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• Algorithm to see if keywords exist inside a string

  - by rksprst

  Let's say I have a set of keywords in an array {"olympics", "sports tennis best", "tennis", "tennis rules"} I then have a large list (up to 50 at a time) of strings (or actually tweets), so they are a max of 140 characters. I want to look at each string and see what keywords are present there. In the case where a keyword is composed of multiple words like "sports tennis best", the words don't have to be together in the string, but all of them have to show up. I've having trouble figuring out an algorithm that does this efficiently. Do you guys have suggestions on a way to do this? Thanks! Edit: To explain a bit better each keyword has an id associated with it, so {1:"olympics", 2:"sports tennis best", 3:"tennis", 4:"tennis rules"} I want to go through the list of strings/tweets and see which group of keywords match. The output should be, this tweet belongs with keyword #4. (multiple matches may be made, so anything that matches keyword 2, would also match 3 -since they both contain tennis). When there are multiple words in the keyword, e.g. "sports tennis best" they don't have to appear together but have to all appear. e.g. this will correctly match: "i just played tennis, i love sports, its the best"... since this string contains "sports tennis best" it will match and be associated with the keywordID (which is 2 for this example).

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• Algorithm for finding the best routes for food distribution in game

  - by Tautrimas

  Hello, I'm designing a city building game and got into a problem. Imagine Sierra's Caesar III game mechanics: you have many city districts with one market each. There are several granaries over the distance connected with a directed weighted graph. The difference: people (here cars) are units that form traffic jams (here goes the graph weights). Note: in Ceasar game series, people harvested food and stockpiled it in several big granaries, whereas many markets (small shops) took food from the granaries and delivered it to the citizens. The task: tell each district where they should be getting their food from while taking least time and minimizing congestions on the city's roads. Map example Sample diagram Suppose that yellow districts need 7, 7 and 4 apples accordingly. Bluish granaries have 7 and 11 apples accordingly. Suppose edges weights to be proportional to their length. Then, the solution should be something like the gray numbers indicated on the edges. Eg, first district gets 4 apples from the 1st and 3 apples from the 2nd granary, while the last district gets 4 apples from only the 2nd granary. Here, vertical roads are first occupied to the max, and then the remaining workers are sent to the diagonal paths. Question What practical and very fast algorithm should I use? I was looking at some papers (Congestion Games: Optimization in Competition etc.) describing congestion games, but could not get the big picture. Any help is very appreciated! P. S. I can post very little links and no images because of new user restriction.

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• Is my heuristic algorithm correct? (Sudoku solver)

  - by Aposperite

  First of -yes this IS a homework- but it's primarily a theoretical question rather than a practical one, I am simply asking a confirmation if I am thinking correctly or any hints if I am not. I have been asked to compile a simple Sudoku solver (on Prolog but that is not so important right now) with the only limitation being that it must utilize a heuristic function using Best-First Algorithm. The only heuristic function I have been able to come up with is explained below: 1. Select an empty cell. 1a. If there are no empty cells and there is a solution return solution. Else return No. 2. Find all possible values it can hold. %% It can't take values currently assigned to cells on the same line/column/box. 3. Set to all those values a heuristic number starting from 1. 4. Pick the value whose heuristic number is the lowest && you haven't checked yet. 4a. If there are no more values return no. 5. If a solution is not found: GoTo 1. Else Return Solution. // I am sorry for errors in this "pseudo code." If you want any clarification let me know. So am I doing this right or is there any other way around and mine is false? Thanks in advance.

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• Discover periodic patterns in a large data-set

  - by Miner

  I have a large sequence of tuples on disk in the form (t1, k1) (t2, k2) ... (tn, kn) ti is a monotonically increasing timestamp and ki is a key (assume a fixed length string if needed). Neither ti nor ki are guaranteed to be unique. However, the number of unique tis and kis is huge (millions). n itself is very large (100 Million+) and the size of k (approx 500 bytes) makes it impossible to store everything in memory. I would like to find out periodic occurrences of keys in this sequence. For example, if I have the sequence (1, a) (2, b) (3, c) (4, b) (5, a) (6, b) (7, d) (8, b) (9, a) (10, b) The algorithm should emit (a, 4) and (b, 2). That is a occurs with a period of 4 and b occurs with a period of 2. If I build a hash of all keys and store the average of the difference between consecutive timestamps of each key and a std deviation of the same, I might be able to make a pass, and report only the ones that have an acceptable std deviation(ideally, 0). However, it requires one bucket per unique key, whereas in practice, I might have very few really periodic patterns. Any better ways?

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• Quickest algorithm for finding sets with high intersection

  - by conradlee

  I have a large number of user IDs (integers), potentially millions. These users all belong to various groups (sets of integers), such that there are on the order of 10 million groups. To simplify my example and get to the essence of it, let's assume that all groups contain 20 user IDs (i.e., all integer sets have a cardinality of 100). I want to find all pairs of integer sets that have an intersection of 15 or greater. Should I compare every pair of sets? (If I keep a data structure that maps userIDs to set membership, this would not be necessary.) What is the quickest way to do this? That is, what should my underlying data structure be for representing the integer sets? Sorted sets, unsorted---can hashing somehow help? And what algorithm should I use to compute set intersection)? I prefer answers that relate C/C++ (especially STL), but also any more general, algorithmic insights are welcome. Update Also, note that I will be running this in parallel in a shared memory environment, so ideas that cleanly extend to a parallel solution are preferred.

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• Need some help understanding this problem about maximizing graph connectivity

  - by Legend

  I was wondering if someone could help me understand this problem. I prepared a small diagram because it is much easier to explain it visually. Problem I am trying to solve: 1. Constructing the dependency graph Given the connectivity of the graph and a metric that determines how well a node depends on the other, order the dependencies. For instance, I could put in a few rules saying that node 3 depends on node 4 node 2 depends on node 3 node 3 depends on node 5 But because the final rule is not "valuable" (again based on the same metric), I will not add the rule to my system. 2. Execute the request order Once I built a dependency graph, execute the list in an order that maximizes the final connectivity. I am not sure if this is a really a problem but I somehow have a feeling that there might exist more than one order in which case, it is required to choose the best order. First and foremost, I am wondering if I constructed the problem correctly and if I should be aware of any corner cases. Secondly, is there a closely related algorithm that I can look at? Currently, I am thinking of something like Feedback Arc Set or the Secretary Problem but I am a little confused at the moment. Any suggestions? PS: I am a little confused about the problem myself so please don't flame on me for that. If any clarifications are needed, I will try to update the question.

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• Fast Lightweight Image Comparisson Metric Algorithm

  - by gav

  Hi All, I am developing an application for the Android platform which contains 1000+ image filters that have been 'evolved'. When a user selects a photo I want to present the most relevant filters first. This 'relevance' should be dependent on previous use cases. I have already developed tools that register when a filtered image is saved; this combination of filter and image can be seen as the training data for my system. The issue is that the comparison must occur between selecting an image and the next screen coming up. From a UI point of view I need the whole process to take less that 4 seconds; select an image- obtain a metric to use for similarity - check against use cases - return 6 closest matches. I figure with 4 seconds I can use animations and progress dialogs to keep the user happy. Due to platform contraints I am fairly limited in the computational expense of the algorithm. I have implemented a technique adapted from various online tutorials for running C code on the G1 and hence this language is available Specific Constraints; Qualcomm® MSM7201A™, 528 MHz Processor 320 x 480 Pixel bitmap in 32 bit ARGB ~ 2 seconds computational time for the native method to get the metric ~ 2 seconds to compare the metric of the current image with training data This is an academic project so all ideas are welcome, anything you can think of or have heard about would be of interest to me. My ideas; I want to keep the complexity down (O(n*m)?) by using pixel data only rather than a neighbourhood function I was looking at using the Colour historgram/Greyscale histogram/Texture/Entropy of the image, combining them to make the measure. There will be an obvious loss of information but I need the resultant metric to be substantially smaller than the memory footprint of the image (~0.512 MB) As I said, any ideas to direct my research would be fantastic. Kind regards, Gavin

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• Warshall Algorithm Logic - Stuck

  - by stan

  I am trying to use this logic to understand what is going on with the adjacency matrix, but i am massivley confused where it says about interspacing for a b c d ..... Could anyone explain what is going on here? Thank you (tagged as java as its the language this was demonstarted to us in, so if anyone posted any code examples they could see it was in that language) http://compprog.wordpress.com/2007/11/15/all-sources-shortest-path-the-floyd-warshall-algorithm/ Here is the code: for (k = 0; k < n; ++k) { for (i = 0; i < n; ++i) for (j = 0; j < n; ++j) /* If i and j are different nodes and if the paths between i and k and between k and j exist, do */ if ((dist[i][k] * dist[k][j] != 0) && (i != j)) /* See if you can't get a shorter path between i and j by interspacing k somewhere along the current path */ if ((dist[i][k] + dist[k][j] < dist[i][j]) || (dist[i][j] == 0)) dist[i][j] = dist[i][k] + dist[k][j];

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• Algorithm for count-down timer that can add on time

  - by Person

  I'm making a general timer that has functionality to count up from 0 or count down from a certain number. I also want it to allow the user to add and subtract time. Everything is simple to implement except for the case in which the timer is counting down from some number, and the user adds or subtracts time from it. For example: (m_clock is an instance of SFML's Clock) float Timer::GetElapsedTime() { if ( m_forward ) { m_elapsedTime += m_clock.GetElapsedTime() - m_elapsedTime; } else { m_elapsedTime -= m_elapsedTime - m_startingTime + m_clock.GetElapsedTime(); } return m_elapsedTime; } To be a bit more clear, imagine that the timer starts at 100 counting down. After 10 seconds, the above function would look like 100 -= 100 - 100 + 10 which equals 90. If it was called after 20 more seconds it would look like 90 -= 90 - 100 + 30 which equals 70. This works for normal counting, but if the user calls AddTime() ( just m_elapsedTime += arg ) then the algorithm for backwards counting fails miserably. I know that I can do this using more members and keeping track of previous times, etc. but I'm wondering whether I'm missing some implementation that is extremely obvious. I'd prefer to keep it as simple as possible in that single operation.

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• problem with binarysearch algorithm

  - by arash

  hi friends,the code below belongs to binary search algorithm,user enter numbers in textbox1 and enter the number that he want to fing with binarysearch in textbox2.i have a problem with it,that is when i enter for example 15,21 in textbox1 and enter 15 in textbox2 and put brakpoint on the line i commented below,and i understood that it doesnt put the number in textbox2 in searchnums(commented),for more explanation i comment in code.thanks in advance public void button1_Click(object sender, EventArgs e) { int searchnums = Convert.ToInt32(textBox2.Text);//the problem is here,the value in textbox2 doesnt exist in searchnums and it has value 0. int result = binarysearch(searchnums); MessageBox.Show(result.ToString()); } public int binarysearch(int searchnum) { string[] source = textBox1.Text.Split(','); int[] nums = new int[source.Length]; for (int i = 0; i < source.Length; i++) { nums[i] = Convert.ToInt32(source[i]); } int first =0; int last = nums.Length; int mid = (int)Math.Floor(nums.Length / 2.0); while (1<= nums.Length) { if (searchnum < nums[mid]) { last = mid - 1; } if (searchnum > nums[mid]) { first = mid + 1; } else { return nums[mid]; } } return -1; }

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• Need some help understanding this problem

  - by Legend

  I was wondering if someone could help me understand this problem. I prepared a small diagram because it is much easier to explain it visually. Problem I am trying to solve: 1. Constructing the dependency graph Given the connectivity of the graph and a metric that determines how well a node depends on the other, order the dependencies. For instance, I could put in a few rules saying that node 3 depends on node 4 node 2 depends on node 3 node 3 depends on node 5 But because the final rule is not "valuable" (again based on the same metric), I will not add the rule to my system. 2. Execute the request order Once I built a dependency graph, execute the list in an order that maximizes the final connectivity. First and foremost, I am wondering if I constructed the problem correctly and if I should be aware of any corner cases. Secondly, is there a closely related algorithm that I can look at? Currently, I am thinking of something like Feedback Arc Set or the Secretary Problem but I am a little confused at the moment. Any suggestions? PS: I am a little confused about the problem myself so please don't flame on me for that. If any clarifications are needed, I will try to update the question.

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• GSM Cell Towers Location & Triangulation Algorithm (Similar to OpenCellID / Skyhook / Google's MyLocation)

  - by ranabra

  Hi all, assuming I have a Fingerprint DB of Cell towers. The data (including Long. & Lat. CellID, signal strength, etc) is achieved by 'wardriving', similar to OpenCellID.org. I would like to be able to get the location of the client mobile phone without GPS (similar to OpenCellID / Skyhook Wireless/ Google's 'MyLocation'), which sends me info on the Cell towers it "sees" at the moment: the Cell tower connected to, and another 6 neighboring cell towers (assuming GSM). I have read and Googled it for a long time and came across several effective theories, such as using SQL 2008 Spatial capabilities, or using an euclidean algorithm, or Markov Model. However, I am lacking a practical solution, preferably in C# or using SQL 2008 :) The location calculation will be done on the server and not on the client mobile phone. the phone's single job is to send via HTTP/GPRS, the tower it's connected to and other neighboring cell towers. Any input is appreciated, I have read so much and so far haven't really advanced much. Thanx

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• Reducing a set of non-unique elements via transformations

  - by Andrey Fedorov

  I have: 1) a "starting set" of not-necessarily-unique elements, e.x. { x, y, z, z }, 2) a set of transformations, e.x. (x,z) = y, (z,z) = z, x = z, y = x, and 3) a "target set" that I am trying to get by applying transformations to the starting set, e.x. { z }. I'd like to find an algorithm to generate the (possibly infinite) possible applications of the transformations to the starting set that result in the target set. For example: { x, y, z, z }, y => x { x, x, z, z }, x => z { z, x, z, z }, x => z { z, z, z, z }, (z, z) => z { z, z, z }, (z, z) => z { z, z }, (z, z) => z { z } This sounds like something that's probably an existing (named) problem, but I don't recognize it. Can anyone help me track it down, or suggest further reading on something similar?

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• Javascript algorithm to find elements in array that are not in another array

  - by Tauren

  I'm looking for a good algorithm to get all the elements in one array that are not elements in another array. So given these arrays: var x = ["a","b","c","t"]; var ?????????y = [???????"d","a","t","e","g"]; I want to end up with this array: var z = ["d","e","g"]; I'm using jquery, so I can take advantage of $.each() and $.inArray(). Here's the solution I've come up with, but it seems like there should be a better way. // goal is to get rid of values in y if they exist in x var x = ["a","b","c","t"]; var y = ["d","a","t","e","g"]; var z = []; $.each(y, function(idx, value){ if ($.inArray(value,x) == -1) { z.push(value); } }); ?alert(z); // should be ["d","e","g"] Here is the code in action. Any ideas?

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• PHP: simplify with algorithm?

  - by tshabala

  Hello. Here's a piece of PHP code I think is not very "pretty", I'm sure it's possible to simplify it with for or something. I'm trying to find and algorithm that would work for this, but I can't figure it out, please help me. Here's the code: if(isset($four)) { if(isset($navi[$one][$two][$three][$four])) echo "/content/" . $one . "/" . $two . "/" . $three . "/" .$four . ".php"; else echo "error"; } else if(isset($three)) { if(isset($navi[$one][$two][$three])) echo "/content/" . $one . "/" . $two . "/" . $three . ".php"; else echo "error"; } else if(isset($two)) { if(isset($navi[$one][$two])) echo "/content/" . $one . "/" . $two . ".php"; else echo "error"; } else if(isset($one)) { if(isset($navi[$one]))echo "/content/" . $one . ".php"; else echo "error"; } else { echo "error"; } Thanks!

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• Algorithm Question

  - by Ravi

  Hi, I am trying to find a O (n) algorithm for this problem but unable to do so even after spending 3 - 4 hours. The brute force method times out (O (n^2)). I am confused as to how to do it ? Does the solution requires dynamic programming solution ? http://acm.timus.ru/problem.aspx?space=1&num=1794 In short the problem is this: There are some students sitting in circle and each one of them has its own choice as to when he wants to be asked a question from a teacher. The teacher will ask the questions in clockwise order only. For example: 5 3 3 1 5 5 This means that there are 5 students and : 1st student wants to go third 2nd student wants to go third 3rd student wants to go first 4th student wants to go fifth 5th student wants to go fifth. The question is as to where should teacher start asking questions so that maximum number of students will get the turn as they want. For this particular example, the answer is 5 because 3 3 1 5 5 2 3 4 5 1 You can see that by starting at fifth student as 1st, 2 students (3 and 5) are getting the choices as they wanted. For this example the answer is 12th student : 12 5 1 2 3 6 3 8 4 10 3 12 7 because 5 1 2 3 6 3 8 4 10 3 12 7 2 3 4 5 6 7 8 9 10 11 12 1 four students get their choices fulfilled. Thanks Ravi

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• barebones sort algorithm

  - by user309322

  i have been asked to make a simple sort aglorithm to sort a random series of 6 numbers into numerical order. However i have been asked to do this using "Barebones" a theoretical language put forward in the Book Computer Science an overview. Some information on the language can be found here http://www.brouhaha.com/~eric/software/barebones/ Just to clarify i am a student teacher and have been doing anaysis on "mini-programing languages" and their uses in a teaching environment, i suggested to my tutor that i look at barebones and asked what sort of exmaple program i should write . He suggested a simple sort algorithm. Now since looking at the language i cant understand how i can do this without using arrays and if statements. The code to swap the value of variables would be while a not 0 do; incr Aux1; decr a; end; while b not 0 do; incr Aux2 decr b end; while Aux1 not 0 do; incr a; decr Aux1; end; while Aux2 not 0 do; incr b; decr Aux2; end; however the language does not provide < or operators

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• C# algorithm for figuring out different possible combinations...

  - by ttomsen

  I have 10 boxes, each box can hold one item from a group/type of items, each 'group' type only fits in one of the 10 box types. The pool can have n number of items. The groups have completely distinct items. Each item has a price, i want an algorithm that will generate all the different possibilities, so i can figure out different price points. so a smaller picture of the problem BOX A - can have item 1,2,3,4 in it BOX B - can have item 6,7,8,9,10,11,12 BOX C - can have item 13,15,16,20,21 The items are stored in a db, they have a column which denotes which box they can go in. All box types are stored in an array, and I can put the items in a generic list. Anyone see a straightforward way to do this. I have tried doing 10 nested foreach's to see if i could find a simpler way. The nested loops will take MANY hours to run. the nested for each's basically pull all combinations, then calculate a rank for each combination, and store the top 10 ranked combination of items for output

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• search algorithm using sentinel

  - by davit-datuashvili

  i am trying to do search algorithm using sentinel which reduce time to 3.87n nanoseconds for example compare to this code int search (int t ){ for (int i=0;i<n;i++) if (x[i]==t) return i; return -1; } it takes 4.06 nanoseconds so i am trying to optimize it here is code public class Search{ public static int search(int a[],int t){ int i; int p=0; int n=a.length; int hold; hold=a[n-1]; a[n-1]=t; for ( i=0;;i++) if (a[i]==t) break; a[n-1]=t; if (i==n){ p= -1; } else{ p= i; } return p; } public static void main(String[]args){ int t=-1; int a[]=new int[]{4,5,2,6,8,7,9}; System.out.println(search(a,t)); } } but is show me that 9 is at position 6 which is correct but if t =1 or something else which is not array it show me position 6 too please help

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• Questions about the Backpropogation Algorithm

  - by Colemangrill

  I have a few questions concerning backpropogation. I'm trying to learn the fundamentals behind neural network theory and wanted to start small, building a simple XOR classifier. I've read a lot of articles and skimmed multiple textbooks - but I can't seem to teach this thing the pattern for XOR. Firstly, I am unclear about the learning model for backpropogation. Here is some pseudo-code to represent how I am trying to train the network. [Lets assume my network is setup properly (ie: multiple inputs connect to a hidden layer connect to an output layer and all wired up properly)]. SET guess = getNetworkOutput() // Note this is using a sigmoid activation function. SET error = desiredOutput - guess SET delta = learningConstant * error * sigmoidDerivative(guess) For Each Node in inputNodes For Each Weight in inputNodes[n] inputNodes[n].weight[j] += delta; // At this point, I am assuming the first layer has been trained. // Then I recurse a similar function over the hidden layer and output layer. // The prime difference being that it further divi's up the adjustment delta. I realize this is probably not enough to go off of, and I will gladly expound on any part of my implementation. Using the above algorithm, my neural network does get trained, kind of. But not properly. The output is always XOR 1 1 [smallest number] XOR 0 0 [largest number] XOR 1 0 [medium number] XOR 0 1 [medium number] I can never train the [1,1] [0,0] to be the same value. If you have any suggestions, additional resources, articles, blogs, etc for me to look at I am very interested in learning more about this topic. Thank you for your assistance, I appreciate it greatly!

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• Search and Matching algorithm

  - by Tony

  Hello everyone. I am trying to come up with an algorithm to do the following: I have total 12 cells that I need to fill until program stops. I have 3 rows and each row has 4 columns. As an example, let me illustrate this as in airplane. So you have 3 rows and each row has 4 columns and you have window/aisle seats. Each row will have a window seat, aisle seat, aisle seat and window seat (|WA AW| Just like seat arrangement in airplane). At each iteration (different set of passengers), there would be some number of passengers (between 1 and 12) and I need to seat them closest together possible (Seat together). And I do this for next group (each iteration) until program stops (It will stop when I am done with every group). For example, I have 3 passengers (A,B,and C) and A wants to seat in Window, B wants to seat in Aisle and C wants to seat in Window. Assuming that all the seats (all 12) are available, I could place them like |A# BC| or |CB #A| and mark the seats dirty (so I don’t pick same seats again for next passengers). And I do this for next group (iteration). I am not sure if this right forum, but if somebody can advise me how I should accomplish, I would really appreciate it. Thanks.

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• Algorithm: Find smallest subset containing K 0's

  - by Vishal

  I have array of 1's and 0's only. Now I want to find contiguous subset/subarray which contains at least K 0's. Example Array is 1 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 and K(6) should be 0 0 1 0 1 1 0 0 0 or 0 0 0 0 1 0 1 1 0.... My Solution Array: 1 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 Index: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Sum: 1 2 2 3 4 4 5 6 6 6 6 6 7 7 8 9 9 9 9 10 11 11 11 Diff(I-S): 0 0 1 1 1 2 2 2 3 4 5 6 6 7 7 7 8 9 10 10 10 11 12 For K(6) Start with 9-15 = Store difference in diff. Next increase difference 8-15(Difference in index) 8-14(Compare Difference in index) So on keep moving to find element with least elements... I am looking for better algorithm for this solution.

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• Issue with angular gradient algorithm

  - by user146780

  I have an angular gradient algorithm: GLuint OGLENGINEFUNCTIONS::CreateAngularGradient( std::vector<ARGBCOLORF> &input,POINTFLOAT start, POINTFLOAT end, int width, int height ) { std::vector<GLubyte> pdata(width * height * 4); float pi = 3.1415; float cx; float cy; float r1; float r2; float ang; float px; float py; float t; cx = start.x; cy = start.y; r1 = 0; r2 = 500; ang = end.x / 100; ARGBCOLORF color; for (unsigned int i = 0; i < height; i++) { for (unsigned int j = 0; j < width; j++) { px = j; py = i; if( px * px + py * py <= r2 * r2 && px * px + py * py >= r1 * r1 ) { t= atan2(py-cy,px-cx) + ang; t= t+ pi; if (t > 2* pi) { t=t-2*pi; t=t/(2*pi); } } //end + start color.r = (0 * t) + (120 * (1 - t)); color.g = (50 * t) + (255 * (1 - t)); color.b = (0 * t) + (50 * (1 - t)); color.a = (255 * t) + (200 * (1 - t)); pdata[i * 4 * width + j * 4 + 0] = (GLubyte) color.r; pdata[i * 4 * width + j * 4 + 1] = (GLubyte) color.g; pdata[i * 4 * width + j * 4 + 2] = (GLubyte) 12; pdata[i * 4 * width + j * 4 + 3] = (GLubyte) 255; } } It works fine except the ang variable only controls the end sweep, not the start sweep. The start sweep is always facing the middle left as seen here: http://img810.imageshack.us/img810/9623/uhoh.png Basically I have no control over the end one going this <- way. How could I control this one? Thanks

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• Algorithm to Render a Horizontal Binary-ish Tree in Text/ASCII form

  - by Justin L.

  It's a pretty normal binary tree, except for the fact that one of the nodes may be empty. I'd like to find a way to output it in a horizontal way (that is, the root node is on the left and expands to the right). I've had some experience expanding trees vertically (root node at the top, expanding downwards), but I'm not sure where to start, in this case. Preferably, it would follow these couple of rules: If a node has only one child, it can be skipped as redundant (an "end node", with no children, is always displayed) All nodes of the same depth must be aligned vertically; all nodes must be to the right of all less-deep nodes and to the left of all deeper nodes. Nodes have a string representation which includes their depth. Each "end node" has its own unique line; that is, the number of lines is the number of end nodes in the tree, and when an end node is on a line, there may be nothing else on that line after that end node. As a consequence of the last rule, the root node should be in either the top left or the bottom left corner; top left is preferred. For example, this is a valid tree, with six end nodes (node is represented by a name, and its depth): [a0]------------[b3]------[c5]------[d8] \ \ \----------[e9] \ \----[f5] \--[g1]--------[h4]------[i6] \ \--------------------[j10] \-[k3] Which represents the horizontal, explicit binary tree: 0 a / \ 1 g * / \ \ 2 * * * / \ \ 3 k * b / / \ 4 h * * / \ \ \ 5 * * f c / \ / \ 6 * i * * / / \ 7 * * * / / \ 8 * * d / / 9 * e / 10 j (branches folded for compactness; * representing redundant, one-child nodes; note that *'s are actual nodes, storing one child each, just with names omitted here for presentation sake) (also, to clarify, I'd like to generate the first, horizontal tree; not this vertical tree) I say language-agnostic because I'm just looking for an algorithm; I say ruby because I'm eventually going to have to implement it in ruby anyway. Assume that each Node data structure stores only its id, a left node, and a right node. A master Tree class keeps tracks of all nodes and has adequate algorithms to find: A node's nth ancestor A node's nth descendant The generation of a node The lowest common ancestor of two given nodes Anyone have any ideas of where I could start? Should I go for the recursive approach? Iterative?

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• Algorithm to retrieve every possible combination of sublists of a two lists

  - by sgmoore

  Suppose I have two lists, how do I iterate through every possible combination of every sublist, such that each item appears once and only once. I guess an example could be if you have employees and jobs and you want split them into teams, where each employee can only be in one team and each job can only be in one team. Eg List<string> employees = new List<string>() { "Adam", "Bob"} ; List<string> jobs = new List<string>() { "1", "2", "3"}; I want Adam : 1 Bob : 2 , 3 Adam : 1 , 2 Bob : 3 Adam : 1 , 3 Bob : 2 Adam : 2 Bob : 1 , 3 Adam : 2 , 3 Bob : 1 Adam : 3 Bob : 1 , 2 Adam, Bob : 1, 2, 3 I tried using the answer to this stackoverflow question to generate a list of every possible combination of employees and every possible combination of jobs and then select one item from each from each list, but that's about as far as I got. I don't know the maximum size of the lists, but it would be certainly be less than 100 and there may be other limiting factors (such as each team can have no more than 5 employees) Update Not sure whether this can be tidied up more and/or simplified, but this is what I have ended up with so far. It uses the Group algorithm supplied by Yorye (see his answer below), but I removed the orderby which I don't need and caused problems if the keys are not comparable. var employees = new List<string>() { "Adam", "Bob" } ; var jobs = new List<string>() { "1", "2", "3" }; int c= 0; foreach (int noOfTeams in Enumerable.Range(1, employees.Count)) { var hs = new HashSet<string>(); foreach( var grouping in Group(Enumerable.Range(1, noOfTeams).ToList(), employees)) { // Generate a unique key for each group to detect duplicates. var key = string.Join(":" , grouping.Select(sub => string.Join(",", sub))); if (!hs.Add(key)) continue; List<List<string>> teams = (from r in grouping select r.ToList()).ToList(); foreach (var group in Group(teams, jobs)) { foreach (var sub in group) { Console.WriteLine(String.Join(", " , sub.Key ) + " : " + string.Join(", ", sub)); } Console.WriteLine(); c++; } } } Console.WriteLine(String.Format("{0:n0} combinations for {1} employees and {2} jobs" , c , employees.Count, jobs.Count)); Since I'm not worried about the order of the results, this seems to give me what I need.

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