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  • How does a template class inherit another template class?

    - by hkBattousai
    I have a "SquareMatrix" template class which inherits "Matrix" template class, like below: SquareMatrix.h: #ifndef SQUAREMATRIX_H #define SQUAREMATRIX_H #include "Matrix.h" template <class T> class SquareMatrix : public Matrix<T> { public: T GetDeterminant(); }; template <class T> // line 49 T SquareMatrix<T>::GetDeterminant() { T t = 0; // Error: Identifier "T" is undefined // line 52 return t; // Error: Expected a declaration // line 53 } // Error: Expected a declaration // line 54 #endif I commented out all other lines, the files contents are exactly as above. I receive these error messages: LINE 49: IntelliSense: expected a declaration LINE 52: IntelliSense: expected a declaration LINE 53: IntelliSense: expected a declaration LINE 54: error C2039: 'GetDeterminant' : is not a member of 'SquareMatrix' LINE 54: IntelliSense: expected a declaration So, what is the correct way of inheriting a template class? And what is wrong with this code? The "Matrix" class: template <class T> class Matrix { public: Matrix(uint64_t unNumRows = 0, uint64_t unNumCols = 0); void GetDimensions(uint64_t & unNumRows, uint64_t & unNumCols) const; std::pair<uint64_t, uint64_t> GetDimensions() const; void SetDimensions(uint64_t unNumRows, uint64_t unNumCols); void SetDimensions(std::pair<uint64_t, uint64_t> Dimensions); uint64_t GetRowSize(); uint64_t GetColSize(); void SetElement(T dbElement, uint64_t unRow, uint64_t unCol); T & GetElement(uint64_t unRow, uint64_t unCol); //Matrix operator=(const Matrix & rhs); // Compiler generate this automatically Matrix operator+(const Matrix & rhs) const; Matrix operator-(const Matrix & rhs) const; Matrix operator*(const Matrix & rhs) const; Matrix & operator+=(const Matrix & rhs); Matrix & operator-=(const Matrix & rhs); Matrix & operator*=(const Matrix & rhs); T& operator()(uint64_t unRow, uint64_t unCol); const T& operator()(uint64_t unRow, uint64_t unCol) const; static Matrix Transpose (const Matrix & matrix); static Matrix Multiply (const Matrix & LeftMatrix, const Matrix & RightMatrix); static Matrix Add (const Matrix & LeftMatrix, const Matrix & RightMatrix); static Matrix Subtract (const Matrix & LeftMatrix, const Matrix & RightMatrix); static Matrix Negate (const Matrix & matrix); // TO DO: static bool IsNull(const Matrix & matrix); static bool IsSquare(const Matrix & matrix); static bool IsFullRowRank(const Matrix & matrix); static bool IsFullColRank(const Matrix & matrix); // TO DO: static uint64_t GetRowRank(const Matrix & matrix); static uint64_t GetColRank(const Matrix & matrix); protected: std::vector<T> TheMatrix; uint64_t m_unRowSize; uint64_t m_unColSize; bool DoesElementExist(uint64_t unRow, uint64_t unCol); };

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  • Implementing a popularity algorithm in Django

    - by TheLizardKing
    I am creating a site similar to reddit and hacker news that has a database of links and votes. I am implementing hacker news' popularity algorithm and things are going pretty swimmingly until it comes to actually gathering up these links and displaying them. The algorithm is simple: Y Combinator's Hacker News: Popularity = (p - 1) / (t + 2)^1.5` Votes divided by age factor. Where` p : votes (points) from users. t : time since submission in hours. p is subtracted by 1 to negate submitter's vote. Age factor is (time since submission in hours plus two) to the power of 1.5.factor is (time since submission in hours plus two) to the power of 1.5. I asked a very similar question over yonder http://stackoverflow.com/questions/1964395/complex-ordering-in-django but instead of contemplating my options I choose one and tried to make it work because that's how I did it with PHP/MySQL but I now know Django does things a lot differently. My models look something (exactly) like this class Link(models.Model): category = models.ForeignKey(Category) user = models.ForeignKey(User) created = models.DateTimeField(auto_now_add = True) modified = models.DateTimeField(auto_now = True) fame = models.PositiveIntegerField(default = 1) title = models.CharField(max_length = 256) url = models.URLField(max_length = 2048) def __unicode__(self): return self.title class Vote(models.Model): link = models.ForeignKey(Link) user = models.ForeignKey(User) created = models.DateTimeField(auto_now_add = True) modified = models.DateTimeField(auto_now = True) karma_delta = models.SmallIntegerField() def __unicode__(self): return str(self.karma_delta) and my view: def index(request): popular_links = Link.objects.select_related().annotate(karma_total = Sum('vote__karma_delta')) return render_to_response('links/index.html', {'links': popular_links}) Now from my previous question, I am trying to implement the algorithm using the sorting function. An answer from that question seems to think I should put the algorithm in the select and sort then. I am going to paginate these results so I don't think I can do the sorting in python without grabbing everything. Any suggestions on how I could efficiently do this? EDIT This isn't working yet but I think it's a step in the right direction: from django.shortcuts import render_to_response from linkett.apps.links.models import * def index(request): popular_links = Link.objects.select_related() popular_links = popular_links.extra( select = { 'karma_total': 'SUM(vote.karma_delta)', 'popularity': '(karma_total - 1) / POW(2, 1.5)', }, order_by = ['-popularity'] ) return render_to_response('links/index.html', {'links': popular_links}) This errors out into: Caught an exception while rendering: column "karma_total" does not exist LINE 1: SELECT ((karma_total - 1) / POW(2, 1.5)) AS "popularity", (S... EDIT 2 Better error? TemplateSyntaxError: Caught an exception while rendering: missing FROM-clause entry for table "vote" LINE 1: SELECT ((vote.karma_total - 1) / POW(2, 1.5)) AS "popularity... My index.html is simply: {% block content %} {% for link in links %} karma-up {{ link.karma_total }} karma-down {{ link.title }} Posted by {{ link.user }} to {{ link.category }} at {{ link.created }} {% empty %} No Links {% endfor %} {% endblock content %} EDIT 3 So very close! Again, all these answers are great but I am concentrating on a particular one because I feel it works best for my situation. from django.db.models import Sum from django.shortcuts import render_to_response from linkett.apps.links.models import * def index(request): popular_links = Link.objects.select_related().extra( select = { 'popularity': '(SUM(links_vote.karma_delta) - 1) / POW(2, 1.5)', }, tables = ['links_link', 'links_vote'], order_by = ['-popularity'], ) return render_to_response('links/test.html', {'links': popular_links}) Running this I am presented with an error hating on my lack of group by values. Specifically: TemplateSyntaxError at / Caught an exception while rendering: column "links_link.id" must appear in the GROUP BY clause or be used in an aggregate function LINE 1: ...karma_delta) - 1) / POW(2, 1.5)) AS "popularity", "links_lin... Not sure why my links_link.id wouldn't be in my group by but I am not sure how to alter my group by, django usually does that.

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  • Common Mercator Projection formulas for Google Maps not working correctly

    - by Tom Halladay
    I am building a Tile Overlay server for Google maps in C#, and have found a few different code examples for calculating Y from Latitude. After getting them to work in general, I started to notice certain cases where the overlays were not lining up properly. To test this, I made a test harness to compare Google Map's Mercator LatToY conversion against the formulas I found online. As you can see below, they do not match in certain cases. Case #1 Zoomed Out: The problem is most evident when zoomed out. Up close, the problem is barely visible. Case #2 Point Proximity to Top & Bottom of viewing bounds: The problem is worse in the middle of the viewing bounds, and gets better towards the edges. This behavior can negate the behavior of Case #1 The Test: I created a google maps page to display red lines using the Google Map API's built in Mercator conversion, and overlay this with an image using the reference code for doing Mercator conversion. These conversions are represented as black lines. Compare the difference. The Results: Check out the top-most and bottom-most lines: The problem gets visually larger but numerically smaller as you zoom in: And it all but disappears at closer zoom levels, regardless of screen orientation. The Code: Google Maps Client Side Code: var lat = 0; for (lat = -80; lat <= 80; lat += 5) { map.addOverlay(new GPolyline([new GLatLng(lat, -180), new GLatLng(lat, 0)], "#FF0033", 2)); map.addOverlay(new GPolyline([new GLatLng(lat, 0), new GLatLng(lat, 180)], "#FF0033", 2)); } Server Side Code: Tile Cutter : http://mapki.com/wiki/Tile_Cutter OpenStreetMap Wiki : http://wiki.openstreetmap.org/wiki/Mercator protected override void ImageOverlay_ComposeImage(ref Bitmap ZipCodeBitMap) { Graphics LinesGraphic = Graphics.FromImage(ZipCodeBitMap); Int32 MapWidth = Convert.ToInt32(Math.Pow(2, zoom) * 255); Point Offset = Cartographer.Mercator2.toZoomedPixelCoords(North, West, zoom); TrimPoint(ref Offset, MapWidth); for (Double lat = -80; lat <= 80; lat += 5) { Point StartPoint = Cartographer.Mercator2.toZoomedPixelCoords(lat, -179, zoom); Point EndPoint = Cartographer.Mercator2.toZoomedPixelCoords(lat, -1, zoom); TrimPoint(ref StartPoint, MapWidth); TrimPoint(ref EndPoint, MapWidth); StartPoint.X = StartPoint.X - Offset.X; EndPoint.X = EndPoint.X - Offset.X; StartPoint.Y = StartPoint.Y - Offset.Y; EndPoint.Y = EndPoint.Y - Offset.Y; LinesGraphic.DrawLine(new Pen(Color.Black, 2), StartPoint.X, StartPoint.Y, EndPoint.X, EndPoint.Y); LinesGraphic.DrawString( lat.ToString(), new Font("Verdana", 10), new SolidBrush(Color.Black), new Point( Convert.ToInt32((width / 3.0) * 2.0), StartPoint.Y)); } } protected void TrimPoint(ref Point point, Int32 MapWidth) { point.X = Math.Max(point.X, 0); point.X = Math.Min(point.X, MapWidth - 1); point.Y = Math.Max(point.Y, 0); point.Y = Math.Min(point.Y, MapWidth - 1); } So, Anyone ever experienced this? Dare I ask, resolved this? Or simply have a better C# implementation of Mercator Project coordinate conversion? Thanks!

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  • Is it possible to implement bitwise operators using integer arithmetic?

    - by Statement
    Hello World! I am facing a rather peculiar problem. I am working on a compiler for an architecture that doesn't support bitwise operations. However, it handles signed 16 bit integer arithmetics and I was wondering if it would be possible to implement bitwise operations using only: Addition (c = a + b) Subtraction (c = a - b) Division (c = a / b) Multiplication (c = a * b) Modulus (c = a % b) Minimum (c = min(a, b)) Maximum (c = max(a, b)) Comparisons (c = (a < b), c = (a == b), c = (a <= b), et.c.) Jumps (goto, for, et.c.) The bitwise operations I want to be able to support are: Or (c = a | b) And (c = a & b) Xor (c = a ^ b) Left Shift (c = a << b) Right Shift (c = a b) (All integers are signed so this is a problem) Signed Shift (c = a b) One's Complement (a = ~b) (Already found a solution, see below) Normally the problem is the other way around; how to achieve arithmetic optimizations using bitwise hacks. However not in this case. Writable memory is very scarce on this architecture, hence the need for bitwise operations. The bitwise functions themselves should not use a lot of temporary variables. However, constant read-only data & instruction memory is abundant. A side note here also is that jumps and branches are not expensive and all data is readily cached. Jumps cost half the cycles as arithmetic (including load/store) instructions do. On other words, all of the above supported functions cost twice the cycles of a single jump. Some thoughts that might help: I figured out that you can do one's complement (negate bits) with the following code: // Bitwise one's complement b = ~a; // Arithmetic one's complement b = -1 - a; I also remember the old shift hack when dividing with a power of two so the bitwise shift can be expressed as: // Bitwise left shift b = a << 4; // Arithmetic left shift b = a * 16; // 2^4 = 16 // Signed right shift b = a >>> 4; // Arithmetic right shift b = a / 16; For the rest of the bitwise operations I am slightly clueless. I wish the architects of this architecture would have supplied bit-operations. I would also like to know if there is a fast/easy way of computing the power of two (for shift operations) without using a memory data table. A naive solution would be to jump into a field of multiplications: b = 1; switch (a) { case 15: b = b * 2; case 14: b = b * 2; // ... exploting fallthrough (instruction memory is magnitudes larger) case 2: b = b * 2; case 1: b = b * 2; } Or a Set & Jump approach: switch (a) { case 15: b = 32768; break; case 14: b = 16384; break; // ... exploiting the fact that a jump is faster than one additional mul // at the cost of doubling the instruction memory footprint. case 2: b = 4; break; case 1: b = 2; break; }

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  • Boost::Spirit::Qi autorules -- avoiding repeated copying of AST data structures

    - by phooji
    I've been using Qi and Karma to do some processing on several small languages. Most of the grammars are pretty small (20-40 rules). I've been able to use autorules almost exclusively, so my parse trees consist entirely of variants, structs, and std::vectors. This setup works great for the common case: 1) parse something (Qi), 2) make minor manipulations to the parse tree (visitor), and 3) output something (Karma). However, I'm concerned about what will happen if I want to make complex structural changes to a syntax tree, like moving big subtrees around. Consider the following toy example: A grammar for s-expr-style logical expressions that uses autorules... // Inside grammar class; rule names match struct names... pexpr %= pand | por | var | bconst; pand %= lit("(and ") >> (pexpr % lit(" ")) >> ")"; por %= lit("(or ") >> (pexpr % lit(" ")) >> ")"; pnot %= lit("(not ") >> pexpr >> ")"; ... which leads to parse tree representation that looks like this... struct var { std::string name; }; struct bconst { bool val; }; struct pand; struct por; struct pnot; typedef boost::variant<bconst, var, boost::recursive_wrapper<pand>, boost::recursive_wrapper<por>, boost::recursive_wrapper<pnot> > pexpr; struct pand { std::vector<pexpr> operands; }; struct por { std::vector<pexpr> operands; }; struct pnot { pexpr victim; }; // Many Fusion Macros here Suppose I have a parse tree that looks something like this: pand / ... \ por por / \ / \ var var var var (The ellipsis means 'many more children of similar shape for pand.') Now, suppose that I want negate each of the por nodes, so that the end result is: pand / ... \ pnot pnot | | por por / \ / \ var var var var The direct approach would be, for each por subtree: - create pnot node (copies por in construction); - re-assign the appropriate vector slot in the pand node (copies pnot node and its por subtree). Alternatively, I could construct a separate vector, and then replace (swap) the pand vector wholesale, eliminating a second round of copying. All of this seems cumbersome compared to a pointer-based tree representation, which would allow for the pnot nodes to be inserted without any copying of existing nodes. My question: Is there a way to avoid copy-heavy tree manipulations with autorule-compliant data structures? Should I bite the bullet and just use non-autorules to build a pointer-based AST (e.g., http://boost-spirit.com/home/2010/03/11/s-expressions-and-variants/)?

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  • URL Rewrite – Multiple domains under one site. Part II

    - by OWScott
    I believe I have it … I’ve been meaning to put together the ultimate outgoing rule for hosting multiple domains under one site.  I finally sat down this week and setup a few test cases, and created one rule to rule them all.  In Part I of this two part series, I covered the incoming rule necessary to host a site in a subfolder of a website, while making it appear as if it’s in the root of the site.  Part II won’t work without applying Part I first, so if you haven’t read it, I encourage you to read it now. However, the incoming rule by itself doesn’t address everything.  Here’s the problem … Let’s say that we host www.site2.com in a subfolder called site2, off of masterdomain.com.  This is the same example I used in Part I.   Using an incoming rewrite rule, we are able to make a request to www.site2.com even though the site is really in the /site2 folder.  The gotcha comes with any type of path that ASP.NET generates (I’m sure other scripting technologies could do the same too).  ASP.NET thinks that the path to the root of the site is /site2, but the URL is /.  See the issue?  If ASP.NET generates a path or a redirect for us, it will always add /site2 to the URL.  That results in a path that looks something like www.site2.com/site2.  In Part I, I mentioned that you should add a condition where “{PATH_INFO} ‘does not match’ /site2”.  That allows www.site2.com/site2 and www.site2.com to both function the same.  This allows the site to always work, but if you want to hide /site2 in the URL, you need to take it one step further. One way to address this is in your code.  Ultimately this is the best bet.  Ruslan Yakushev has a great article on a few considerations that you can address in code.  I recommend giving that serious consideration.  Additionally, if you have upgraded to ASP.NET 3.5 SP1 or greater, it takes care of some of the references automatically for you. However, what if you inherit an existing application?  Or you can’t easily go through your existing site and make the code changes?  If this applies to you, read on. That’s where URL Rewrite 2.0 comes in.  With URL Rewrite 2.0, you can create an outgoing rule that will remove the /site2 before the page is sent back to the user.  This means that you can take an existing application, host it in a subfolder of your site, and ensure that the URL never reveals that it’s in a subfolder. Performance Considerations Performance overhead is something to be mindful of.  These outbound rules aren’t simply changing the server variables.  The first rule I’ll cover below needs to parse the HTML body and pull out the path (i.e. /site2) on the way through.  This will add overhead, possibly significant if you have large pages and a busy site.  In other words, your mileage may vary and you may need to test to see the impact that these rules have.  Don’t worry too much though.  For many sites, the performance impact is negligible. So, how do we do it? Creating the Outgoing Rule There are really two things to keep in mind.  First, ASP.NET applications frequently generate a URL that adds the /site2 back into the URL.  In addition to URLs, they can be in form elements, img elements and the like.  The goal is to find all of those situations and rewrite it on the way out.  Let’s call this the ‘URL problem’. Second, and similarly, ASP.NET can send a LOCATION redirect that causes a redirect back to another page.  Again, ASP.NET isn’t aware of the different URL and it will add the /site2 to the redirect.  Form Authentication is a good example on when this occurs.  Try to password protect a site running from a subfolder using forms auth and you’ll quickly find that the URL becomes www.site2.com/site2 again.  Let’s term this the ‘redirect problem’. Solving the URL Problem – Outgoing Rule #1 Let’s create a rule that removes the /site2 from any URL.  We want to remove it from relative URLs like /site2/something, or absolute URLs like http://www.site2.com/site2/something.  Most URLs that ASP.NET creates will be relative URLs, but I figure that there may be some applications that piece together a full URL, so we might as well expect that situation. Let’s get started.  First, create a new outbound rule.  You can create the rule within the /site2 folder which will reduce the performance impact of the rule.  Just a reminder that incoming rules for this situation won’t work in a subfolder … but outgoing rules will. Give it a name that makes sense to you, for example “Outgoing – URL paths”. Precondition.  If you place the rule in the subfolder, it will only run for that site and folder, so there isn’t need for a precondition.  Run it for all requests.  If you place it in the root of the site, you may want to create a precondition for HTTP_HOST = ^(www\.)?site2\.com$. For the Match section, there are a few things to consider.  For performance reasons, it’s best to match the least amount of elements that you need to accomplish the task.  For my test cases, I just needed to rewrite the <a /> tag, but you may need to rewrite any number of HTML elements.  Note that as long as you have the exclude /site2 rule in your incoming rule as I described in Part I, some elements that don’t show their URL—like your images—will work without removing the /site2 from them.  That reduces the processing needed for this rule. Leave the “matching scope” at “Response” and choose the elements that you want to change. Set the pattern to “^(?:site2|(.*//[_a-zA-Z0-9-\.]*)?/site2)(.*)”.  Make sure to replace ‘site2’ with your subfolder name in both places.  Yes, I realize this is a pretty messy looking rule, but it handles a few situations.  This rule will handle the following situations correctly: Original Rewritten using {R:1}{R:2} http://www.site2.com/site2/default.aspx http://www.site2.com/default.aspx http://www.site2.com/folder1/site2/default.aspx Won’t rewrite since it’s a sub-sub folder /site2/default.aspx /default.aspx site2/default.aspx /default.aspx /folder1/site2/default.aspx Won’t rewrite since it’s a sub-sub folder. For the conditions section, you can leave that be. Finally, for the rule, set the Action Type to “Rewrite” and set the Value to “{R:1}{R:2}”.  The {R:1} and {R:2} are back references to the sections within parentheses.  In other words, in http://domain.com/site2/something, {R:1} will be http://domain.com and {R:2} will be /something. If you view your rule from your web.config file (or applicationHost.config if it’s a global rule), it should look like this: <rule name="Outgoing - URL paths" enabled="true"> <match filterByTags="A" pattern="^(?:site2|(.*//[_a-zA-Z0-9-\.]*)?/site2)(.*)" /> <action type="Rewrite" value="{R:1}{R:2}" /> </rule> Solving the Redirect Problem Outgoing Rule #2 The second issue that we can run into is with a client-side redirect.  This is triggered by a LOCATION response header that is sent to the client.  Forms authentication is a common example.  To reproduce this, password protect your subfolder and watch how it redirects and adds the subfolder path back in. Notice in my test case the extra paths: http://site2.com/site2/login.aspx?ReturnUrl=%2fsite2%2fdefault.aspx I want to remove /site2 from both the URL and the ReturnUrl querystring value.  For semi-readability, let’s do this in 2 separate rules, one for the URL and one for the querystring. Create a second rule.  As with the previous rule, it can be created in the /site2 subfolder.  In the URL Rewrite wizard, select Outbound rules –> “Blank Rule”. Fill in the following information: Name response_location URL Precondition Don’t set Match: Matching Scope Server Variable Match: Variable Name RESPONSE_LOCATION Match: Pattern ^(?:site2|(.*//[_a-zA-Z0-9-\.]*)?/site2)(.*) Conditions Don’t set Action Type Rewrite Action Properties {R:1}{R:2} It should end up like so: <rule name="response_location URL"> <match serverVariable="RESPONSE_LOCATION" pattern="^(?:site2|(.*//[_a-zA-Z0-9-\.]*)?/site2)(.*)" /> <action type="Rewrite" value="{R:1}{R:2}" /> </rule> Outgoing Rule #3 Outgoing Rule #2 only takes care of the URL path, and not the querystring path.  Let’s create one final rule to take care of the path in the querystring to ensure that ReturnUrl=%2fsite2%2fdefault.aspx gets rewritten to ReturnUrl=%2fdefault.aspx. The %2f is the HTML encoding for forward slash (/). Create a rule like the previous one, but with the following settings: Name response_location querystring Precondition Don’t set Match: Matching Scope Server Variable Match: Variable Name RESPONSE_LOCATION Match: Pattern (.*)%2fsite2(.*) Conditions Don’t set Action Type Rewrite Action Properties {R:1}{R:2} The config should look like this: <rule name="response_location querystring"> <match serverVariable="RESPONSE_LOCATION" pattern="(.*)%2fsite2(.*)" /> <action type="Rewrite" value="{R:1}{R:2}" /> </rule> It’s possible to squeeze the last two rules into one, but it gets kind of confusing so I felt that it’s better to show it as two separate rules. Summary With the rules covered in these two parts, we’re able to have a site in a subfolder and make it appear as if it’s in the root of the site.  Not only that, we can overcome automatic redirecting that is caused by ASP.NET, other scripting technologies, and especially existing applications. Following is an example of the incoming and outgoing rules necessary for a site called www.site2.com hosted in a subfolder called /site2.  Remember that the outgoing rules can be placed in the /site2 folder instead of the in the root of the site. <rewrite> <rules> <rule name="site2.com in a subfolder" enabled="true" stopProcessing="true"> <match url=".*" /> <conditions logicalGrouping="MatchAll" trackAllCaptures="false"> <add input="{HTTP_HOST}" pattern="^(www\.)?site2\.com$" /> <add input="{PATH_INFO}" pattern="^/site2($|/)" negate="true" /> </conditions> <action type="Rewrite" url="/site2/{R:0}" /> </rule> </rules> <outboundRules> <rule name="Outgoing - URL paths" enabled="true"> <match filterByTags="A" pattern="^(?:site2|(.*//[_a-zA-Z0-9-\.]*)?/site2)(.*)" /> <action type="Rewrite" value="{R:1}{R:2}" /> </rule> <rule name="response_location URL"> <match serverVariable="RESPONSE_LOCATION" pattern="^(?:site2|(.*//[_a-zA-Z0-9-\.]*)?/site2)(.*)" /> <action type="Rewrite" value="{R:1}{R:2}" /> </rule> <rule name="response_location querystring"> <match serverVariable="RESPONSE_LOCATION" pattern="(.*)%2fsite2(.*)" /> <action type="Rewrite" value="{R:1}{R:2}" /> </rule> </outboundRules> </rewrite> If you run into any situations that aren’t caught by these rules, please let me know so I can update this to be as complete as possible. Happy URL Rewriting!

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  • Sorting Algorithms

    - by MarkPearl
    General Every time I go back to university I find myself wading through sorting algorithms and their implementation in C++. Up to now I haven’t really appreciated their true value. However as I discovered this last week with Dictionaries in C# – having a knowledge of some basic programming principles can greatly improve the performance of a system and make one think twice about how to tackle a problem. I’m going to cover briefly in this post the following: Selection Sort Insertion Sort Shellsort Quicksort Mergesort Heapsort (not complete) Selection Sort Array based selection sort is a simple approach to sorting an unsorted array. Simply put, it repeats two basic steps to achieve a sorted collection. It starts with a collection of data and repeatedly parses it, each time sorting out one element and reducing the size of the next iteration of parsed data by one. So the first iteration would go something like this… Go through the entire array of data and find the lowest value Place the value at the front of the array The second iteration would go something like this… Go through the array from position two (position one has already been sorted with the smallest value) and find the next lowest value in the array. Place the value at the second position in the array This process would be completed until the entire array had been sorted. A positive about selection sort is that it does not make many item movements. In fact, in a worst case scenario every items is only moved once. Selection sort is however a comparison intensive sort. If you had 10 items in a collection, just to parse the collection you would have 10+9+8+7+6+5+4+3+2=54 comparisons to sort regardless of how sorted the collection was to start with. If you think about it, if you applied selection sort to a collection already sorted, you would still perform relatively the same number of iterations as if it was not sorted at all. Many of the following algorithms try and reduce the number of comparisons if the list is already sorted – leaving one with a best case and worst case scenario for comparisons. Likewise different approaches have different levels of item movement. Depending on what is more expensive, one may give priority to one approach compared to another based on what is more expensive, a comparison or a item move. Insertion Sort Insertion sort tries to reduce the number of key comparisons it performs compared to selection sort by not “doing anything” if things are sorted. Assume you had an collection of numbers in the following order… 10 18 25 30 23 17 45 35 There are 8 elements in the list. If we were to start at the front of the list – 10 18 25 & 30 are already sorted. Element 5 (23) however is smaller than element 4 (30) and so needs to be repositioned. We do this by copying the value at element 5 to a temporary holder, and then begin shifting the elements before it up one. So… Element 5 would be copied to a temporary holder 10 18 25 30 23 17 45 35 – T 23 Element 4 would shift to Element 5 10 18 25 30 30 17 45 35 – T 23 Element 3 would shift to Element 4 10 18 25 25 30 17 45 35 – T 23 Element 2 (18) is smaller than the temporary holder so we put the temporary holder value into Element 3. 10 18 23 25 30 17 45 35 – T 23   We now have a sorted list up to element 6. And so we would repeat the same process by moving element 6 to a temporary value and then shifting everything up by one from element 2 to element 5. As you can see, one major setback for this technique is the shifting values up one – this is because up to now we have been considering the collection to be an array. If however the collection was a linked list, we would not need to shift values up, but merely remove the link from the unsorted value and “reinsert” it in a sorted position. Which would reduce the number of transactions performed on the collection. So.. Insertion sort seems to perform better than selection sort – however an implementation is slightly more complicated. This is typical with most sorting algorithms – generally, greater performance leads to greater complexity. Also, insertion sort performs better if a collection of data is already sorted. If for instance you were handed a sorted collection of size n, then only n number of comparisons would need to be performed to verify that it is sorted. It’s important to note that insertion sort (array based) performs a number item moves – every time an item is “out of place” several items before it get shifted up. Shellsort – Diminishing Increment Sort So up to now we have covered Selection Sort & Insertion Sort. Selection Sort makes many comparisons and insertion sort (with an array) has the potential of making many item movements. Shellsort is an approach that takes the normal insertion sort and tries to reduce the number of item movements. In Shellsort, elements in a collection are viewed as sub-collections of a particular size. Each sub-collection is sorted so that the elements that are far apart move closer to their final position. Suppose we had a collection of 15 elements… 10 20 15 45 36 48 7 60 18 50 2 19 43 30 55 First we may view the collection as 7 sub-collections and sort each sublist, lets say at intervals of 7 10 60 55 – 20 18 – 15 50 – 45 2 – 36 19 – 48 43 – 7 30 10 55 60 – 18 20 – 15 50 – 2 45 – 19 36 – 43 48 – 7 30 (Sorted) We then sort each sublist at a smaller inter – lets say 4 10 55 60 18 – 20 15 50 2 – 45 19 36 43 – 48 7 30 10 18 55 60 – 2 15 20 50 – 19 36 43 45 – 7 30 48 (Sorted) We then sort elements at a distance of 1 (i.e. we apply a normal insertion sort) 10 18 55 60 2 15 20 50 19 36 43 45 7 30 48 2 7 10 15 18 19 20 30 36 43 45 48 50 55 (Sorted) The important thing with shellsort is deciding on the increment sequence of each sub-collection. From what I can tell, there isn’t any definitive method and depending on the order of your elements, different increment sequences may perform better than others. There are however certain increment sequences that you may want to avoid. An even based increment sequence (e.g. 2 4 8 16 32 …) should typically be avoided because it does not allow for even elements to be compared with odd elements until the final sort phase – which in a way would negate many of the benefits of using sub-collections. The performance on the number of comparisons and item movements of Shellsort is hard to determine, however it is considered to be considerably better than the normal insertion sort. Quicksort Quicksort uses a divide and conquer approach to sort a collection of items. The collection is divided into two sub-collections – and the two sub-collections are sorted and combined into one list in such a way that the combined list is sorted. The algorithm is in general pseudo code below… Divide the collection into two sub-collections Quicksort the lower sub-collection Quicksort the upper sub-collection Combine the lower & upper sub-collection together As hinted at above, quicksort uses recursion in its implementation. The real trick with quicksort is to get the lower and upper sub-collections to be of equal size. The size of a sub-collection is determined by what value the pivot is. Once a pivot is determined, one would partition to sub-collections and then repeat the process on each sub collection until you reach the base case. With quicksort, the work is done when dividing the sub-collections into lower & upper collections. The actual combining of the lower & upper sub-collections at the end is relatively simple since every element in the lower sub-collection is smaller than the smallest element in the upper sub-collection. Mergesort With quicksort, the average-case complexity was O(nlog2n) however the worst case complexity was still O(N*N). Mergesort improves on quicksort by always having a complexity of O(nlog2n) regardless of the best or worst case. So how does it do this? Mergesort makes use of the divide and conquer approach to partition a collection into two sub-collections. It then sorts each sub-collection and combines the sorted sub-collections into one sorted collection. The general algorithm for mergesort is as follows… Divide the collection into two sub-collections Mergesort the first sub-collection Mergesort the second sub-collection Merge the first sub-collection and the second sub-collection As you can see.. it still pretty much looks like quicksort – so lets see where it differs… Firstly, mergesort differs from quicksort in how it partitions the sub-collections. Instead of having a pivot – merge sort partitions each sub-collection based on size so that the first and second sub-collection of relatively the same size. This dividing keeps getting repeated until the sub-collections are the size of a single element. If a sub-collection is one element in size – it is now sorted! So the trick is how do we put all these sub-collections together so that they maintain their sorted order. Sorted sub-collections are merged into a sorted collection by comparing the elements of the sub-collection and then adjusting the sorted collection. Lets have a look at a few examples… Assume 2 sub-collections with 1 element each 10 & 20 Compare the first element of the first sub-collection with the first element of the second sub-collection. Take the smallest of the two and place it as the first element in the sorted collection. In this scenario 10 is smaller than 20 so 10 is taken from sub-collection 1 leaving that sub-collection empty, which means by default the next smallest element is in sub-collection 2 (20). So the sorted collection would be 10 20 Lets assume 2 sub-collections with 2 elements each 10 20 & 15 19 So… again we would Compare 10 with 15 – 10 is the winner so we add it to our sorted collection (10) leaving us with 20 & 15 19 Compare 20 with 15 – 15 is the winner so we add it to our sorted collection (10 15) leaving us with 20 & 19 Compare 20 with 19 – 19 is the winner so we add it to our sorted collection (10 15 19) leaving us with 20 & _ 20 is by default the winner so our sorted collection is 10 15 19 20. Make sense? Heapsort (still needs to be completed) So by now I am tired of sorting algorithms and trying to remember why they were so important. I think every year I go through this stuff I wonder to myself why are we made to learn about selection sort and insertion sort if they are so bad – why didn’t we just skip to Mergesort & Quicksort. I guess the only explanation I have for this is that sometimes you learn things so that you can implement them in future – and other times you learn things so that you know it isn’t the best way of implementing things and that you don’t need to implement it in future. Anyhow… luckily this is going to be the last one of my sorts for today. The first step in heapsort is to convert a collection of data into a heap. After the data is converted into a heap, sorting begins… So what is the definition of a heap? If we have to convert a collection of data into a heap, how do we know when it is a heap and when it is not? The definition of a heap is as follows: A heap is a list in which each element contains a key, such that the key in the element at position k in the list is at least as large as the key in the element at position 2k +1 (if it exists) and 2k + 2 (if it exists). Does that make sense? At first glance I’m thinking what the heck??? But then after re-reading my notes I see that we are doing something different – up to now we have really looked at data as an array or sequential collection of data that we need to sort – a heap represents data in a slightly different way – although the data is stored in a sequential collection, for a sequential collection of data to be in a valid heap – it is “semi sorted”. Let me try and explain a bit further with an example… Example 1 of Potential Heap Data Assume we had a collection of numbers as follows 1[1] 2[2] 3[3] 4[4] 5[5] 6[6] For this to be a valid heap element with value of 1 at position [1] needs to be greater or equal to the element at position [3] (2k +1) and position [4] (2k +2). So in the above example, the collection of numbers is not in a valid heap. Example 2 of Potential Heap Data Lets look at another collection of numbers as follows 6[1] 5[2] 4[3] 3[4] 2[5] 1[6] Is this a valid heap? Well… element with the value 6 at position 1 must be greater or equal to the element at position [3] and position [4]. Is 6 > 4 and 6 > 3? Yes it is. Lets look at element 5 as position 2. It must be greater than the values at [4] & [5]. Is 5 > 3 and 5 > 2? Yes it is. If you continued to examine this second collection of data you would find that it is in a valid heap based on the definition of a heap.

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  • How to make negate_unary work with any type?

    - by Chan
    Hi, Following this question: How to negate a predicate function using operator ! in C++? I want to create an operator ! can work with any functor that inherited from unary_function. I tried: template<typename T> inline std::unary_negate<T> operator !( const T& pred ) { return std::not1( pred ); } The compiler complained: Error 5 error C2955: 'std::unary_function' : use of class template requires template argument list c:\program files\microsoft visual studio 10.0\vc\include\xfunctional 223 1 Graphic Error 7 error C2451: conditional expression of type 'std::unary_negate<_Fn1>' is illegal c:\program files\microsoft visual studio 10.0\vc\include\ostream 529 1 Graphic Error 3 error C2146: syntax error : missing ',' before identifier 'argument_type' c:\program files\microsoft visual studio 10.0\vc\include\xfunctional 222 1 Graphic Error 4 error C2065: 'argument_type' : undeclared identifier c:\program files\microsoft visual studio 10.0\vc\include\xfunctional 222 1 Graphic Error 2 error C2039: 'argument_type' : is not a member of 'std::basic_ostream<_Elem,_Traits>::sentry' c:\program files\microsoft visual studio 10.0\vc\include\xfunctional 222 1 Graphic Error 6 error C2039: 'argument_type' : is not a member of 'std::basic_ostream<_Elem,_Traits>::sentry' c:\program files\microsoft visual studio 10.0\vc\include\xfunctional 230 1 Graphic Any idea? Update Follow "templatetypedef" solution, I got new error: Error 3 error C2831: 'operator !' cannot have default parameters c:\visual studio 2010 projects\graphic\graphic\main.cpp 39 1 Graphic Error 2 error C2808: unary 'operator !' has too many formal parameters c:\visual studio 2010 projects\graphic\graphic\main.cpp 39 1 Graphic Error 4 error C2675: unary '!' : 'is_prime' does not define this operator or a conversion to a type acceptable to the predefined operator c:\visual studio 2010 projects\graphic\graphic\main.cpp 52 1 Graphic Update 1 Complete code: #include <iostream> #include <functional> #include <utility> #include <cmath> #include <algorithm> #include <iterator> #include <string> #include <boost/assign.hpp> #include <boost/assign/std/vector.hpp> #include <boost/assign/std/map.hpp> #include <boost/assign/std/set.hpp> #include <boost/assign/std/list.hpp> #include <boost/assign/std/stack.hpp> #include <boost/assign/std/deque.hpp> struct is_prime : std::unary_function<int, bool> { bool operator()( int n ) const { if( n < 2 ) return 0; if( n == 2 || n == 3 ) return 1; if( n % 2 == 0 || n % 3 == 0 ) return 0; int upper_bound = std::sqrt( static_cast<double>( n ) ); for( int pf = 5, step = 2; pf <= upper_bound; ) { if( n % pf == 0 ) return 0; pf += step; step = 6 - step; } return 1; } }; /* template<typename T> inline std::unary_negate<T> operator !( const T& pred, typename T::argument_type* dummy = 0 ) { return std::not1<T>( pred ); } */ inline std::unary_negate<is_prime> operator !( const is_prime& pred ) { return std::not1( pred ); } template<typename T> inline void print_con( const T& con, const std::string& ms = "", const std::string& sep = ", " ) { std::cout << ms << '\n'; std::copy( con.begin(), con.end(), std::ostream_iterator<typename T::value_type>( std::cout, sep.c_str() ) ); std::cout << "\n\n"; } int main() { using namespace boost::assign; std::vector<int> nums; nums += 1, 3, 5, 7, 9; nums.erase( remove_if( nums.begin(), nums.end(), !is_prime() ), nums.end() ); print_con( nums, "After remove all primes" ); } Thanks, Chan Nguyen

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