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• KMeans clustering for more than 5 million vectors

  - by Wajih

  I have hit a real problem. I need to do some Kmeans clustering for 5 million vectors, each containing about 32 cols. I tried out Mahout which requires linux and I am on windows, I am restrained from using a Linux OS and any sort of simulator. Can anyone suggest a KMeans clustering algorithm that is scalable upto 5M vectors and can converge quickly? I have tested a few but they wont scale. Which means they are slow and take forever to complete. Thanks

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• Planning a competition

  - by Jérôme

  I need to produce the schedule of a sport-event. There are 30 teams. Each team has to play 8 matches. This means that it is not possible for each team to compete again all other teams, but I need to avoid that two team compete more than once against each other. My idea was to generate all possible matches (for 30 teams: (30*29)/2 = 435 matches) and select from this list 120 matches (8 match for each team: 8 * 30 / 2 = 120 matches). This is where I'm having a hard time: how can I select these 120 matches? I tried some simple solutions (take first match of the list, then the last, and so on) but they don't seem to work with 30 teams. I also tried to generate all possible match combination and find which one is working but with 30 team, this is too much calculation time. Is there an existing algorithm that I could implement?

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• Optimally reducing maximum flow

  - by ArIck

  Given a parameter k, I'm trying to delete k edges from a directed graph such that the maximum flow is reduced by as much as possible. The graph has a source s and a sink t, and the capacity of each edge is one. The graph may or may not contain cycles. My proposed solution would be to first perform a topological sorting on the graph, using an algorithm that "forgives" cycles -- perhaps by ignoring edges that lead us back to the source. Then (assuming k = 1): i = 0 for each vertex u order by topological(u) for each edge (u, v) order by topological(v) descending if topological(v) > topological(u) then delete (u, v) if ++i = k then return else // edge doesn't contribute to max flow, ignore Would this work, or am I totally off-track here?

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• How to return arrays with the biggest elements in C#?

  - by theateist

  I have multiple int arrays: 1) [1 , 202,4 ,55] 2) [40, 7] 3) [2 , 48 ,5] 4) [40, 8 ,90] I need to get the array that has the biggest numbers in all positions. In my case that would be array #4. Explanation: arrays #2, #4 have the biggest number in 1st position, so after the first iteration these 2 arrays will be returned ([40, 7] and [40, 8 ,90]) now after comparing 2nd position of the returned array from previous iteration we will get array #4 because 8 7 and so on... Can you suggest an efficient algorithm for this? Doing with Linq will be preferable. UPDATE There is no limitation for the length, but as soon as some number in any position is greater, so this array is the biggest.

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• Worked Example of Digital Signature Algorithm

  - by drelihan

  Hi Folks, Does anybody have a DSA worked example with simple values on how to calculate r,s and verify v == r. As this standard has been around awhile and is implemented in librarys e.g. the Java Cryptography Extension I'm finding it very hard to find an example of how the algorithm works. Compute r=(gk mod p) mod q Compute s=(k-1 * (x * r + i)) mod q Verifying a signature; again i is the input, and (r,s) is the signature. u1 = (s-1 * i) mod q u2 = (s-1 * r) mod q v = ((gu1 * yu2) mod p) mod q If v equals r, the signature is valid. Thanks,

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• Smart pagination algorithm

  - by silvertab

  I'm looking for an example algorithm of smart pagination. By smart, what I mean is that I only want to show, for example, 2 adjacent pages to the current page, so instead of ending up with a ridiculously long page list, I truncate it. Here's a quick example to make it clearer... this is what I have now: Pages: 1 2 3 4 [5] 6 7 8 9 10 11 This is what I want to end up with: Pages: ... 3 4 [5] 6 7 ... (In this example, I'm only showing 2 adjacent pages to the current page) I'm implementing it in PHP/Mysql, and the "basic" pagination (no trucating) is already coded, I'm just looking for an example to optimize it... It can be an example in any language, as long as it gives me an idea as to how to implement it...

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• Is it hard problem?

  - 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.

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• How can I maximally partition a set?

  - by Gregory Higley

  I'm trying to solve one of the Project Euler problems. As a consequence, I need an algorithm that will help me find all possible partitions of a set, in any order. For instance, given the set 2 3 3 5: 2 | 3 3 5 2 | 3 | 3 5 2 | 3 3 | 5 2 | 3 | 3 | 5 2 5 | 3 3 and so on. Pretty much every possible combination of the members of the set. I've searched the net of course, but haven't found much that's directly useful to me, since I speak programmer-ese not advanced-math-ese. Can anyone help me out with this? I can read pretty much any programming language, from BASIC to Haskell, so post in whatever language you wish.

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• Trouble with a sequential search algorithm

  - by shinjuo

  I need to use this sequential search algorithm, but I am not really sure how. I need to use it with an array. Can someone point me in the correct direction or something on how to use this. bool seqSearch (int list[], int last, int target, int* locn){ int looker; looker = 0; while(looker < last && target != list[looker]){ looker++; } *locn = looker; return(target == list[looker]); }

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• Extracting rightmost N bits of an integer

  - by srandpersonia

  In the yester Code Jam Qualification round http://code.google.com/codejam/contest/dashboard?c=433101#s=a&a=0 , there was a problem called Snapper Chain. From the contest analysis I came to know the problem requires bit twiddling stuff like extracting the rightmost N bits of an integer and checking if they all are 1. I saw a contestant's(Eireksten) code which performed the said operation like below: (((K&(1<<N)-1))==(1<<N)-1) I couldn't understand how this works. What is the use of -1 there in the comparison?. If somebody can explain this, it would be very much useful for us rookies. Also, Any tips on identifying this sort of problems would be much appreciated. I used a naive algorithm to solve this problem and ended up solving only the smaller data set.(It took heck of a time to compile the larger data set which is required to be submitted within 8 minutes.). Thanks in advance.

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• Efficient most common suffix algorithm?

  - by taw

  I have a few GBs worth of strings, and for every prefix I want to find 10 most common suffixes. Is there an efficient algorithm for that? An obvious solution would be: Store sorted list of <string, count> pairs. Identify by binary search extent for prefix we're searching. Find 10 highest counts in this extent. Possibly precompute it for all short prefixes, so it doesn't ever need to look at large portion of data. I'm not sure if that would actually be efficient at all. Is there a better way I overlooked? Answers must be real time, but it can take as much preprocessing as necessary.

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• Practical Python-based visual programming environment?

  - by Who8MyLunch

  I am looking for a practical visual programming environment based on Python. My primary application is algorithm development for processing remote-sensing imagery. I was initially inspired by LabVIEW from National Instruments, but that is more geared towards laboratory measurements and simulations. I write a lot of prototype code in Python and do a lot of interactive analysis with IPython. Does there exist a visual framework where a "program" is represented by connected nodes which each read data, do some work, and output data to the next node? I would like to use Python to write the code residing in each node. So far the best I've seen is Orange http://www.ailab.si/orange/, but it does not have the ability to start/stop individual nodes.

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• Eliminating cyclic flows from a graph

  - by Jon Harrop

  I have a directed graph with flow volumes along edges and I would like to simplify it by removing all cyclic flows. This can be done by finding the minimum of the flow volumes along each edge in any given cycle and reducing the flows of every edge in the cycle by that minimum volume, deleting edges with zero flow. When all cyclic flows have been removed the graph will be acyclic. For example, if I have a graph with vertices A, B and C with flows of 1 from A?B, 2 from B?C and 3 from C?A then I can rewrite this with no flow from A?B, 1 from B?C and 2 from C?A. The number of edges in the graph has reduced from 3 to 2 and the resulting graph is acyclic. Which algorithm(s), if any, solve this problem?

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• some examples for using specific searchalgorithm

  - by Robert

  I could understand the following search algorithms: Constraint Satisfaction with Arc Consistency, Uninformed search A* Search MinMax I would understand the definition and working principles of the above algorithm,but could you please give me some real world examples that the above algorithms will be suitable?My idea would be: For CSP with Arc Consistency,assign students to groups that each group must contain both technical and management students,and no 2 technical students in a same group. Uniformed Search: search for a file under UNIX directoy. A* Search: search a way (staring from home) to go to mulitple stores to buy things then get back home with minimum total travelling time. MinMax:Go or other Chess. Please correct me if I am wrong.

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• VB.net Network Graph code/algorithm

  - by Jens

  For a school project we need to visualise a computer network graph. The number of computers with specific properties are read from an XML file, and then a graph should be created. Ad random computers are added and removed. Is there any open source project or algorithm that could help us visualising this in VB.net? Or would you suggest us to switch to java. Update: We eventually switched java and used the Jung libraries because this was easier for us to understand and implement.

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• Return parent of node in Binary Tree

  - by user188995

  I'm writing a code to return the parent of any node, but I'm getting stuck. I don't want to use any predefined ADTs. //Assume that nodes are represented by numbers from 1...n where 1=root and even //nos.=left child and odd nos=right child. public int parent(Node node){ if (node % 2 == 0){ if (root.left==node) return root; else return parent(root.left); } //same case for right } But this program is not working and giving wrong results. My basic algorithm is that the program starts from the root checks if it is on left or on the right. If it's the child or if the node that was queried else, recurses it with the child.

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• Algorithm for calculating indefinite integrals

  - by mbac32768

  Suppose I have an integral that's bounded on one (or both) ends by (-)infinity. AFAICT, I can't analytically solve this problem, it takes brute force (e.g. using a Left Riemann Sum). I'm having trouble generalizing the algorithm so that it sets the proper subdivisions; I'll either do far too much work to calculate something trivial, or not do nearly enough and have huge aliasing errors. Answering in any language is cool, but maybe someone with better google-fu can end this quickly. :) Is what I'm looking for as impossible as trying to measure the British coastline?

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• find a duplicate entry in an array in constant space and O(n) time [closed]

  - by Anubhav Agarwal

  Possible Duplicate: Algorithm to find a duplicate entry in constant space and O(n) time Given an array of N integer such that only one integer is repeated. Find the repeated integer in O(n) time and constant space. There is no range for the value of integers or the value of N For example given an array of 6 integers as 23 45 67 87 23 47. The answer is 23 (I hope this covers ambiguous and vague part) I searched on the net but was unable to find any such question in which range of integers was not fixed. Also here is an example that answers a similar question to mine but here he created a hash table with the highest integer value in C++.But the cpp does not allow such to create an array with 2^64 element(on a 64-bit computer).

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• One-way flight trip problem.

  - by psihodelia

  You are going on a one-way indirect flight trip that includes billions transfers. You are not stopping twice in the same airport. You have 1 ticket for each part of your trip. Each ticket contains src and dst airport. All the tickets you have are randomly sorted. You forgot the original departure airport (very first src) and your destination (last dst). Design an algorithm to reconstruct your trip with minimum big-O complexity.

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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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• Efficiently remove points with same slope

  - by Ram

  Hi, In one of mine applications I am dealing with graphics objects. I am using open source GPC library to clip/merge two shapes. To improve accuracy I am sampling (adding multiple points between two edges) existing shapes. But before displaying back the merged shape I need to remove all the points between two edges. But I am not able to find an efficient algorithm that will remove all points between two edges which has same slope with minimum CPU utilization. Currently all points are of type PointF Any pointer on this will be a great help.

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• Visit neighbor of a position in a 2d-array

  - by Martin

  I have the following two dimensional array: static int[,] arr = new int[5, 5] { { 00, 00, 00, 01, 00 }, { 00, 00, 01, 01, 00 }, { 00, 00, 01, 01, 00 }, { 00, 00, 01, 01, 00 }, { 00, 00, 00, 01, 00 }, }; I have to a implement a method called Hit(int x, int y). When we hit a 0 in the array (i.e. Hit(0, 0), Hit(1, 1), but not Hit(3, 0)) I would like all the adjacent zeros to the zero we hit to be incremented by 10. So if I call Hit(1, 1), the array should become the following. static int[,] arr = new int[5, 5] { { 10, 10, 10, 01, 00 }, { 10, 10, 01, 01, 00 }, { 10, 10, 01, 01, 00 }, { 10, 10, 01, 01, 00 }, { 10, 10, 10, 01, 00 }, }; Any idea how I could implement that? It sounds to me like a Depth First Search/Recursive sort-of algorithm should do the job, but I haven't been able to implement it for an 2d array. Thanks for the help!

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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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• 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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• 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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