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• Algorithm for calculating definite integrals with bounds at infinity

  - by mbac32768

  Suppose I have an integral that's bounded on one (or both) end 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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• Reverse Breadth First traversal in C#

  - by Ngu Soon Hui

  Anyone has a ready implementation of the Reverse Breadth First traversal algorithm in C#? By Reverse Breadth First traversal , I mean instead of searching a tree starting from a common node, I want to search the tree from the bottom and gradually converged to a common node. Let's see the below figure, this is the output of a Breadth First traversal : In my reverse breadth first traversal , 9,10,11 and 12 will be the first few nodes found ( the order of them are not important as they are all first order). 5, 6, 7 and 8 are the second few nodes found, and so on. 1 would be the last node found. Any ideas or pointers? Edit: Change "Breadth First Search" to "Breadth First traversal" to clarify the question

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• Splitting a double vector into equal parts

  - by Cosmin

  Greetings, Any input on a way to divide a std::vector into two equal parts ? I need to find the smallest possible difference between |part1 - part2|. This is how I'm doing it now, but from what you can probably tell it will yield a non-optimal split in some cases. auto mid = std::find_if(prim, ultim, [&](double temp) -> bool { if(tempsum >= sum) return true; tempsum += temp; sum -= temp; return false; }); The vector is sorted, highest to lowest, values can indeed appear twice. I'm not expecting part1 and part2 to have the same numbers of elements, but sum(part1) should be as close as possible to sum(part2) For example if we would have { 2.4, 0.12, 1.26, 0.51, 0.70 }, the best split would be { 2.4, 0.12 } and { 1.26, 0.51, 0.70 }. If it helps, I'm trying to achieve the splitting algorithm for the Shannon Fano encoding. Any input is appreciated, thanks!

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• Given a string of red and blue balls, find min number of swaps to club the colors together

  - by efficiencyIsBliss

  We are given a string of the form: RBBR, where R - red and B - blue. We need to find the minimum number of swaps required in order to club the colors together. In the above case that answer would be 1 to get RRBB or BBRR. I feel like an algorithm to sort a partially sorted array would be useful here since a simple sort would give us the number of swaps, but we want the minimum number of swaps. Any ideas? This is allegedly a Microsoft interview question according to this.

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• Element point map for html5 canvas element, need algorithm

  - by Artiom Chilaru

  I'm currently working on a pure html 5 canvas implementation of the "flying tag cloud sphere", which many of you have undoubtedly seen as a flash object in some pages. The tags are drawn fine, and the performance is satisfactory, but there's one thing in the canvas element that's kind of breaking this idea: you can't identify the objects that you've drawn on a canvas, as it's just a simple flat "image".. What I have to do in this case is catch the click event, and try to "guess" which element was clicked. So I have to have some kind of matrix, which stores a link to a tag object for each pixel on the canvas, AND I have to update this matrix on every redraw. Now this sounds incredibly inefficient, and before I even start trying to implement this, I want to ask the community - is there some "well known" algorithm that would help me in this case? Or maybe I'm just missing something, and the answer is right behind the corner? :)

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• Writing a post search algorithm.

  - by MdaG

  I'm trying to write a free text search algorithm for finding specific posts on a wall (similar kind of wall as Facebook uses). A user is suppose to be able to write some words in a search field and get hits on posts that contain the words; with the best match on top and then other posts in decreasing order according to match score. I'm using the edit distance (Levenshtein) "e(x, y) = e" to calculate the score for each post when compared to the query word "x" and post word "y" according to: score(x, y) = 2^(2 - e)(1 - min(e, |x|) / |x|) Each word in a post contributes to the total score for that specific post. This approach seems to work well when the posts are of roughly the same size, but sometime certain large posts manages to rack up score solely on having a lot of words in them while in practice not being relevant to the query. Am I approaching this problem in the wrong way or is there some way to normalize the score that I haven't thought of?

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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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• Determine if a string contains only alphanumeric characters (or a space)

  - by dreamlax

  I'm learning C++ and I am writing a function that determines whether a string contains only alphanumeric characters and spaces. I suppose I am effectively testing whether it matches the regular expression ^[[:alnum:] ]+$ but without using regular expressions. I have seen a lot of algorithms revolve around iterators, so I tried to find a solution that made use of iterators, and this is what I have: #include <algorithm> static inline bool is_not_alnum_space(char c) { return !(isalpha(c) || isdigit(c) || (c == ' ')); } bool string_is_valid(const std::string &str) { return find_if(str.begin(), str.end(), is_not_alnum_space) == str.end(); } Is there a better solution, or a “more C++” way to do this?

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

  - 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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• 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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• 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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• 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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• Selecting items from events, as evenly spaced as possible

  - by Matt Warren

  If I have an event that happens 15 times a second (numbered 1 - 15), but I only want to process it 3 times I can choose [1], [6] and [11],. It's important that the events I process are as evenly spaced as possible and take into account wrap-around, i.e. the events are continuous 13, 14, 15, 1, 2, 3 etc. If I want 4 items the best I can do is [1], [5], [9] & [13]. Is there a general algorithm that will calculate which events I need to process given the total number of events (total) and the number to process (processAmount).

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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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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• 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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