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  • Calculate minimum moves to solve a puzzle

    - by Luke
    I'm in the process of creating a game where the user will be presented with 2 sets of colored tiles. In order to ensure that the puzzle is solvable, I start with one set, copy it to a second set, then swap tiles from one set to another. Currently, (and this is where my issue lies) the number of swaps is determined by the level the user is playing - 1 swap for level 1, 2 swaps for level 2, etc. This same number of swaps is used as a goal in the game. The user must complete the puzzle by swapping a tile from one set to the other to make the 2 sets match (by color). The order of the tiles in the (user) solved puzzle doesn't matter as long as the 2 sets match. The problem I have is that as the number of swaps I used to generate the puzzle approaches the number of tiles in each set, the puzzle becomes easier to solve. Basically, you can just drag from one set in whatever order you need for the second set and solve the puzzle with plenty of moves left. What I am looking to do is after I finish building the puzzle, calculate the minimum number of moves required to solve the puzzle. Again, this is almost always less than the number of swaps used to create the puzzle, especially as the number of swaps approaches the number of tiles in each set. My goal is to calculate the best case scenario and then give the user a "fudge factor" (i.e. 1.2 times the minimum number of moves). Solving the puzzle in under this number of moves will result in passing the level. A little background as to how I currently have the game configured: Levels 1 to 10: 9 tiles in each set. 5 different color tiles. Levels 11 to 20: 12 tiles in each set. 7 different color tiles. Levels 21 to 25: 15 tiles in each set. 10 different color tiles. Swapping within a set is not allowed. For each level, there will be at least 2 tiles of a given color (one for each set in the solved puzzle). Is there any type of algorithm anyone could recommend to calculate the minimum number of moves to solve a given puzzle?

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  • syntax to express mathematical formula concisely in your language of choice

    - by aaa
    hello. I am developing functional domain specific embedded language within C++ to translate formulas into working code as concisely and accurately as possible. Right now my language looks something like this: // implies two nested loops j=0:N, i=0,j (range(i) < j < N)[T(i,j) = (T(i,j) - T(j,i))/e(i+j)]; // implies summation over above expression sum(range(i) < j < N))[(T(i,j) - T(j,i))/e(i+j)]; I am looking for possible syntax improvements/extensions or just different ideas about expressing mathematical formulas as clearly and precisely as possible. Can you give me some syntax examples relating to my question which can be accomplished in your language of choice which consider useful. In particular, if you have some ideas about how to translate the above code segments, I would be happy to hear them Thank you

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  • I know my Before Tax Pay and my After Tax Pay, how can I work out how much I get taxed?

    - by Pete
    I've been entering some data into an Excel spreadsheet to work out my monthly earnings, etc. and was wondering how I can I find out how much I'm getting taxed? Say this is my current spreadsheet: Hours Worked 37.5 39.5 37.5 30 Hourly Rate $25 $25 $25 $25 Before Tax 937.50 987.50 937.50 750.00 After Tax 260.00 276.00 260.00 ??? How can I use this known data to work out my After Tax pay for the 4th column? :/

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  • Counting point size based on chart area during zooming/unzoomin

    - by Gacek
    Hi folks. I heave a quite simple task. I know (I suppose) it should be easy, but from the reasons I cannot understand, I try to solve it since 2 days and I don't know where I'm making the mistake. So, the problem is as follows: - we have a chart with some points - The chart starts with some known area and points have known size - we would like to "emulate" the zooming effect. So when we zoom to some part of the chart, the size of points is getting proportionally bigger. In other words, the smaller part of the chart we select, the bigger the point should get. So, we have something like that. We know this two parameters: initialArea; // Initial area - area of the whole chart, counted as width*height initialSize; // initial size of the points Now lets assume we are handling some kind of OnZoom event. We selected some part of the chart and would like to count the current size of the points float CountSizeOnZoom() { float currentArea = CountArea(...); // the area is counted for us. float currentSize = initialSize * initialArea / currentArea; return currentSize; } And it works. But the rate of change is too fast. In other words, the points are getting really big too soon. So I would like the currentSize to be invertly proportional to currentArea, but with some scaling coefficient. So I created the second function: float CountSizeOnZoom() { float currentArea = CountArea(...); % the area is counted for us. // Lets assume we want the size of points to change ten times slower, than area of the chart changed. float currentSize = initialSize + 0.1f* initialSize * ((initialArea / currentArea) -1); return currentSize; } Lets do some calculations in mind. if currentArea is smaller than initialArea, initialArea/currentArea > 1 and then we add "something" small and postive to initialSize. Checked, it works. Lets check what happens if we would un-zoom. currentArea will be equal to initialArea, so we would have 0 at the right side (1-1), so new size should be equal to initialSize. Right? Yeah. So lets check it... and it doesn't work. My question is: where is the mistake? Or maybe you have any ideas how to count this scaled size depending on current area in some other way?

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  • Find the centroid of a polygon with weighted vertices

    - by Calle Kabo
    Hi, I know how to find the centroid (center of mass) of a regular polygon. This assumes that every part of the polygon weighs the same. But how do I calculate the centroid of a weightless polygon (made from aerogel perhaps :), where each vertex has a weight? Simplified illustration of what I mean using straight line: 5kg-----------------5kg ^center of gravity 10kg---------------5kg ^center of gravity offset du to weight of vertices Of course, I know how to calculate the center of gravity on a straight line with weighted vertices, but how do I do it on a polygon with weighted vertices? Thanks for your time!

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  • Why does C++ mandate that complex only be instantiated for float, double, or long double?

    - by templatetypedef
    According to the C++ ISO spec, §26.2/2: The effect of instantiating the template complex for any type other than float, double or long double is unspecified. Why would the standard authors explicitly add this restriction? This makes it unspecified, for example, what happens if you make complex<int> or a complex<MyCustomFixedPointType> and seems like an artificial restriction. Is there a reason for this limitation? Is there a workaround if you want to instantiate complex with your own custom type? I'm primarily asking this question because of this earlier question, in which the OP was confused as to why abs was giving bizarre outputs for complex<int>. That said, this still doesn't quite make sense given that we also might want to make complex numbers out of fixed-points types, higher-precision real numbers, etc. Thanks!

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  • Fast, Vectorizable method of taking floating point number modulus of special primes?

    - by caffiend
    Is there a fast method for taking the modulus of a floating point number? With integers, there are tricks for Mersenne primes, so that its possible to calculate y = x MOD 2^31 without needing division. Can any similar tricks be applied for floating point numbers? Preferably, in a way that can be converted into vector/SIMD operations, or moved into GPGPU code. The primes I'm interested in would be 2^7 and 2^31, although if there are more efficient ones for floating point numbers, those would be welcome.

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  • Paperclip + ImageMagick on Windows 7: Image display fails when I add styles to attached_file in mode

    - by Brian Roisentul
    I'm working with Ruby on rails 2.3.8, NetBeans IDE. I've installed paperclip and I could show/save images successfully. Now, I've installed ImageMagick-6.6.2-4-Q16(for windows 7, 64bits). Until that moment, my model looked like this(and worked fine): has_attached_file :photo Now, after installing ImageMagick, when I add the :style line it fails: has_attached_file :photo, :styles => {:thumb => "100x100#", :small => "150x150>", :large => "400x400>" } and it throws the following error message when I try to upload an image: TypeError in ProfilesController#update backtrace must be Array of String The only thing I'm doing in the update action of that controller is the following: @profile.update_attributes(params[:profile]) @profile.update_attribute(:photo, params[:profile][:photo]) I've also installed miniMagick gem(because I read somewhere I had to do it). What am I missing?

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  • JQuery JEditable stay in edit mode on error

    - by Justin
    I'm successfully using jeditable to submit via a function using jQuery.ajax and the async : false option , but am having an issue aborting if an error is returned. How can I get the edit box to stay activated and / or revert back to the original value if there are errors? I'm returning http status codes. so something like async : false .ajax submit here... if (xhr.status == 200) { return value; else { alert ('returned error'); // keep edit box activated but available for another try, or revert back to original value } I tried not returning a value from the function, which keeps the edit box activated and ready for another submit, but then the ESC key doesn't work anymore and if I click outside the edit area, the edit box stays. Thanks in advance!

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  • Get Windows mobile sound level, especially silent mode

    - by Sam
    In Windows Mobile (5,6) you can have different sound volume settings. The volume itself is easy, but how do I differ between the two silent settings? There is one volume setting "vibration only" and one "no sound, no vibration at all". Since my program is using vibration, I'd like to know if windows mobile is set to "no vibration at all", so I don't annoy the user when he wants his phone to be absolutely silent.

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  • optimized grid for rectangular items

    - by peterchen
    I have N rectangular items with an aspect ratio Aitem (X:Y). I have a rectangular display area with an aspect ratio Aview The items should be arranged in a table-like layout (i.e. r rows, c columns). what is the ideal grid rows x columns, so that individual items are largest? (rows * colums = N, of course - i.e. there may be "unused" grid places). A simple algorithm could iterate over rows = 1..N, calculate the required number of columns, and keep the row/column pair with the largest items. I wonder if there's a non-iterative algorithm, though (e.g. for Aitem = Aview = 1, rows / cols can be approximated by sqrt(N)).

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  • 6^x = 5 equation, how to solve it?

    - by Tom
    If it would be 6^x = 1 or 6^x = 6 or 6^x = 36 it would be extremely easy, but how to solve this equation: 6^x = 5 I don't need an answer, I want to find out how to solve equations like this one, I need solution. Thanks.

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  • How to interpolate rotations?

    - by uhuu
    I have two vectors describing rotations; a start rotation A and a target rotation B. How would I best go about interpolating A by a factor F to approach B? Using a simple lerp on the vectors fails to work when more than one dimension needs to be interpolated (i.e. produces undesirable rotations). Maybe building quaternions from the rotation vectors and using slerp is the way to go. But how, then, could I extract a vector describing the new rotation from the resulting quaternion? Thanks in advance.

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  • summing functions handles in matlab

    - by user552231
    Hi I am trying to sum two function handles, but it doesn't work. for example: y1=@(x)(x*x); y2=@(x)(x*x+3*x); y3=y1+y2 The error I receive is "??? Undefined function or method 'plus' for input arguments of type 'function_handle'." This is just a small example, in reality I actually need to iteratively sum about 500 functions that are dependent on each other. EDIT The solution by Clement J. indeed works but I couldn't manage to generalize this into a loop and ran into a problem. I have the function s=@(x,y,z)((1-exp(-x*y)-z)*exp(-x*y)); And I have a vector v that contains 536 data points and another vector w that also contains 536 data points. My goal is to sum up s(v(i),y,w(i)) for i=1...536 Thus getting one function in the variable y which is the sum of 536 functions. The syntax I tried in order to do this is: sum=@(y)(s(v(1),y,z2(1))); for i=2:536 sum=@(y)(sum+s(v(i),y,z2(i))) end

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  • Arrange points in sequence.

    - by Himadri
    I have some points in 3D which are in a single plane. I want to arrange them in clock wise or counter clockwise order. The points can create a concave or convex polygon in a single plane. Can any body give any suggestions?

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  • Can we find out the difference between 2 RGb colors to find out a 3rd color?

    - by AK
    2 colors are mixed together. If i have the RGB for the resultant color and RGB for one of the colors mixed, then somehow i could calculate the 2nd color? I will try to explain visually what i am trying to say. Here is a flickr link http://www.flickr.com/photos/48150615@N08/4407414157 I know that the circle in the middle has an opacity of 20% Is there any way to know the color value of the circle so that i can deduct that to get the same color value as the background color.

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  • Formview doesn't change Mode

    - by Vinzcent
    When I try to change my formview to Edit, he stays in de ReadOnlyMode. I can't figure out why. This is my code. <asp:FormView ID="fvDetailOrder" runat="server" AllowPaging="True" DataKeyNames="ID" OnModeChanging="fvDetailOrder_ModeChanging"> <EditItemTemplate> // I want to see this, when I click edit <asp:LinkButton ForeColor="#003366" ID="UpdateButton" runat="server" CausesValidation="True" CommandName="Update" Text="Update" /> &nbsp;<asp:LinkButton ForeColor="#003366" ID="UpdateCancelButton" runat="server" CausesValidation="False" CommandName="Cancel" Text="Cancel" /> </EditItemTemplate> <InsertItemTemplate> Insert here <asp:LinkButton ForeColor="#003366" ID="InsertButton" runat="server" CausesValidation="True" CommandName="Insert" Text="Insert" /> &nbsp;<asp:LinkButton ForeColor="#003366" ID="InsertCancelButton" runat="server" CausesValidation="False" CommandName="Cancel" Text="Cancel" /> </InsertItemTemplate> <ItemTemplate> Read only <asp:LinkButton ForeColor="#003366" ID="EditButton" runat="server" CausesValidation="False" CommandName="Edit" Text="Edit" /> &nbsp;<asp:LinkButton ForeColor="#003366" ID="DeleteButton" runat="server" CausesValidation="False" CommandName="Delete" Text="Delete" OnClientClick="return confirm('Are you certain you want to delete this product?');" /> &nbsp;<asp:LinkButton ForeColor="#003366" ID="NewButton" runat="server" CausesValidation="False" CommandName="New" Text="New" /> </ItemTemplate> <PagerStyle ForeColor="#003366" /> </asp:FormView> Eventhandler protected void fvDetailOrder_ModeChanging(Object sender, FormViewModeEventArgs e) { fvDetailOrder.ChangeMode(e.NewMode); }

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