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• Spaced repetition (SRS) for learning

  - by Fredrik Johansson

  A client has asked me to add a simple spaced repeition algorithm (SRS) for an onlinebased learning site. But before throwing my self into it, I'd like to discuss it with the community. Basically the site asks the user a bunch of questions (by automatically selecting say 10 out of 100 total questions from a database), and the user gives either a correct or incorrect answer. The users result are then stored in a database, for instance: userid questionid correctlyanswered dateanswered 1 123 0 (no) 2010-01-01 10:00 1 124 1 (yes) 2010-01-01 11:00 1 125 1 (yes) 2010-01-01 12:00 Now, to maximize a users ability to learn all answers, I should be able to apply an SRS algorithm so that a user, next time he takes the quiz, receives questions incorrectly answered more often; than questions answered correctly. Also, questions that are previously answered incorrectly, but recently often answered correctly should occur less often. Have anyone implemented something like this before? Any tips or suggestions? Theese are the best links I've found: http://en.wikipedia.org/wiki/Spaced_repetition http://www.mnemosyne-proj.org/principles.php http://www.supermemo.com/english/ol/sm2.htm

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• Calculate total batch upload transfer percent with limited information

  - by GONeale

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

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• Code golf: combining multiple sorted lists into a single sorted list

  - by Alabaster Codify

  Implement an algorithm to merge an arbitrary number of sorted lists into one sorted list. The aim is to create the smallest working programme, in whatever language you like. For example: input: ((1, 4, 7), (2, 5, 8), (3, 6, 9)) output: (1, 2, 3, 4, 5, 6, 7, 8, 9) input: ((1, 10), (), (2, 5, 6, 7)) output: (1, 2, 5, 6, 7, 10) Note: solutions which concatenate the input lists then use a language-provided sort function are not in-keeping with the spirit of golf, and will not be accepted: sorted(sum(lists,[])) # cheating: out of bounds! Apart from anything else, your algorithm should be (but doesn't have to be) a lot faster! Clearly state the language, any foibles and the character count. Only include meaningful characters in the count, but feel free to add whitespace to the code for artistic / readability purposes. To keep things tidy, suggest improvement in comments or by editing answers where appropriate, rather than creating a new answer for each "revision". EDIT: if I was submitting this question again, I would expand on the "no language provided sort" rule to be "don't concatenate all the lists then sort the result". Existing entries which do concatenate-then-sort are actually very interesting and compact, so I won't retro-actively introduce a rule they break, but feel free to work to the more restrictive spec in new submissions. Inspired by http://stackoverflow.com/questions/464342/combining-two-sorted-lists-in-python

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• Using generics to make an algorithm work on lists of "something" instead of only String's

  - by Binary255

  Hi, I have a small algorithm which replaces the position of characters in a String: class Program { static void Main(string[] args) { String pairSwitchedStr = pairSwitch("some short sentence"); Console.WriteLine(pairSwitchedStr); Console.ReadKey(); } private static String pairSwitch(String str) { StringBuilder pairSwitchedStringBuilder = new StringBuilder(); for (int position = 0; position + 1 < str.Length; position += 2) { pairSwitchedStringBuilder.Append((char)str[position + 1]); pairSwitchedStringBuilder.Append((char)str[position]); } return pairSwitchedStringBuilder.ToString(); } } I would like to make it as generic as possible, possibly using Generics. What I'd like to have is something which works with: Anything that is built up using a list of instances. Including strings, arrays, linked lists I suspect that the solution must use generics as the algorithm is working on a list of instances of T (there T is ... something). Version of C# isn't of interest, I guess the solution will be nicer if features from C# version 2.0 is used.

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• categorize a set of phrases into a set of similar phrases

  - by Dingo

  I have a few apps that generate textual tracing information (logs) to log files. The tracing information is the typical printf() style - i.e. there are a lot of log entries that are similar (same format argument to printf), but differ where the format string had parameters. What would be an algorithm (url, books, articles, ...) that will allow me to analyze the log entries and categorize them into several bins/containers, where each bin has one associated format? Essentially, what I would like is to transform the raw log entries into (formatA, arg0 ... argN) instances, where formatA is shared among many log entries. The formatA does not have to be the exact format used to generate the entry (even more so if this makes the algo simpler). Most of the literature and web-info I found deals with exact matching, a max substring matching, or a k-difference (with k known/fixed ahead of time). Also, it focuses on matching a pair of (long) strings, or a single bin output (one match among all input). My case is somewhat different, since I have to discover what represents a (good-enough) match (generally a sequence of discontinuous strings), and then categorize each input entries to one of the discovered matches. Lastly, I'm not looking for a perfect algorithm, but something simple/easy to maintain. Thanks!

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• What does O(log n) mean exactly?

  - by Andreas Grech

  I am currently learning about Big O Notation running times and amortized times. I understand the notion of O(n) linear time, meaning that the size of the input affects the growth of the algorithm proportionally...and the same goes for, for example, quadratic time O(n2) etc..even algorithms, such as permutation generators, with O(n!) times, that grow by factorials. For example, the following function is O(n) because the algorithm grows in proportion to its input n: f(int n) { int i; for (i = 0; i < n; ++i) printf("%d", i); } Similarly, if there was a nested loop, the time would be O(n2). But what exactly is O(log n)? For example, what does it mean to say that the height of a complete binary tree is O(log n)? I do know (maybe not in great detail) what Logarithm is, in the sense that: log10 100 = 2, but I cannot understand how to identify a function with a logarithmic time.

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• Need simple advice for graph solving problem

  - by sap

  Hi there, a collegue of mine proposed to me an exercise from an online judge website, which is basically a graph solving problem of an evacuation plan on a small town. i dont need the answer (nor do i want it) i just need an advice on which is the best approach to solving it since im kinda new to these kind of problems. the problem consists of town buildings with workers and fallout shelters in case of a nuclear attack. i have to build an algorithm that will assign the workers of each building to one or more fallout shelters but in a way that some shelters wont became too overcrowded while others remain almost empty (else i would just make the workers go to the nearest one). the problem is this: http://acm.timus.ru/problem.aspx?space=1&num=1237 in case its offline heres the google cached version of it: http://webcache.googleusercontent.com/search?q=cache:t2EPCzezs7AJ:acm.timus.ru/problem.aspx%3Fspace%3D1%26num%3D1237+vladimir+kotov+evacuation+problem&cd=1&hl=pt-PT&ct=clnk&gl=pt what i've done so far is for each building get the nearest shelter and move the number of workers from that build equal to the shelter capacity. then move to the next building. but sometimes the number of workers is greater than the shelter capacity, in that case after i iterate through every building, ill just iterate then again apllying the same algorithm until every building has 0 workers in it, problem is this is hardly the best way to solve it. any tip is welcome, please dont feel like im asking for the answer, i just want an advice in the right direction of solving it. thanks in advance.

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• Practical rules for premature optimization

  - by DougW

  It seems that the phrase "Premature Optimization" is the buzz-word of the day. For some reason, iphone programmers in particular seem to think of avoiding premature optimization as a pro-active goal, rather than the natural result of simply avoiding distraction. The problem is, the term is beginning to be applied more and more to cases that are completely inappropriate. For example, I've seen a growing number of people say not to worry about the complexity of an algorithm, because that's premature optimization (eg http://stackoverflow.com/questions/2190275/help-sorting-an-nsarray-across-two-properties-with-nssortdescriptor/2191720#2191720). Frankly, I think this is just laziness, and appalling to disciplined computer science. But it has occurred to me that maybe considering the complexity and performance of algorithms is going the way of assembly loop unrolling, and other optimization techniques that are now considered unnecessary. What do you think? Are we at the point now where deciding between an O(n^n) and O(n!) complexity algorithm is irrelevant? What about O(n) vs O(n*n)? What do you consider "premature optimization"? What practical rules do you use to consciously or unconsciously avoid it? This is a bit vague, but I'm curious to hear other peoples' opinions on the topic.

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• split line of text

  - by plys

  Hi all, I was wondering if there is an algorithm to split a line into multiple lines, so that the resulting set of multiple lines fit into a square shape rather than a rectangle. Let me give some examples, Input: Hi this is a really long line. Output: Hi this is a really long line Input: a b c d e f Output: a b c d e f Input: This is really such looooooooooooooooooooong line.This is the end. Output: This is really such looooooooooooooooooooong line This is the end. If you see in the above examples, input line fits into a wide rectangle. But the output more or less fits into a square shape. Essentially what needs to be done here is simply count the number of characters in the line, take the square root of that number. Then put square root number of characters in each line. But in the above example, the splitting needs to be done by respecting word wraps instead of characters. Is there any standard algorithm for this? Any code examples/ pointers would be appreciated!

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• Find the Algorithm that generates the checksum

  - by knivmannen

  I have a sensing device that transmits a 6-byte message along with an 1-byte counter and supposely a checksum. The data looks something like this: ------DATA----------- -Counter- --Checksum?-- 55 FF 00 00 EC FF ---- 60---------- 1F The last four bits in the counter are always set 0, i.e those bits are probably not used. The last byte is assumed to be the checksum since it has a quite peculiar nature. It tends to randomly change as data changes. Now what i need is to find the algorithm to compute this checksum based on --DATA--. what i have tried is all possible CRC-8 polynomials, for each polynomial i have tried to reflect data, toggle it, initiate it with non-zeroes etc etc. Ive come to the conclusion that i am not dealing with a normal crc-algorithm. I have also tried some flether and adler methods without succes, xor stuff back and forth but still i have no clue how to generate the checksum. My biggest concern is, how is the counter used??? Same data but with different countervalue generates different checksums. I have tried to include the counter in my computations but without any luck. Here are some other datasamples: 55 FF 00 00 F0 FF A0 38 66 0B EA FF BF FF C0 CA 5E 18 EA FF B7 FF 60 BD F6 30 16 00 FC FE 10 81 One more thing that might be worth mentioning is that the last byte in the data only takes on the values FF or FE Plz if u have any tips or tricks that i may try post them here, I am truly desperate. Thx

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• Enumerate all paths in a weighted graph from A to B where path length is between C1 and C2

  - by awmross

  Given two points A and B in a weighted graph, find all paths from A to B where the length of the path is between C1 and C2. Ideally, each vertex should only be visited once, although this is not a hard requirement. I supose I could use a heuristic to sort the results of the algorithm to weed out "silly" paths (e.g. a path that just visits the same two nodes over and over again) I can think of simple brute force algorithms, but are there any more sophisticed algorithms that will make this more efficient? I can imagine as the graph grows this could become expensive. In the application I am developing, A & B are actually the same point (i.e. the path must return to the start), if that makes any difference. Note that this is an engineering problem, not a computer science problem, so I can use an algorithm that is fast but not necessarily 100% accurate. i.e. it is ok if it returns most of the possible paths, or if most of the paths returned are within the given length range.

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• Machine leaning algorithm for data classification.

  - by twk

  Hi all, I'm looking for some guidance about which techniques/algorithms I should research to solve the following problem. I've currently got an algorithm that clusters similar-sounding mp3s using acoustic fingerprinting. In each cluster, I have all the different metadata (song/artist/album) for each file. For that cluster, I'd like to pick the "best" song/artist/album metadata that matches an existing row in my database, or if there is no best match, decide to insert a new row. For a cluster, there is generally some correct metadata, but individual files have many types of problems: Artist/songs are completely misnamed, or just slightly mispelled the artist/song/album is missing, but the rest of the information is there the song is actually a live recording, but only some of the files in the cluster are labeled as such. there may be very little metadata, in some cases just the file name, which might be artist - song.mp3, or artist - album - song.mp3, or another variation A simple voting algorithm works fairly well, but I'd like to have something I can train on a large set of data that might pick up more nuances than what I've got right now. Any links to papers or similar projects would be greatly appreciated. Thanks!

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• The mathematics of Schellings segregation model

  - by Bruce

  For those who don't know the model. You can read this pdf. I want to find what is the probability that 2 nodes are each others neighbors when the algorithm converges (i.e. when all nodes are happy). Here's the model in a gist. You have a grid (say 10x10). You have nodes of two kind (red and green) 45 each. So we have 10 empty spaces. We randomly place the nodes on the grid. Now we scan through this grid (Exact order does not matter according to Schelling). Each node wants a specific percentage of people of same kind in its Moore neighborhood (say b = 50% for each red and green). We calculate the happiness of each node (a = Number of neighbors of same kind/Number of neighbors of different kind). If a node is unhappy (a < b) it moves to an empty cell where it knows it will be happy. This movement can change the dynamics of old as well as new neighborhood. Algorithm converges when all nodes are happy. PS - I am looking for links for any mathematical analysis of the Schelling's model.

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• Simple encryption - Sum of Hashes in C

  - by Dogbert

  I am attempting to demonstrate a simple proof of concept with respect to a vulnerability in a piece of code in a game written in C. Let's say that we want to validate a character login. The login is handled by the user choosing n items, (let's just assume n=5 for now) from a graphical menu. The items are all medieval themed: eg: _______________________________ | | | | | Bow | Sword | Staff | |-----------|-----------|-------| | Shield | Potion | Gold | |___________|___________|_______| The user must click on each item, then choose a number for each item. The validation algorithm then does the following: Determines which items were selected Drops each string to lowercase (ie: Bow becomes bow, etc) Calculates a simple string hash for each string (ie: `bow = b=2, o=15, w=23, sum = (2+15+23=40) Multiplies the hash by the value the user selected for the corresponding item; This new value is called the key Sums together the keys for each of the selected items; this is the final validation hash IMPORTANT: The validator will accept this hash, along with non-zero multiples of it (ie: if the final hash equals 1111, then 2222, 3333, 8888, etc are also valid). So, for example, let's say I select: Bow (1) Sword (2) Staff (10) Shield (1) Potion (6) The algorithm drops each of these strings to lowercase, calculates their string hashes, multiplies that hash by the number selected for each string, then sums these keys together. eg: Final_Validation_Hash = 1*HASH(Bow) + 2*HASH(Sword) + 10*HASH(Staff) + 1*HASH(Shield) + 6*HASH(Potion) By application of Euler's Method, I plan to demonstrate that these hashes are not unique, and want to devise a simple application to prove it. in my case, for 5 items, I would essentially be trying to calculate: (B)(y) = (A_1)(x_1) + (A_2)(x_2) + (A_3)(x_3) + (A_4)(x_4) + (A_5)(x_5) Where: B is arbitrary A_j are the selected coefficients/values for each string/category x_j are the hash values for each string/category y is the final validation hash (eg: 1111 above) B,y,A_j,x_j are all discrete-valued, positive, and non-zero (ie: natural numbers) Can someone either assist me in solving this problem or point me to a similar example (ie: code, worked out equations, etc)? I just need to solve the final step (ie: (B)(Y) = ...). Thank you all in advance.

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• Determining polygon intersection and containment

  - by Victor Liu

  I have a set of simple (no holes, no self-intersections) polygons, and I need to check that they don't intersect each other (one can be entirely contained in another; that is okay). I can check this by simply checking the per-vertex inside-ness of one polygon versus other polygons. I also need to determine the containment tree, which is the set of relationships that say which polygon contains any given polygon. Since no polygon can intersect any other, then any contained polygon has a unique container; the "next-bigger" one. In other words, if A contains B contains C, then A is the parent of B, and B is the parent of C, and we don't consider A the parent of C. The question: How do I efficiently determine the containment relationships and check the non-intersection criterion? I ask this as one question because maybe a combined algorithm is more efficient than solving each problem separately. The algorithm should take as input a list of polygons, given by a list of their vertices. It should produce a boolean B indicating if none of the polygons intersect any other polygon, and also if B = true, a list of pairs (P, C) where polygon P is the parent of child C. This is not homework. This is for a hobby project I am working on.

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• PHP Resize image down and crop using imagemagick

  - by mr12086

  I'm trying to downsize image uploaded by users at the time of upload. This is no problem but I want to get specific with sizes now. I'm looking for some advice on an algorithm im struggling to produce that will take any shape image - square or rectangle of any widths/heights and downsize it. This image needs to be downsized to a target box size (this changes but is stored in a variable).. So it needs to downsize the image so that both the width and height are larger than the width and height of the target maintaining aspect ratio. but only just.. The target size will be used to crop the image so there is no white space around the edges etc. I'm looking for just the algorithm behind creating the correct resize based on different dimension images - I can handle the cropping, even resizing in most cases but it fails in a few so i'm reaching out. I'm not really asking for PHP code more pseudo. Either is fine obviously. Thanks Kindly.

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• How to use Caret to tell which line it is in from JTextPane? (Java)

  - by Alex Cheng

  Hi all. Problem: I have CaretListener and DocumentListener listening on a JTextPane. I need an algorithm that is able to tell which line is the caret at in a JTextPane, here's an illustrative example: Result: 3rd line Result: 2nd line Result: 4th line and if the algorithm can tell which line the caret is in the JTextPane, it should be fairly easy to substring whatever that is in between the parentheses as the picture (caret is at character m of metadata): -- This is how I divide the entire text that I retrieved from the JTextPane into sentences: String[] lines = textPane.getText().split("\r?\n|\r", -1); The sentences in the textPane is separated with \n. Problem is, how can I manipulate the caret to let me know at which position and which line it is in? I know the dot of the caret says at which position it is, but I can't tell which line it is at. Assuming if I know which line the caret is, then I can just do lines[<line number>] and manipulate the string from there. In Short: How do I use CaretListener and/or DocumentListener to know which line the caret is currently at, and retrieve the line for further string manipulation? Please help. Thanks. Do let me know if further clarification is needed. Thanks for your time.

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• Endianness and C API's: Specifically OpenSSL.

  - by Hassan Syed

  I have an algorithm that uses the following OpenSSL calls: HMAC_update() / HMAC_final() // ripe160 EVP_CipherUpdate() / EVP_CipherFinal() // cbc_blowfish These algorithm take a unsigned char * into the "plain text". My input data is comes from a C++ std::string::c_str() which originate from a protocol buffer object as a encoded UTF-8 string. UTF-8 strings are meant to be endian neutrial. However I'm a bit paranoid about how OpenSSL may perform operations on the data. My understanding is that encryption algorithms work on 8-bit blocks of data, and if a unsigned char * is used for pointer arithmetic when the operations are performed the algorithms should be endian neutral and I do not need to worry about anything. My uncertainty is compounded by the fact that I am working on a little-endian machine and have never done any real cross-architecture programming. My beliefs/reasoning are/is based on the following two properties std::string (not wstring) internally uses a 8-bit ptr and a the resulting c_str() ptr will itterate the same way regardless of the CPU architecture. Encryption algorithms are either by design, or by implementation, endian neutral. I know the best way to get a definitive answer is to use QEMU and do some cross-platform unit tests (which I plan to do). My question is a request for comments on my reasoning, and perhaps will assist other programmers when faced with similar problems.

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• computes the number of possible orderings of n objects under the relations < and =

  - by hilal

  Here is the problem : Give a algorithm that takes a positive integer n as input, and computes the number of possible orderings of n objects under the relations < and =. For example, if n = 3 the 13 possible orderings are as follows: a = b = c, a = b < c, a < b = c, a < b < c, a < c < b, a = c < b, b < a = c, b < a < c, b < c < a, b = c < a, c < a = b, c < a < b, c < b < a. Your algorithm should run in time polynomial in n. I'm null to this problem. Can you find any solution to this dynamic-programming problem?

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• Optimizing a bin-placement algorithm

  - by user258651

  Alright, I've got two collections, and I need to place elements from collection1 into the bins (elements) of collection2, based on whether their value falls within a given bin's range. For a concrete example, assume I have a sorted collection objects (bins) which have an int range ([1...4], [5..10], etc). I need to determine the range an int falls in, and place it in the appropriate bin. foreach(element n in collection1) { foreach(bin m in collection2) { if (m.inRange(n)) { m.add(n); break; } } } So the obvious NxM complexity algorithm is there, but I really would like to see Nxlog(M). To do this I'd like to use BinarySearch in place of the inner foreach loop. To use BinarySearch, I need to implement an IComparer class to do the searching for me. The problem I'm running into is this approach would require me to make an IComparer.Compare function that compares two different types of objects (an element to its bin), and that doesn't seem possible or correct. So I'm asking, how should I write this algorithm?

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• Find the number of congruent triangles?

  - by avd

  Say I have a square from (0,0) to (z,z). Given a triangle within this square which has integer coordinates for all its vertices. Find out the number of triangles within this square which are congruent to this triangle and have integer coordinates. My algorithm is as follows-- 1) Find out the minimum bounding rectangle(MBR) for the given triangle. 2) Find out the number of congruent triangles, y within that MBR, obtained after reflection, rotation of the given triangle. y can be either 2,4 or 8. 3) Now find out how many such MBR's can be drawn within the given big square, say x; (This is similar to finding number of squares on a chess board) 4) x*y is the required answer. Am I counting some triangles more than once or I am missing something by this algorithm? It is a problem on online judge? It gives me wrong answer. I have thought a lot about it, but I am not able to figure it out.

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• Resource placement (optimal strategy)

  - by blackened

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

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• Fastest way to perform subset test operation on a large collection of sets with same domain

  - by niktech

  Assume we have trillions of sets stored somewhere. The domain for each of these sets is the same. It is also finite and discrete. So each set may be stored as a bit field (eg: 0000100111...) of a relatively short length (eg: 1024). That is, bit X in the bitfield indicates whether item X (of 1024 possible items) is included in the given set or not. Now, I want to devise a storage structure and an algorithm to efficiently answer the query: what sets in the data store have set Y as a subset. Set Y itself is not present in the data store and is specified at run time. Now the simplest way to solve this would be to AND the bitfield for set Y with bit fields of every set in the data store one by one, picking the ones whose AND result matches Y's bitfield. How can I speed this up? Is there a tree structure (index) or some smart algorithm that would allow me to perform this query without having to AND every stored set's bitfield? Are there databases that already support such operations on large collections of sets?

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• Go and a bad prime number algorithm

  - by anonymous

  I wrote this prime number sieving algorithm and it doesn't run properly. I can't find the error in the algorithm itself. Could someone help me? This is what it's supposed to print: [2 3 5 7 11 13 17 19 23 29] Versus what it actually prints: [3 5 7 11 13 17 19 23 25 29] . package main import "fmt" func main() { var primes = sieve(makeNumbers(29)) fmt.Printf("%d\n", primes); } func makeNumbers(n int) []int { var numbers = make([]int, n - 1) for i := 0; i < len(numbers); i++ { numbers[i] = i + 2 } return numbers } func sieve(numbers []int) []int { var numCopy = numbers var max = numbers[len(numbers)-1] var sievedNumbers = make([]int, 0) for i := 0; numCopy[i]*numCopy[i] <= max; i++ { for j := i; j < len(numCopy); j++ { if numCopy[j] % numCopy[i] != 0 || j == i { sievedNumbers = append(sievedNumbers, numCopy[j]) } } numCopy = sievedNumbers sievedNumbers = make([]int, 0) } return numCopy }

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• Measuring how "heavily linked" a node is in a graph

  - by Eduardo León

  I have posted this question at MathOverflow.com as well. I am no mathematician and English is not my first language, so please excuse me if my question is too stupid, it is poorly phrased, or both. I am developing a program that creates timetables. My timetable-creating algorithm, besides creating the timetable, also creates a graph whose nodes represent each class I have already programmed, and whose arcs represent which pairs of classes should not be programmed at the same time, even if they have to be reprogrammed. The more "heavily linked" a node is, the more inflexible its associated class is with respect to being reprogrammed. Sometimes, in the middle of the process, there will be no option but to reprogram a class that has already been programmed. I want my program to be able to choose a class that, if reprogrammed, affects the least possible number of other already-programmed classes. That would mean choosing a node in the graph that is "not very heavily linked", subject to some constraints with respect to which nodes can be chosen. EDIT: The question was... Do you know any algorithm that measures how "heavily linked" a node is?

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