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  • Speeding up a group by date query on a big table in postgres

    - by zaius
    I've got a table with around 20 million rows. For arguments sake, lets say there are two columns in the table - an id and a timestamp. I'm trying to get a count of the number of items per day. Here's what I have at the moment. SELECT DATE(timestamp) AS day, COUNT(*) FROM actions WHERE DATE(timestamp) >= '20100101' AND DATE(timestamp) < '20110101' GROUP BY day; Without any indices, this takes about a 30s to run on my machine. Here's the explain analyze output: GroupAggregate (cost=675462.78..676813.42 rows=46532 width=8) (actual time=24467.404..32417.643 rows=346 loops=1) -> Sort (cost=675462.78..675680.34 rows=87021 width=8) (actual time=24466.730..29071.438 rows=17321121 loops=1) Sort Key: (date("timestamp")) Sort Method: external merge Disk: 372496kB -> Seq Scan on actions (cost=0.00..667133.11 rows=87021 width=8) (actual time=1.981..12368.186 rows=17321121 loops=1) Filter: ((date("timestamp") >= '2010-01-01'::date) AND (date("timestamp") < '2011-01-01'::date)) Total runtime: 32447.762 ms Since I'm seeing a sequential scan, I tried to index on the date aggregate CREATE INDEX ON actions (DATE(timestamp)); Which cuts the speed by about 50%. HashAggregate (cost=796710.64..796716.19 rows=370 width=8) (actual time=17038.503..17038.590 rows=346 loops=1) -> Seq Scan on actions (cost=0.00..710202.27 rows=17301674 width=8) (actual time=1.745..12080.877 rows=17321121 loops=1) Filter: ((date("timestamp") >= '2010-01-01'::date) AND (date("timestamp") < '2011-01-01'::date)) Total runtime: 17038.663 ms I'm new to this whole query-optimization business, and I have no idea what to do next. Any clues how I could get this query running faster?

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  • CodeIgniter - the right way to create "block" elements on web page

    - by kikkoman90
    Hello. I've been searching for a solutions for this problem a while but haven't seen any "valid mvc" solution for this. I hope I can explain my problem clearly enough for you guys. I need to create a dynamic block of HTML on my website. (eg. a block containing user's latest blog comments). I have a template view file (a file containing header, content container and a footer) where I need to add some content AND this block element. The problem is that I don't want to duplicate this block code on every controller. It just feels stupid and I'm sure there's a better way to do this than just duplicating same stuff all over again on all the controller files? I can add view inside another view just fine, but what bugs me is how to actually generate that dynamic content to this block's view-file. I can't call controller from view file, controller from controller filem or model from view file because what I understand that just isn't the "mvc" way? Anyone got any tricks or tips for this?

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  • Visual studio 2008 unit test keeps failing

    - by Gerbrand
    I've create a method that calculates the harmonic mean based on a list of doubles. But when I'm running the test it keeps failing even thou the output result are the same. My harmonic mean method: public static double GetHarmonicMean(List<double> parameters) { var cumReciprocal = 0.0d; var countN = parameters.Count; foreach( var param in parameters) { cumReciprocal += 1.0d/param; } return 1.0d/(cumReciprocal/countN); } My test method: [TestMethod()] public void GetHarmonicMeanTest() { var parameters = new List<double> { 1.5d, 2.3d, 2.9d, 1.9d, 5.6d }; const double expected = 2.32432293165495; var actual = OwnFunctions.GetHarmonicMean(parameters); Assert.AreEqual(expected, actual); } After running the test the following message is showing: Assert.AreEqual failed. Expected:<2.32432293165495. Actual:<2.32432293165495. For me that are both the same values. Can somebody explain this? Or am I doing something wrong?

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  • XCode Obj-C: Make new NSArray from one key each out of an Array of Dictionaries

    - by user323772
    This actually could be a multipart question. But here's the first part ... I have an array (actually in a plist) of dictionaries. Each dictionary has 3 keys in it: (title), (points), and (description). I am trying to make a NEW array with the values of the key "title" from each dictionary in that first array. Let me explain WHY I am doing this and maybe that will provide a better all around explanation. I am trying to let people pick from a pre-determined list. Heck, if this was a web page it would be very simple since all I really care about are the "points" and the "Title". On a web site I could simply do a drop down combo-box with the "points" being the value and the title being the text for each row. But this is not a web page. So what I am trying to do here is pop out a modal picker when they click the text field. The modal picker shows the alphabetical ordered "titles" from our new array. And whichever one they select, it closes the modal view and assigns that "title" text to the UITextField which cannot be edited by the user. I have some code to get my modal picker to pop out. But I need to feed it an array of just the "titles" of each dictionary in my real array. Thanks in advance (and yes I am a newbie)

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  • PHP: Adding arrays together

    - by Svish
    Could someone help me explain this? I have two snippets of code, one works as I expect, but the other does not. This works $a = array('a' => 1, 'b' => 2); $b = array('c' => 3); $c = $a + $b; print_r($c); // Output Array ( [a] => 1 [b] => 2 [c] => 3 ) This does not $a = array('a', 'b'); $b = array('c'); $c = $a + $b; print_r($c); // Output Array ( [a] => 1 [b] => 2 ) What is going on here?? Why doesn't the second version also add the two arrays together? What have I misunderstood? What should I be doing instead? Or is it a bug in PHP?

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  • What is the event dispatching thread?

    - by Roman
    I know what "thread" means and if I understand the event dispatching thread (EDT) as "just a thread", it explains a lot but, apparently, it does not explain everything. I do not understand what is special about this thread. For example I do not understand why we should start a GUI in a the EDT? Why the "main" thread is bed for GUI? Well, if we just do not want to occupy the main thread why we cannot start GUI just in "another thread" why it should be some "special" thread called EDT? Then I do not understand why we cannot start the EDT like any other thread? Why we should use some special tool (called invokeLater). And why GUI, unlike any other thread, does not start immediately. We should wait until it is ready to accept our job. Is it because EDT can, potentially execute several task simultaneously? If you decide to answer this question, could you pleas use a really simple terminology because otherwise, I am afraid, I will not be able to understand the answer.

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  • How to gracefully handle YouTube thumbnail broken images when videos are taken down?

    - by mrjf
    Our site contains some lists of YouTube videos with their thumbnails linked to the movies themselves. We fetch the thumbnail URLs from the YouTube API, and hotlink to them in situ on YouTube's servers. So our image tags look like: <img src="http://i.ytimg.com/vi/o6CHqSN7O-o/2.jpg" alt="" width="133" height="78" /> The problem is that sometimes a video gets removed -- and so does the thumbnail. We don't know when that might happen, and our thumbnails just turn into broken images. How can we handle this? There are a number of solutions: Download thumbnails and store them locally -- movie won't work, but that's ok, it will explain it was removed, and we avoid the broken image Check periodically with the API to see if the image thumbnail has changed -- if it no longer exists, substitute our own "movie removed" thumbnail. This is pretty heavy on the API calling! Use JavaScript to replace broken images (don't like this one much) Our ideal solution would be to point the img src to a location on YouTube that would display a friendly "move removed" image when a movie goes down. However, that doesn't seem to exist. Anyone else dealt with this? Thanks!

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  • C++: how serialize/deserialize objects without any library?

    - by Winte Winte
    I try to understand how serializing/deserializing works in c++, so I want to do that without any libs. But I really stuck with that. I start with simple objects but when I try to deserilize a vector I understand that I can't get a vector without if I don't write it size before. Moreover, I don't know which format of file I should choose because if digits will be existed before size of vector I haven't chance to read it right. However it is only the vector but I also want to do that with classes and map container. My task is serialize/deserialize a objects as this: PersonInfo { unsigned int age_; string name_; enum { undef, man, woman } sex_; } Person : PersonInfo { vector<Person> children_; map<string, PersonInfo> addrBook_; } Currently I know how to serialize simple objects in way as this: vector<PersonInfo> vecPersonInfo; vecPersonInfo.push_back(*personInfo); vecPersonInfo.push_back(*oneMorePersonInfo); ofstream file("file", ios::out | ios::binary); if (!file) { cout<<"can not open file"; } else { vector<PersonInfo>::const_iterator iterator = vecPersonInfo.begin(); for (; iterator != vecPersonInfo.end(); iterator++) { file<<*iterator; } Could you please suggest how I can do this for this conplex object or a good tutorial that explain it clearly?

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  • Nested modal view controller gives strange message under iOS6?

    - by user1840362
    I am presenting a modal view controller from another modal view controller, and this worked fine under all iOS versions prior to iOS6. But under iOS6 I am getting the following warning message in the emulator: Warning: Attempt to present <UINavigationController: 0x14e93680> on <UINavigationController: 0x9fc6b70> while a presentation is in progress! The modal view controller is not shown if this warning appears. Basically I am using code like this to show the modal view controller: WebAuthViewController *authController = [[WebAuthViewController alloc] initWithNibName:nil bundle:nil]; authController.challenge = challenge; authController.delegate = self; UINavigationController *aNavController = [[UINavigationController alloc] initWithRootViewController:authController]; [self presentModalViewController:aNavController animated:YES]; [aNavController release]; [authController release]; The view that is already shown is a UIWebView also shown in a modal view, like this: WebViewController *addController = [[WebViewController alloc] initWithNibName:nil bundle:nil]; addController.urlToLoad = [NSURL URLWithString:urlString]; addController.delegate = self; UINavigationController *navigationController = [[UINavigationController alloc] initWithRootViewController:addController]; navigationController.modalTransitionStyle = UIModalTransitionStyleFlipHorizontal; [self presentModalViewController:navigationController animated:YES]; [navigationController release]; [addController release]; The apple docs still suggest that one is supposed to be able to stack navigation controllers like this, so I am at a loss to explain why this happens. Any hints?

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  • C++ new memory allocation fragmentation

    - by tamulj
    I was trying to look at the behavior of the new allocator and why it doesn't place data contiguously. My code: struct ci { char c; int i; } template <typename T> void memTest() { T * pLast = new T(); for(int i = 0; i < 20; ++i) { T * pNew = new T(); cout << (pNew - pLast) << " "; pLast = pNew; } } So I ran this with char, int, ci. Most allocations were a fixed length from the last, sometimes there were odd jumps from one available block to another. sizeof(char) : 1 Average Jump: 64 bytes sizeof(int): 4 Average Jump: 16 sizeof(ci): 8 (int has to be placed on a 4 byte align) Average Jump: 9 Can anyone explain why the allocator is fragmenting memory like this? Also why is the jump for char so much larger then ints and a structure that contains both an int and char.

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  • "Address of" (&) an array / address of being ignored be gcc?

    - by dbarbosa
    Hi, I am a teaching assistant of a introductory programming course, and some students made this type of error: char name[20]; scanf("%s",&name); which is not surprising as they are learning... What is surprising is that, besides gcc warning, the code works (at least this part). I have been trying to understand and I wrote the following code: void foo(int *str1, int *str2) { if (str1 == str2) printf("Both pointers are the same\n"); else printf("They are not the same\n"); } int main() { int test[50]; foo(&test, test); if (&test == test) printf("Both pointers are the same\n"); else printf("They are not the same\n"); } Compiling and executing: $ gcc test.c -g test.c: In function ‘main’: test.c:12: warning: passing argument 1 of ‘foo’ from incompatible pointer type test.c:13: warning: comparison of distinct pointer types lacks a cast $ ./a.out Both pointers are the same Both pointers are the same Can anyone explain why they are not different? I suspect it is because I cannot get the address of an array (as I cannot have & &x), but in this case the code should not compile.

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  • Clarification on ZVals

    - by Beachhouse
    I was reading this: http://www.dereleased.com/2011/04/27/the-importance-of-zvals-and-circular-references/ And there's an example that lost me a bit. $foo = &$bar; $bar = &$foo; $baz = 'baz'; $foo = &$baz; var_dump($foo, $bar); /* string(3) "baz" NULL */ If you’ve been following along, this should make perfect sense. $foo is created, and pointed at a ZVal location identified by $bar; when $bar is created, it points at the same place $foo was pointed. That location, of course, is null. When $foo is reassigned, the only thing that changes is to which ZVal $foo points; if we had assigned a different value to $foo first, then $bar would still retain that value. I learned to program in C. I understand that PHP is different and it uses ZVals instead of memory locations as references. But when you run this code: $foo = &$bar; $bar = &$foo; It seems to me that there would be two ZVals. In C there would be two memory locations (and the values would be of the opposite memory location). Can someone explain?

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  • Dojo's nested BorderContainer disappear in IE

    - by h4b0
    I have this terrible problem with IE 7/8/9. I wrote an app using Dojo toolkit 1.8.0 and Play! framework. It works fine in all browser except for IE. Its 'developers tools' show no error, so does firebug. The problematic code section is here: <div data-dojo-type="dijit.layout.BorderContainer" data-dojo-props="design: 'headline'"> <div data-dojo-type="dijit.layout.ContentPane" id="head" region="top"> </div> <div data-dojo-type="dijit.layout.BorderContainer" data-dojo-props="region: 'center'"> <div data-dojo-type="dijit.layout.ContentPane" id="menu" region="left"> </div> <div data-dojo-type="dijit.layout.BorderContainer" data-dojo-props="region: 'center'"> <div data-dojo-type="dijit.layout.ContentPane" id="content_1" region="top"> </div> <div data-dojo-type="dijit.layout.ContentPane" id="content_2" region="bottom"> </div> </div> </div> <div data-dojo-type="dijit.layout.ContentPane" id="foot" region="bottom"> </div> </div> The result, in all browsers except for IE is like that: But in IE it is shown like that: Can anyone explain why there are such differences? At first I thought that in IE content is hidden, so I set overflow: auto, but no scrollbar appeared after page load.

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  • Array Assignment

    - by Mahesh
    Let me explain with an example - #include <iostream> void foo( int a[2], int b[2] ) // I understand that, compiler doesn't bother about the // array index and converts them to int *a, int *b { a = b ; // At this point, how ever assignment operation is valid. } int main() { int a[] = { 1,2 }; int b[] = { 3,4 }; foo( a, b ); a = b; // Why is this invalid here. return 0; } Is it because, array decays to a pointer when passed to a function foo(..), assignment operation is possible. And in main, is it because they are of type int[] which invalidates the assignment operation. Doesn't a,b in both the cases mean the same ? Thanks. Edit 1: When I do it in a function foo, it's assigning the b's starting element location to a. So, thinking in terms of it, what made the language developers not do the same in main(). Want to know the reason.

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  • Big-Oh running time of code in Java (are my answers accurate

    - by Terry Frederick
    the Method hasTwoTrueValues returns true if at least two values in an array of booleans are true. Provide the Big-Oh running time for all three implementations proposed. // Version 1 public boolean has TwoTrueValues( boolean [ ] arr ) { int count = 0; for( int i = 0; i < arr. length; i++ ) if( arr[ i ] ) count++; return count >= 2; } // Version 2 public boolean hasTwoTrueValues( boolean [ ] arr ) { for( int i = 0; i < arr.length; i++ ) for( int j = i + 1; j < arr.length; j++ ) if( arr[ i ] && arr[ j ] ) return true; } // Version 3 public boolean hasTwoTrueValues( boolean [ ] arr ) { for( int i = 0; i < arr.length; i++ if( arr[ i ] ) for( int j = i + 1; j < arr.length; j++ ) if( arr[ j ] ) return true; return false; } For Version 1 I say the running time is O(n) Version 2 I say O(n^2) Version 3 I say O(n^2) I am really new to this Big Oh Notation so if my answers are incorrect could you please explain and help.

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  • Target to a page inside an iframe

    - by Marcelo Srougi
    I will try to explain again: I have 3 images in my index.html that when clicked i'd like to point respectively to ourmission.html, ourvalues.html and ourvision.html. But this 3 pages are inside an iframe located in the page ourcompany.html as you can see below: <aside class="sidebar"> <h4>Our Company</h4> <ul class="nav nav-list primary pull-bottom"> <li><a href="contactus.html"target="conteudo">Contact Us</a></li> <li><a href="ourmission.html" target="conteudo">Our Mission</a></li> <li><a href="ourvalues.html" target="conteudo">Our Values</a></li> <li><a href="ourvision.html"target="conteudo">Our Vision</a></li> </ul> </aside> <iframe src="contactus.html" frameborder='0' name="conteudo" width="700" height="700"> </iframe> How do i to point them directly, so the page ourcompany.html will load with the specific iframe opened.

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  • c# Find value in a range using lambda

    - by n4rzul
    I'm trying to find an item in a list of values based on another value using a lambda expression using the Find method. In this example I'm expecting to get back -1000, but for the life of me, I just can't come up with the proper lamda expression. If that sounds confusing I hope the code and comments below explain it better. TIA. using System; using System.Collections.Generic; namespace TestingStuff { class Program { static void Main(string[] args) { double amount = -200; //The Range of values List<MyValue> values = new List<MyValue>(); values.Add(new MyValue(-1000)); values.Add(new MyValue(-100)); values.Add(new MyValue(-10)); values.Add(new MyValue(0)); values.Add(new MyValue(100)); values.Add(new MyValue(1000)); //Find it!!! MyValue fVal = values.Find(x => (x.Value > amount) && (x.Value < amount)); //Expecting -1000 as a result here since -200 falls between -1000 and -100 //if it were -90 I'd expect -100 since it falls between -100 and 0 if (fVal != null) Console.WriteLine(fVal.Value); Console.ReadKey(); } } public class MyValue { public double Value { get; set; } public MyValue(double value) { Value = value; } } }

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  • Memcached getDelayed alternative implementation

    - by iBobo
    I would like to use getDelayed on the PHP Memcached extension but I think it's not implemented in the right way. Right now you ask for some keys and then retrieve all of them with fetch() and fetchAll(). But imagine a scenario where I need to retrieve 15 keys used in different parts of the page which I don't know in advance, but I can ask the various objects to give me the list. What I want is give the Memcached instance this list (each component would give its part) then later when I need them retrieve from the instance, but not all of them at once: each component would take the one it needs. Basically if I were to implement this I would prohibit using getDelayed alone and implement a bookGet($keys) method where you would add the keys to book (which actually calls getDelayed), and redefine get to handle these three cases: key is booked and retrieved - return the value; key is booked but not retrieved - go and force the fetch of the booked keys and return the correct value; key not booked - do a normal lookup. I want to know if this makes sense, your thoughts on the subject and if someone already implemented this or maybe PECL Memcached already works this way and actually the documentation doesn't explain it correctly.

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  • Is there a selector or a work around to select any element with no children.

    - by rnaud
    Looking at the CSS3 specs, I can't find any way to select any element that has no children. Let me explain. <body> <h1>Main Page</h1> <div id="main"> <div class="post"> <h2>Article 1</h1> <p>some text</p> </div> <div class="post"> <h2>Article 2</h1> <p>some text</p> </div> </div> </body> I'm looking for a CSS syntax to select the h1, the two h2 and the two p. A way to select in any page, all elements with no children. Any suggestion ? Sorry, I forgot to add the "empty" part, I am actually already using the *:empty selector, but it's not working for any tag that has a nodeText as a child. So it's working for any input, image, object, but not for h2, h1, or any p.

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  • PHP array minor problem

    - by Sennheiser
    I'm really not sure how to explain this. It's so simple I can't fathom why it's not working. I have a loop. It puts a bunch of strings into an array. If I fill a single variable with any given string, it will output it perfectly. But filling an array with the strings will make it give me the dreaded: Array Array Array Array Array Array Array Array Note: my strings are not all 'Array'. The way I loop is: while(...) { $arr[] = $resultFromLoop; } Here is my var_dump. array(1) { ["tagName"]=> string(5) "magic" } array(1) { ["tagName"]=> string(4) "nunu" } array(1) { ["tagName"]=> string(5) "books" } array(1) { ["tagName"]=> string(0) "" } array(1) { ["tagName"]=> string(3) "zzz" } array(1) { ["tagName"]=> string(4) "grey" } array(1) { ["tagName"]=> string(3) "new" } array(1) { ["tagName"]=> string(6) "flight" }

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  • Why doesn't Firefox redownload images already on a page?

    - by vvo
    Hello, i just read this article : https://developer.mozilla.org/en/HTTP_Caching_FAQ There's a firefox behavior (and some other browsers i guess) i'd like to understand : if i take any webpage and try to insert the same image multiple times in javascript, the image is only downloaded ONCE even if i specifiy all needed headers to say "do no ever use cache". (see article) I know there are workarounds (like addind query strings to end of urls etc) but why do firefox act like that, if i say that an image do not have to be cached, why is the image still taken from cache when i try to re-insert it ? Plus, what cache is used for this ? (I guess it's the memory cache) Is this behavior the same for dynamic inclusion for example ? ANSWSER IS NO :) I just tested it and the same headers for a js script will make firefox redownload it each time you append the script to the DOM. PS: I know you're wondering WHY i need to do that (appending same image multiple times and force to redownload but this is the way our app works) thank you The good answer is : firefox will store images for the current page load in the memory cache even if you specify he doesnt have to cache them. You can't change this behavior but this is odd because it's not the same for javascript files for example Could someone explain or link to a document describing how firefox cache WORKS?

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  • TFS merging for users that are used to VSS

    - by JacksonD
    I just migrated a team of 7 developers from VSS to TFS. I migrated all of their code into a DEV folder which I then branched into a QA folder (which I branched into a PROD folder). The developers usually don't work on the same files, but there are some shared utility classes. All of the code is for a large ASP.NET web site. When the developers are ready to merge from DEV to QA, they only want to merge their changes. For example, let's say that Developer1 has been working on a project for the last 3 months and he's ready to merge all of his code into QA. However, Developer2 has been working on a different project for the last 2 months which is not ready to be merged. Developer1 and Developer2's changes are not in any way dependent on each other, but they are not separated into different folder structures and they each regularly do a get latest. There doesn't seem to be a way for developer1 to only merge his changes without also merging all of developer2's changes. Currently, developer1 is going through the Pending Changes window and 'Undoing Pending Changes' for all of Developer2's changes, but this is time consuming. They could merge each file individually, but this is also time consuming. Is there an easier way? I am going to have a coronary if I hear one more person explain how much easier it was to work in VSS.

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  • Checking Selected Radio Button after POST

    - by coffeeaddict
    I've been using ASP.NET controls which perform a lot of the manual for you. But I'm going back to the basics, what everyone else does. I'm using standard input tags. So for example if I have a radio button group and I select a button. When the form submits and does a POST back to whatever action="MyPage.aspx" then to grab and check the radio button's value that was selected is it always done like this below? <label><input type="radio" name="rbGroup" value='<%# ((Action)Container.DataItem).ID %>'/><%# ((Action)Container.DataItem).Name %></label> So here I'm appending the ID to the value. And then when it hits the page that my action specifies, I'm checking to see which was selected by trimming off and getting that ID from the value: string selection = Request.Form["rbGroup"]; string dbRecordIdSelected = int.Parse(selection.Substring(1)); so now I can check the id they selected...that is the ID of the db record that gave that selected radio it's name. Is that how you basically always check what radio was selected by checking the name/value pair that comes across for that selected radioButton group name? And then you can append stuff like IDs or whatever you want to grab and parse out to then do additional logic on the server-side once that header reaches the server and your specified page in the action attribute? The above code is not production code, just something to explain what I'm talking about.

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  • Bizarre static_cast trick?

    - by Rob
    While perusing the Qt source code I came across this gem: template <class T> inline T qgraphicsitem_cast(const QGraphicsItem *item) { return int(static_cast<T>(0)->Type) == int(QGraphicsItem::Type) || (item && int(static_cast<T>(0)->Type) == item->type()) ? static_cast<T>(item) : 0; } Notice the static_cast<T>(0)->Type? I've been using C++ for many years but have never seen 0 being used in a static_cast before. What is this code doing and is it safe? Background: If you derive from QGraphicsItem you are meant to declare an unique enum value called Type that and implement a virtual function called type that returns it, e.g.: class Item : public QGraphicsItem { public: enum { Type = MAGIC_NUMBER }; int type() const { return Type; } ... }; You can then do this: QGraphicsItem* item = new Item; ... Item* derivedItem = qgraphicsitem_cast<Item*>(item); This will probably help explain what that static_cast is trying to do.

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  • please help me to solve problem

    - by davit-datuashvili
    first of all this is not homework and nobody tag it as homewrok i did not understand this porblem can anybody explain me?this is not english problem it is just misunderstanding what problem say Consider the problem of neatly printing a paragraph on a printer. The input text is a sequence of n words of lengths l1 , l2 , . . . , ln , measured in characters. We want to print this paragraph neatly on a number of lines that hold a maximum of M characters each. Our criterion of “neatness” is as follows. If a given line contains words i through j , where i = j , and we leave exactly one space between words, the number of extra space characters at the end of the line is M - j + i -(k=i,k< j,k++) lk , which must be nonnegative so that the words fit on the line. We wish to minimize the sum, over all lines except the last, of the cubes of the numbers of extra space characters at the ends of lines. Give a dynamic-programming algorithm to print a paragraph of n words neatly on a printer. Analyze the running time and space requirements of your algorithm.

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