } return true; } static void MarkPrimes(int startNumber,int stopNumber,int ThreadNr) { for (int j = startNumber; j < stopNumber; j++) nums[j] = isPrime(j); lock (typeof(Program)) { ThreadsFinished[ThreadNr] = true; } } static void Main(string[] args) { int nrNums = 100; int nrThreads = 10; //var threadStartNums = new List<int>(); ThreadsFinished = new bool[nrThreads]; nums = new bool[nrNums]; //var nums = new List<bool>(); nums[0] = false; nums[1] = false; for(int i=2;i<nrNums;i++) nums[i] = true; int interval = (int)(nrNums / nrThreads); //threadStartNums.Add(2); //int aux = firstStartNum; //int i = 2; //while (aux < interval) //{ // aux = interval*i; // i=i+1; // threadStartNums.Add(aux); //} int startNum = 0; for (int i = 0; i < nrThreads; i++) { var _thread = new System.Threading.Thread(() => MarkPrimes(startNum, Math.Min(startNum + interval, nrNums), i)); startNum = startNum + interval; //set the thread to run in the background _thread.IsBackground = true; //start our thread _thread.Start(); } while (!AllThreadsFinished()) { Thread.Sleep(1); } for (int i = 0; i < nrNums; i++) if(nums[i]) Console.WriteLine(i); } } } This should be a pretty simple program that is supposed to find and output the first nrNums prime numbers using nrThreads threads working in parallel. So, I just split nrNums into nrThreads equal chunks (well, the last one won't be equal; if nrThreads doesn't divide by nrNums, it will also contain the remainder, of course). I start nrThreads threads. They all test each number in their respective chunk and see if it is prime or not; they mark everything out in a bool array that keeps a tab on all the primes. The threads all turn a specific element in another boolean array ThreadsFinished to true when they finish. Now the weird part begins: The threads never all end. If I debug, I find that ThreadNr is not what I assign to it in the loop but another value. I guess this is normal since the threads execute afterwards and the counter (the variable i) is already increased by then but I cannot understand how to make the code be right. Can anyone help? Thank you in advance. P.S.: I know the algorithm is not very efficient; I am aiming at a solution using the sieve of Eratosthenes also with x given threads. But for now I can't even get this one to work and I haven't found any examples of any implementations of that algorithm anywhere in a language that I can understand.

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• Modify a given number to find the required sum?

  - by Gaurav

  A friend of mine sent me this question. I haven't really been able to come up with any kind of algorithm to solve this problem. You are provided with a no. say 123456789 and two operators * and +. Now without changing the sequence of the provided no. and using these operators as many times as you wish, evaluate the given value: eg: given value 2097 Solution: 1+2+345*6+7+8+9 Any ideas on how to approach problems like these?

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• How to calculate median of a Map<Int,Int>?

  - by Chris

  For a map where the key represents a number of a sequence and the value the count how often this number appeared in the squence, how would an implementation of an algorithm in java look like to calculate the median? For example: 1,1,2,2,2,2,3,3,3,4,5,6,6,6,7,7 in a map: Map<Int,Int> map = ... map.put(1,2) map.put(2,4) map.put(3,3) map.put(4,1) map.put(5,1) map.put(6,3) map.put(7,2) double median = calculateMedian(map); print(median); would result in: > print(median); 3 > So what i am looking for is a java implementation of calculateMedian.

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