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  • Efficient Context-Free Grammar parser, preferably Python-friendly

    - by Max Shawabkeh
    I am in need of parsing a small subset of English for one of my project, described as a context-free grammar with (1-level) feature structures (example) and I need to do it efficiently . Right now I'm using NLTK's parser which produces the right output but is very slow. For my grammar of ~450 fairly ambiguous non-lexicon rules and half a million lexical entries, parsing simple sentences can take anywhere from 2 to 30 seconds, depending it seems on the number of resulting trees. Lexical entries have little to no effect on performance. Another problem is that loading the (25MB) grammar+lexicon at the beginning can take up to a minute. From what I can find in literature, the running time of the algorithm used to parse such a grammar (Earley or CKY) should be linear to the size of the grammar and cubic to the size of the input token list. My experience with NLTK indicates that ambiguity is what hurts the performance most, not the absolute size of the grammar. So now I'm looking for a CFG parser to replace NLTK. I've been considering PLY but I can't tell whether it supports feature structures in CFGs, which are required in my case, and the examples I've seen seem to be doing a lot of procedural parsing rather than just specifying a grammar. Can anybody show me an example of PLY both supporting feature structs and using a declarative grammar? I'm also fine with any other parser that can do what I need efficiently. A Python interface is preferable but not absolutely necessary.

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  • Most efficient algorithm for merging sorted IEnumerable<T>

    - by franck
    Hello, I have several huge sorted enumerable sequences that I want to merge. Theses lists are manipulated as IEnumerable but are already sorted. Since input lists are sorted, it should be possible to merge them in one trip, without re-sorting anything. I would like to keep the defered execution behavior. I tried to write a naive algorithm which do that (see below). However, it looks pretty ugly and I'm sure it can be optimized. It may exist a more academical algorithm... IEnumerable<T> MergeOrderedLists<T, TOrder>(IEnumerable<IEnumerable<T>> orderedlists, Func<T, TOrder> orderBy) { var enumerators = orderedlists.ToDictionary(l => l.GetEnumerator(), l => default(T)); IEnumerator<T> tag = null; var firstRun = true; while (true) { var toRemove = new List<IEnumerator<T>>(); var toAdd = new List<KeyValuePair<IEnumerator<T>, T>>(); foreach (var pair in enumerators.Where(pair => firstRun || tag == pair.Key)) { if (pair.Key.MoveNext()) toAdd.Add(pair); else toRemove.Add(pair.Key); } foreach (var enumerator in toRemove) enumerators.Remove(enumerator); foreach (var pair in toAdd) enumerators[pair.Key] = pair.Key.Current; if (enumerators.Count == 0) yield break; var min = enumerators.OrderBy(t => orderBy(t.Value)).FirstOrDefault(); tag = min.Key; yield return min.Value; firstRun = false; } } The method can be used like that: // Person lists are already sorted by age MergeOrderedLists(orderedList, p => p.Age); assuming the following Person class exists somewhere: public class Person { public int Age { get; set; } } Duplicates should be conserved, we don't care about their order in the new sequence. Do you see any obvious optimization I could use?

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  • addSublayer vs addSubView which is more efficient?

    - by soonio
    I have 5 UIImageViews for displaying 5 images. For my app, I need swap the order of them depending on some events. I achieve this by calling: [anImageView1 removeFromSuperview]; [self.view insertSubview:anImageView1 aboveSubview:anImageView2]; Recently, I've come across a different method for doing this using 1 UIView and 5 UIImageViews. Each layer of UIImageViews are added to this UIView by calling [aView.layer addSublayer:anImageView1.layer]; [aView.layer addSublayer:anImageView2.layer]; etc. and then in order to swap the order of things by calling [anImageView1.layer removeFromSuperLayer]; [aView.layer insertSublayer:anImageView1 above: anImageView2] Both methods work fine, but can someone please point out which method is better and why? I really can't seem to be able to find much on CALayer... Please help! Thank you so much!

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  • Grails efficient hasMany-Relationship in View

    - by Jan
    Hi folks, I'm saving contacts (email, mobile phone, ICQ, AIM etc.) for people like this: class Person { static hasMany = { contacts: Contact } } class Contact { String code ContactType type } class ContactType { String name } In my view, I've written some Templates for displaying each contact with a select-box for the contact-type and a textfield for the code, spiced up with some JavaScript for adding and deleting. My question is: Is there an easy and elegant way to update the data similar to personInstance.properties = params or do I have to read out all the fields, deleting removed, updating changed and adding new ones?

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  • Efficient Map Overlays in on Android Google Map...

    - by Ahsan
    Hi Friends, I want to do the following and am kind of stuck on these for a few days.... 1) I have used helloItemizedOverlay to add about 150 markers and it gets very very slow.....any idea what to do ? I was thinking about threads....(handler) ... 2) I was trying to draw poly lines ( I have encoded polylines, but have managed to decoded those) that move when I move the map.....(the only solution that I found was for Geopoints to be transformed into screen co-ordinates...which wont move if I move the map !) 3) I was looking for some sort of a timer function that executes a given function, say, every 1 minute or so.... 4) I was also looking for ways to clear the Google map from all the markers/lines etc.... Thanks a lot... :) - ahsan

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  • Isn't INT more efficient than UNIQUEIDENTIFIER?

    - by ck
    I have a parent table and child table where the columns that join them together are the UNIQUEIDENTIFIER type. The child table has a clustered index on the column that joins it to the parent table (its PK, which is also clustered). I have created a copy of both of these tables but changed the relationship columns to be INTs instead, have rebuilt the indexes so that they are essentially the same structure and can be queried in the same way. When I query for a known 20 records from the parent table, pulling in all the related records from the child tables, I get identical query costs across both, i.e. 50/50 cost for the batches. If this is true, then my giant project to change all of the tables like this appears to be pointless, other than speeding up inserts. Can anyone provide any light on the situation?

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  • Most efficient method to query a Young Tableau

    - by Matthieu M.
    A Young Tableau is a 2D matrix A of dimensions M*N such that: i,j in [0,M)x[0,N): for each p in (i,M), A[i,j] <= A[p,j] for each q in (j,N), A[i,j] <= A[i,q] That is, it's sorted row-wise and column-wise. Since it may contain less than M*N numbers, the bottom-right values might be represented either as missing or using (in algorithm theory) infinity to denote their absence. Now the (elementary) question: how to check if a given number is contained in the Young Tableau ? Well, it's trivial to produce an algorithm in O(M*N) time of course, but what's interesting is that it is very easy to provide an algorithm in O(M+N) time: Bottom-Left search: Let x be the number we look for, initialize i,j as M-1, 0 (bottom left corner) If x == A[i,j], return true If x < A[i,j], then if i is 0, return false else decrement i and go to 2. Else, if j is N-1, return false else increment j This algorithm does not make more than M+N moves. The correctness is left as an exercise. It is possible though to obtain a better asymptotic runtime. Pivot Search: Let x be the number we look for, initialize i,j as floor(M/2), floor(N/2) If x == A[i,j], return true If x < A[i,j], search (recursively) in A[0:i-1, 0:j-1], A[i:M-1, 0:j-1] and A[0:i-1, j:N-1] Else search (recursively) in A[i+1:M-1, 0:j], A[i+1:M-1, j+1:N-1] and A[0:i, j+1:N-1] This algorithm proceed by discarding one of the 4 quadrants at each iteration and running recursively on the 3 left (divide and conquer), the master theorem yields a complexity of O((N+M)**(log 3 / log 4)) which is better asymptotically. However, this is only a big-O estimation... So, here are the questions: Do you know (or can think of) an algorithm with a better asymptotical runtime ? Like introsort prove, sometimes it's worth switching algorithms depending on the input size or input topology... do you think it would be possible here ? For 2., I am notably thinking that for small size inputs, the bottom-left search should be faster because of its O(1) space requirement / lower constant term.

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  • The SPARC SuperCluster

    - by Karoly Vegh
    Oracle has been providing a lead in the Engineered Systems business for quite a while now, in accordance with the motto "Hardware and Software Engineered to Work Together." Indeed it is hard to find a better definition of these systems.  Allow me to summarize the idea. It is:  Build a compute platform optimized to run your technologies Develop application aware, intelligently caching storage components Take an impressively fast network technology interconnecting it with the compute nodes Tune the application to scale with the nodes to yet unseen performance Reduce the amount of data moving via compression Provide this all in a pre-integrated single product with a single-pane management interface All these ideas have been around in IT for quite some time now. The real Oracle advantage is adding the last one to put these all together. Oracle has built quite a portfolio of Engineered Systems, to run its technologies - and run those like they never ran before. In this post I'll focus on one of them that serves as a consolidation demigod, a multi-purpose engineered system.  As you probably have guessed, I am talking about the SPARC SuperCluster. It has many great features inherited from its predecessors, and it adds several new ones. Allow me to pick out and elaborate about some of the most interesting ones from a technological point of view.  I. It is the SPARC SuperCluster T4-4. That is, as compute nodes, it includes SPARC T4-4 servers that we learned to appreciate and respect for their features: The SPARC T4 CPUs: Each CPU has 8 cores, each core runs 8 threads. The SPARC T4-4 servers have 4 sockets. That is, a single compute node can in parallel, simultaneously  execute 256 threads. Now, a full-rack SPARC SuperCluster has 4 of these servers on board. Remember the keyword demigod.  While retaining the forerunner SPARC T3's exceptional throughput, the SPARC T4 CPUs raise the bar with single performance too - a humble 5x better one than their ancestors.  actually, the SPARC T4 CPU cores run in both single-threaded and multi-threaded mode, and switch between these two on-the-fly, fulfilling not only single-threaded OR multi-threaded applications' needs, but even mixed requirements (like in database workloads!). Data security, anyone? Every SPARC T4 CPU core has a built-in encryption engine, that is, encryption algorithms cast into silicon.  A PCI controller right on the chip for customers who need I/O performance.  Built-in, no-cost Virtualization:  Oracle VM for SPARC (the former LDoms or Logical Domains) is not a server-emulation virtualization technology but rather a serverpartitioning one, the hypervisor runs in the server firmware, and all the VMs' HW resources (I/O, CPU, memory) are accessed natively, without performance overhead.  This enables customers to run a number of Solaris 10 and Solaris 11 VMs separated, independent of each other within a physical server II. For Database performance, it includes Exadata Storage Cells - one of the main reasons why the Exadata Database Machine performs at diabolic speed. What makes them important? They provide DB backend storage for your Oracle Databases to run on the SPARC SuperCluster, that is what they are built and tuned for DB performance.  These storage cells are SQL-aware.  That is, if a SPARC T4 database compute node executes a query, it doesn't simply request tons of raw datablocks from the storage, filters the received data, and throws away most of it where the statement doesn't apply, but provides the SQL query to the storage node too. The storage cell software speaks SQL, that is, it is able to prefilter and through that transfer only the relevant data. With this, the traffic between database nodes and storage cells is reduced immensely. Less I/O is a good thing - as they say, all the CPUs of the world do one thing just as fast as any other - and that is waiting for I/O.  They don't only pre-filter, but also provide data preprocessing features - e.g. if a DB-node requests an aggregate of data, they can calculate it, and handover only the results, not the whole set. Again, less data to transfer.  They support the magical HCC, (Hybrid Columnar Compression). That is, data can be stored in a precompressed form on the storage. Less data to transfer.  Of course one can't simply rely on disks for performance, there is Flash Storage included there for caching.  III. The low latency, high-speed backbone network: InfiniBand, that interconnects all the members with: Real High Speed: 40 Gbit/s. Full Duplex, of course. Oh, and a really low latency.  RDMA. Remote Direct Memory Access. This technology allows the DB nodes to do exactly that. Remotely, directly placing SQL commands into the Memory of the storage cells. Dodging all the network-stack bottlenecks, avoiding overhead, placing requests directly into the process queue.  You can also run IP over InfiniBand if you please - that's the way the compute nodes can communicate with each other.  IV. Including a general-purpose storage too: the ZFSSA, which is a unified storage, providing NAS and SAN access too, with the following features:  NFS over RDMA over InfiniBand. Nothing is faster network-filesystem-wise.  All the ZFS features onboard, hybrid storage pools, compression, deduplication, snapshot, replication, NFS and CIFS shares Storageheads in a HA-Cluster configuration providing availability of the data  DTrace Live Analytics in a web-based Administration UI Being a general purpose application data storage for your non-database applications running on the SPARC SuperCluster over whichever protocol they prefer, easily replicating, snapshotting, cloning data for them.  There's a lot of great technology included in Oracle's SPARC SuperCluster, we have talked its interior through. As for external scalability: you can start with a half- of full- rack SPARC SuperCluster, and scale out to several racks - that is, stacking not separate full-rack SPARC SuperClusters, but extending always one large instance of the size of several full-racks. Yes, over InfiniBand network. Add racks as you grow.  What technologies shall run on it? SPARC SuperCluster is a general purpose scaleout consolidation/cloud environment. You can run Oracle Databases with RAC scaling, or Oracle Weblogic (end enjoy the SPARC T4's advantages to run Java). Remember, Oracle technologies have been integrated with the Oracle Engineered Systems - this is the Oracle on Oracle advantage. But you can run other software environments such as SAP if you please too. Run any application that runs on Oracle Solaris 10 or Solaris 11. Separate them in Virtual Machines, or even Oracle Solaris Zones, monitor and manage those from a central UI. Here the key takeaways once again: The SPARC SuperCluster: Is a pre-integrated Engineered System Contains SPARC T4-4 servers with built-in virtualization, cryptography, dynamic threading Contains the Exadata storage cells that intelligently offload the burden of the DB-nodes  Contains a highly available ZFS Storage Appliance, that provides SAN/NAS storage in a unified way Combines all these elements over a high-speed, low-latency backbone network implemented with InfiniBand Can grow from a single half-rack to several full-rack size Supports the consolidation of hundreds of applications To summarize: All these technologies are great by themselves, but the real value is like in every other Oracle Engineered System: Integration. All these technologies are tuned to perform together. Together they are way more than the sum of all - and a careful and actually very time consuming integration process is necessary to orchestrate all these for performance. The SPARC SuperCluster's goal is to enable infrastructure operations and offer a pre-integrated solution that can be architected and delivered in hours instead of months of evaluations and tests. The tedious and most importantly time and resource consuming part of the work - testing and evaluating - has been done.  Now go, provide services.   -- charlie  

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  • efficient algorithm for drawing circle arcs?

    - by banister
    I am using the mid-point circle algorithm (bresenham circle) to efficiently draw whole circles. Is there something similar to draw circle arcs? I would like to specify a start angle and end angle and have only that portion of the circle drawn. Thanks in advance! EDIT: I would like to draw filled circle arcs too, i.e pie-slices. :)

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  • Most efficient sorting of calculation on DataTable column calculation

    - by byte
    Lets say you have a DataTable that has columns of "id", "cost", "qty": DataTable dt = new DataTable(); dt.Columns.Add("id", typeof(int)); dt.Columns.Add("cost", typeof(double)); dt.Columns.Add("qty", typeof(int)); And it's keyed on "id": dt.PrimaryKey = new DataColumn[1] { dt.Columns["id"] }; Now what we are interested in is the cost per quantity. So, in other words if you had a row of: id | cost | qty ---------------- 42 | 10.00 | 2 The cost per quantity is 5.00. My question then is, given the preceeding table, assume it's constructed with many thousands of rows, and you're interested in the top 3 cost per quantity rows. The information needed is the id, cost per quantity. You cannot use LINQ. In SQL it would be trivial; how BEST (most efficiently) would you accomplish it in C# without LINQ?

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  • Efficient data importing?

    - by Kevin
    We work with a lot of real estate, and while rearchitecting how the data is imported, I came across an interesting issue. Firstly, the way our system works (loosely speaking) is we run a Coldfusion process once a day that retrieves data provided from an IDX vendor via FTP. They push the data to us. Whatever they send us is what we get. Over the years, this has proven to be rather unstable. I am rearchitecting it with PHP on the RETS standard, which uses SOAP methods of retrieving data, which is already proven to be much better than what we had. When it comes to 'updating' existing data, my initial thought was to query only for data that was updated. There is a field for 'Modified' that tells you when a listing was last updated, and the code I have will grab any listing updated within the last 6 hours (give myself a window in case something goes wrong). However, I see a lot of real estate developers suggest creating 'batch' processes that run through all listings regardless of updated status that is constantly running. Is this the better way to do it? Or am I fine with just grabbing the data I know I need? It doesn't make a lot of sense to me to do more processing than necessary. Thoughts?

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  • Efficient cron job utilizing Zend_Mail_Storage_Imap.

    - by fireeyedboy
    I'm new to the IMAP protocol and Zend_Mail_Storage and I'm writing a small php script for a cron job that should regularly poll an IMAP account and check for new messages, and send an e-mail if new messages have arrived. As you can imagine, I want to only poll the IMAP account for relevant messages, and I only want to send a new e-mail if new messages have arrived since the last polled new message. So I thought of keeping track of the last message I polled with some unique identifier for a message. But I'm a bit uncertain about whether the methods I want to utilize for this do what I expect them to do though. So my questions are: Does the iterator position of Zend_Mail_Storage_Imap actually resemble some IMAP unique identifier for messages, or is it simply only and internal position of Zend_Mail_Storage_Abstract? For instance, if I tell it to seek() to message 5 (which I stored from an earlier session) will it indeed seek to the appropriate message on the IMAP server, even if for instance messages have been deleted since last session? Would keeping track of this latest polled message id in a file suffice for a cron job that, say, polls the account every 5 or 10 minutes? Or is this too naive, and should I be using a database for instance. Or is there maybe a much easier way to keep track of such state with Zend_Mail_Storage_Abstract? Also, do I need to poll every IMAP folder? Or is everything accumulated when I poll INBOX? If you could shed some light on any of these matters, I'ld appreciate it. Thanks in advance.

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  • Efficient code to avoid circular references in c# object model

    - by Kumar
    I have an excel like grid where values can be typed referencing other rows To check for circular references when a new value is entered, i traverse the tree and create a list of values referenced thus far, if the current value is found in this list, i return an error thus avoiding a circular reference. This is infrequent enough where extreme performance is not an issue but... Question - is there a better way ? I'm told it's not the most optimal but no answer was provided so on to the experts @ SO :)

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  • Most efficient way to send images across processes

    - by Heinrich Ulbricht
    Goal Pass images generated by one process efficiently and at very high speed to another process. The two processes run on the same machine and on the same desktop. The operating system may be WinXP, Vista and Win7. Detailled description The first process is solely for controlling the communication with a device which produces the images. These images are about 500x300px in size and may be updated up to several hundred times per second. The second process needs these images to display them. The first process uses a third party API to paint the images from the device to a HDC. This HDC has to be provided by me. Note: There is already a connection open between the two processes. They are communicating via anonymous pipes and share memory mapped file views. Thoughts How would I achieve this goal with as little work as possible? And I mean both work for me and the computer. I am using Delphi, so maybe there is some component available for doing this? I think I could always paint to any image component's HDC, save the content to memory stream, copy the contents via the memory mapped file, unpack it on the other side and paint it there to the destination HDC. I also read about a IPicture interface which can be used to marshall images. What are your ideas? I appreciate every thought on this!

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  • Writing more efficient xquery code (avoiding redundant iteration)

    - by Coquelicot
    Here's a simplified version of a problem I'm working on: I have a bunch of xml data that encodes information about people. Each person is uniquely identified by an 'id' attribute, but they may go by many names. For example, in one document, I might find <person id=1>Paul Mcartney</person> <person id=2>Ringo Starr</person> And in another I might find: <person id=1>Sir Paul McCartney</person> <person id=2>Richard Starkey</person> I want to use xquery to produce a new document that lists every name associated with a given id. i.e.: <person id=1> <name>Paul McCartney</name> <name>Sir Paul McCartney</name> <name>James Paul McCartney</name> </person> <person id=2> ... </person> The way I'm doing this now in xquery is something like this (pseudocode-esque): let $ids := distinct-terms( [all the id attributes on people] ) for $id in $ids return <person id={$id}> { for $unique-name in distinct-values ( for $name in ( [all names] ) where $name/@id=$id return $name ) return <name>{$unique-name}</name> } </person> The problem is that this is really slow. I imagine the bottleneck is the innermost loop, which executes once for every id (of which there are about 1200). I'm dealing with a fair bit of data (300 MB, spread over about 800 xml files), so even a single execution of the query in the inner loop takes about 12 seconds, which means that repeating it 1200 times will take about 4 hours (which might be optimistic - the process has been running for 3 hours so far). Not only is it slow, it's using a whole lot of virtual memory. I'm using Saxon, and I had to set java's maximum heap size to 10 GB (!) to avoid getting out of memory errors, and it's currently using 6 GB of physical memory. So here's how I'd really like to do this (in Pythonic pseudocode): persons = {} for id in ids: person[id] = set() for person in all_the_people_in_my_xml_document: persons[person.id].add(person.name) There, I just did it in linear time, with only one sweep of the xml document. Now, is there some way to do something similar in xquery? Surely if I can imagine it, a reasonable programming language should be able to do it (he said quixotically). The problem, I suppose, is that unlike Python, xquery doesn't (as far as I know) have anything like an associative array. Is there some clever way around this? Failing that, is there something better than xquery that I might use to accomplish my goal? Because really, the computational resources I'm throwing at this relatively simple problem are kind of ridiculous.

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  • Most efficient way to store list structure in XML

    - by Mike
    Starting a new project and was planning on storing all of my web content in XML. I do not have access to a database so this seemed like the next best thing. One thing I'm struggling with is how to structure the XML for links (which will later be transformed using XSLT). It needs to be fairly flexible as well. Below is what I started with, but I'm starting to question it. <links> <link> <url>http://google.com</url> <description>Google</description> <link> <link> <url>http://yahoo.com</url> <description>Yahoo</description> <links> <url>http://yahoo.com/search</url> <description>Search</description> </link> <link> </links> That should get transformed into Google Yahoo Search Perhaps something like this might work better. <links> <link href="http://google.com">Google</link> <link href="http://yahoo.com">Yahoo <link href="http://yahoo.com/search">Search</link> </link> </links> Does anyone perhaps have a link that talks about structuring web content properly in XML? Thank you. :)

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  • Algorithm: efficient way to remove duplicate integers from an array

    - by ejel
    I got this problem from an interview with Microsoft. Given an array of random integers, write an algorithm in C that removes duplicated numbers and return the unique numbers in the original array. E.g Input: {4, 8, 4, 1, 1, 2, 9} Output: {4, 8, 1, 2, 9, ?, ?} One caveat is that the expected algorithm should not required the array to be sorted first. And when an element has been removed, the following elements must be shifted forward as well. Anyway, value of elements at the tail of the array where elements were shifted forward are negligible. Update: The result must be returned in the original array and helper data structure (e.g. hashtable) should not be used. However, I guess order preservation is not necessary. Update2: For those who wonder why these impractical constraints, this was an interview question and all these constraints are discussed during the thinking process to see how I can come up with different ideas.

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  • C#: What is the best collection class to store very similar string items for efficient serialization

    - by Gregor
    Hi, I would like to store a list of entityIDs of outlook emails to a file. The entityIDs are strings like: "000000005F776F08B736B442BCF7B6A7060B509A64002000" "000000005F776F08B736B442BCF7B6A7060B509A84002000" "000000005F776F08B736B442BCF7B6A7060B509AA4002000" as you can notice, the strings are very similar. I would like to save these strings in a collection class that would be stored as efficiently as possible when I serialize it to a file. Do you know of any collection class that could be used for this? Thank you in advance for any information... Gregor

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  • Building an *efficient* if/then interface for non-technical users to build flow-control in PHP

    - by Brendan
    I am currently building an internal tool to be used by our management to control the flow of traffic. I have built an if/then interface allowing the user to set conditions for certain outcomes, however it is inefficient to use the switch statement to control the flow. How can I improve the efficiency of my code? Example of code: if($previous['route_id'] == $condition['route_id'] && $failed == 0) //if we have not moved on to a new set of rules and we haven't failed yet { switch($condition['type']) { case 0 : $type = $user['hour']; break; case 1 : $type = $user['location']['region_abv']; break; case 2 : $type = $user['referrer_domain']; break; case 3 : $type = $user['affiliate']; break; case 4 : $type = $user['location']['country_code']; break; case 5 : $type = $user['location']['city']; break; } $type = strtolower($type); $condition['value'] = strtolower($condition['value']); switch($condition['operator']) { case 0 : if($type == $condition['value']); else $failed = '1'; break; case 1 : if($type != $condition['value']); else $failed = '1'; break; case 2 : if($type > $condition['value']); else $failed = '1'; break; case 3 : if($type >= $condition['value']); else $failed = '1'; break; case 4 : if($type < $condition['value']); else $failed = '1'; break; case 5 : if($type <= $condition['value']); else $failed = '1'; break; } }

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  • Efficient algorithm to generate all solutions of a linear diophantine equation with ai=1

    - by Ben
    I am trying to generate all the solutions for the following equations for a given H. With H=4 : 1) ALL solutions for x_1 + x_2 + x_3 + x_4 =4 2) ALL solutions for x_1 + x_2 + x_3 = 4 3) ALL solutions for x_1 + x_2 = 4 4) ALL solutions for x_1 =4 For my problem, there are always 4 equations to solve (independently from the others). There are a total of 2^(H-1) solutions. For the previous one, here are the solutions : 1) 1 1 1 1 2) 1 1 2 and 1 2 1 and 2 1 1 3) 1 3 and 3 1 and 2 2 4) 4 Here is an R algorithm which solve the problem. library(gtools) H<-4 solutions<-NULL for(i in seq(H)) { res<-permutations(H-i+1,i,repeats.allowed=T) resum<-apply(res,1,sum) id<-which(resum==H) print(paste("solutions with ",i," variables",sep="")) print(res[id,]) } However, this algorithm makes more calculations than needed. I am sure it is possible to go faster. By that, I mean not generating the permutations for which the sums is H Any idea of a better algorithm for a given H ?

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  • Which is more Efficient HTML DOM or JQuery

    - by Quasar the space thing
    I am trying to add new Elements in an HTML page body by using document.createElement via Javascript, I am doing this with few if/else case and function callings. All is working fine. Recently I came to know that I can do this with JQuery, too. I have not done too much of coding yet so I was wondering which way is the best in terms of efficiency ? Using native DOM methods or using JQuery to add elements dynamically on the page?

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