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  • important question on Android 2.2

    - by poeschlorn
    Hi guys, I've just updated my nexus one to 2.2...now all of my (own and some from the market) apps throw exceptions and were closed... It's weird, in the app i'm developing atm, there it displays only my start page with buttons, but when i tap on one button to fire an intent to another activity my app gets closed with an exception. Yesterday before the update everything worked fine... The same thing in my emulator: I have two devices, one with API level 7 and one with level 8...Level 7 worked fine, but level 8 killed my app :( What is the problem and how can I solve this? I'm desperatly trying to get it working again :( I hope someone can help me fixing this

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  • how to get unique values set from a repeating values list

    - by Mariselvam
    I need to parse a large log file (flat file), which contains two column of values (column-A , column-B). Values in both columns are repeating. I need to find for each unique value in column-A , I need to find a set of column-B values. Is this can be done using unix shell command or need to write any perl or python script? What are the ways this can be done? Example: xxxA 2 xxxA 1 xxxB 2 XXXC 3 XXXA 3 xxxD 4 output: xxxA - 2,1,3 xxxB - 2 xxxC - 3 xxxD - 4

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  • While programming, what to do when facing with a seemingly unsolvable situation with a time limit?

    - by Ersan Tasan
    This is not a technical question, but rather a social and methodical one. I am a computer sciences student and I usually have really tough programming assignments. I don`t know if it is only happening to me but sometimes, particularly when deadline is approaching, i find myself in a harsh situation. I cannot find my mistake in the code or come up with a another great idea. Then boredom comes in and the problem begins to seem unsolvable. I know there are more-than-great professional coders here. I would like to learn their ideas to cope with this situation. Is it better to focus on something else for a while and try again or try harder and harder and look for the solution on the net etc...

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  • Simple dynamic memory allocation bug.

    - by M4design
    I'm sure you (pros) can identify the bug's' in my code, I also would appreciate any other comments on my code. BTW, the code crashes after I run it. #include <stdlib.h> #include <stdio.h> #include <stdbool.h> typedef struct { int x; int y; } Location; typedef struct { bool walkable; unsigned char walked; // number of times walked upon } Cell; typedef struct { char name[40]; // Name of maze Cell **grid; // 2D array of cells int rows; // Number of rows int cols; // Number of columns Location entrance; } Maze; Maze *maz_new() { int i = 0; Maze *mazPtr = (Maze *)malloc(sizeof (Maze)); if(!mazPtr) { puts("The memory couldn't be initilised, Press ENTER to exit"); getchar(); exit(-1); } else { // allocating memory for the grid mazPtr->grid = (Cell **) malloc((sizeof (Cell)) * (mazPtr->rows)); for(i = 0; i < mazPtr->rows; i++) mazPtr->grid[i] = (Cell *) malloc((sizeof (Cell)) * (mazPtr->cols)); } return mazPtr; } void maz_delete(Maze *maz) { int i = 0; if (maz != NULL) { for(i = 0; i < maz->rows; i++) free(maz->grid[i]); free(maz->grid); } } int main() { Maze *ptr = maz_new(); maz_delete(ptr); getchar(); return 0; } Thanks in advance.

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  • Set asisde space for ADT when reading integers from file

    - by That Guy
    I'm using C to make maze solver. The program should be able read a maze from a text file containing a grid of 1 and 0 representing walls and paths. This file could be of any size as the user selects which maze to use. The program should then show the maze being solved. As the maze is being solved it should show where has been walked and how many steps have been taken. I have made an ADT called Cell containing a bool for wall or path and an integer for steps taken. I now need to populate a 2D array of Cells which means I need to set aside enough space to store a Cell for every integer in the maze file. What would be the best way to do this?

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  • What techniques are used in solving code golf problems?

    - by Lord Torgamus
    "Regular" golf vs. code golf: Both are competitions. Both have a well-defined set of rules, which I'll leave out for simplicity. Both have well-defined goals; in short, "use fewer hits/characters than your competitors." To win matches, athletic golfers rely on equipment Some situations call for a sand wedge; others, a 9-iron. techniques The drive works better when your feet are about shoulder width apart and your arms are relaxed. and strategies Sure, you could take that direct shortcut to the hole... but do you really want to risk the water hazard or sand bunker when those trees are in the way and the wind is so strong? It might be better to go around the long way. What do code golfers have that's analagous to athletic golfers' equipment, techniques and strategies? Sample answer to get this started: use the right club! Choose GolfScript instead of C#.

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  • How to share problem solving knowledge in a multiteam group?

    - by jonathan
    I've been working in multiteam groups for as long as I'm a webdeveloper, for me a team can be a lonely soldier or several people, generally a company will have multiple teams working in different projects and once the project is out in the wild, any team can perform the maintenance. This is a small picture since I'm not talking only about project wise knowledge, but "craft wise" knowledge, but it gives the picture of how I'm used to work, so: Since we work on modularised teams, sometimes I feel like the teams are too tightly enclosed in their projects, I've seen cases where after an hour of discussion, someone asked the question aloud and other person totally unrelated answered in a much simpler fashion. The problem is not so simple to solve as people tend not to be available all the time, also sometimes people can't afford the time to go through a problem with the "asker", but could do it alone. I've thought about software based solutions, something in the lines of SE, but I'd like to know other programmers opinions on the subject. EDIT I don't know if this is a wikipedia complex, but I feel that Wikis don't encourage the user to actually ask questions, but rather to write articles, and sometimes we don't know the knowledge we need, before needing it.

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  • When to skip solving the general problem and settling for the specific problem?

    - by Peter Smith
    I've been working hard on trying to develop a general solution to my problem, but I cannot seem to formulate a proper algorithm for it, at least one that doesn't take a ton of inaccurate grunt work building a lookup table. I have a solution already for the specific requirement, but it requires the software's configuration to be changed every time the software is loaded with a different geographic area's datasets. So is it better to be finished and move on for now, or to keep attempting to solve the general problem knowing that the specific problems will keep popping up?

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  • Solving “The Select operation is not supported by .. unless the SelectMethod is specified.”

    - by anas
    In most cases, You will get that error when you are using a data source control(like ObjectDataSource) without setting it’s SelectMethod as data source for the DetailsView control. If you want to display one record in the detailsView control to allow the user to edit it, then you should set the SelectMethod for the DataSource control,otherwise the detailsView control will not be able to get the record from the underlying datasource. But what if you are only using the DetailsView for only inserting...(read more)

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  • Solving &ldquo;XmlSchemaException: The global element '&lt;elementName&gt;' has already been declare

    - by ChrisD
    I recently encountered this error when I attempted to consume a new hosted WCF service.  The service used the Request/Response model and had been properly decorated.  The response and request objects were marked as DataContracts and had a specified namespace.   My WCF service interface was marked as a ServiceContract and shared the namespace attribute value.   Everything should have been fine, right? [ServiceContract(Namespace = "http://schemas.myclient.com/09/12")] public interface IProductActivationService { [OperationContract] ActivateSoftwareResponse ActivateSoftware(ActivateSoftwareRequest request); } well, not exactly.  Apparently the WSDL generator was having an issue: System.Xml.Schema.XmlSchemaException: The global element 'http://schemas.myclient.com/09/12:ActivateSoftwareResponse' has already been declared. After digging I’ve found the problem; the WSDL generator has some reserved suffixes for its entities, including Response, Request, Solicit (see http://msdn.microsoft.com/en-us/library/ms731045.aspx).  The error message is actually the result of a naming conflict.  The WSDL generator uses the namespace of the service to build its reserved types.  The service contract and data contract share a namespace, which coupled with the response/request name suffixes I was using in my class names, resulted in the SchemaException. The Fix: Two options: Rename my data contract entities to use a non-reserved keyword suffix (i.e.  change ActivateSoftwareResponse to ActivateSoftwareResp). or; Change the namespace of the data contracts to differ from the service contract namespace. I chose option 2 and changed all my data contracts to use a “http://schemas.myclient.com/09/12/data” namespace value. This avoided a name collision and I was able to produce my WSDL and consume my service.

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  • Is it a good idea to always use Google as the first step to solving a problem? [closed]

    - by The Rubber Duck
    Possible Duplicate: Importance of learning to google efficiently for a programmer? Avoiding lengthy discussions, as a senior level student in CS, how can I get away from Googling problems I run into? I find myself using it too much; I seemingly reach for the instant answer and then blindly copy and paste code, hoping it works. Anyone can do that. I've read the related threads about being a better programmer, but mostly those recommend practicing on pet projects, which I have done, but again I feel EVERY wall encountered, from design through completion, was hurdled with Google. Do professionals instantly "research" their problem? Or do you guys step back and try and figure it out yourselves? I'm talking about both 'algorithm/design' problems as well as compiler issues.

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  • I am making a maze type of game using javascript and HTML and need some questions answered [on hold]

    - by Timothy Bilodeau
    First off, i am a noob to JavaScript but am willing to learn. :) I found a simple JavaScript moment engine created by another member on this site. Using that i made it so my character can walk around within a rectangle/square shaped room. I want to make it so the character can walk through a "doorway" within a wall to the next room. Either that or make it so if the character moves over a certain image within the room it will take the player to another webpage in which the character "spawns" into the room and so on and so fourth. Here is a link to what i have made so far as to get an idea. http://bit.ly/1fSMesA Any help would be much appreciated. Here is the javascript code for the character movement and boundaries. <script type='text/javascript'> // movement vars var xpos = 100; var ypos = 100; var xspeed = 1; var yspeed = 0; var maxSpeed = 5; // boundary var minx = 37; var miny = 41; var maxx = 187; // 10 pixels for character's width var maxy = 178; // 10 pixels for character's width // controller vars var upPressed = 0; var downPressed = 0; var leftPressed = 0; var rightPressed = 0; function slowDownX() { if (xspeed > 0) xspeed = xspeed - 1; if (xspeed < 0) xspeed = xspeed + 1; } function slowDownY() { if (yspeed > 0) yspeed = yspeed - 1; if (yspeed < 0) yspeed = yspeed + 1; } function gameLoop() { // change position based on speed xpos = Math.min(Math.max(xpos + xspeed,minx),maxx); ypos = Math.min(Math.max(ypos + yspeed,miny),maxy); // or, without boundaries: // xpos = xpos + xspeed; // ypos = ypos + yspeed; // change actual position document.getElementById('character').style.left = xpos; document.getElementById('character').style.top = ypos; // change speed based on keyboard events if (upPressed == 1) yspeed = Math.max(yspeed - 1,-1*maxSpeed); if (downPressed == 1) yspeed = Math.min(yspeed + 1,1*maxSpeed) if (rightPressed == 1) xspeed = Math.min(xspeed + 1,1*maxSpeed); if (leftPressed == 1) xspeed = Math.max(xspeed - 1,-1*maxSpeed); // deceleration if (upPressed == 0 && downPressed == 0) slowDownY(); if (leftPressed == 0 && rightPressed == 0) slowDownX(); // loop setTimeout("gameLoop()",10); } function keyDown(e) { var code = e.keyCode ? e.keyCode : e.which; if (code == 38) upPressed = 1; if (code == 40) downPressed = 1; if (code == 37) leftPressed = 1; if (code == 39) rightPressed = 1; } function keyUp(e) { var code = e.keyCode ? e.keyCode : e.which; if (code == 38) upPressed = 0; if (code == 40) downPressed = 0; if (code == 37) leftPressed = 0; if (code == 39) rightPressed = 0; } </script> here is the HTML code to follow <!-- The Level --> <img src="room1.png" /> <!-- The Character --> <img id='character' src='../texture packs/characters/snazgel.png' style='position:absolute;left:100;top:100;height:40;width:26;'/>

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  • Using GA in GUI

    - by AlexT
    Sorry if this isn't clear as I'm writing this on a mobile device and I'm trying to make it quick. I've written a basic Genetic Algorithm with a binary encoding (genes) that builds a fitness value and evolves through several iterations using tournament selection, mutation and crossover. As a basic command-line example it seems to work. The problem I've got is with applying a genetic algorithm within a GUI as I am writing a maze-solving program that uses the GA to find a method through a maze. How do I turn my random binary encoded genes and fitness function (add all the binary values together) into a method to control a bot around a maze? I have built a basic GUI in Java consisting of a maze of labels (like a grid) with the available routes being in blue and the walls being in black. To reiterate my GA performs well and contains what any typical GA would (fitness method, get and set population, selection, crossover, etc) but now I need to plug it into a GUI to get my maze running. What needs to go where in order to get a bot that can move in different directions depending on what the GA says? Rough pseudocode would be great if possible As requested, an Individual is built using a separate class (Indiv), with all the main work being done in a Pop class. When a new individual is instantiated an array of ints represent the genes of said individual, with the genes being picked at random from a number between 0 and 1. The fitness function merely adds together the value of these genes and in the Pop class handles selection, mutation and crossover of two selected individuals. There's not much else to it, the command line program just shows evolution over n generations with the total fitness improving over each iteration. EDIT: It's starting to make a bit more sense now, although there are a few things that are bugging me... As Adamski has suggested I want to create an "Agent" with the options shown below. The problem I have is where the random bit string comes into play here. The agent knows where the walls are and has it laid out in a 4 bit string (i.e. 0111), but how does this affect the random 32 bit string? (i.e. 10001011011001001010011011010101) If I have the following maze (x is the start place, 2 is the goal, 1 is the wall): x 1 1 1 1 0 0 1 0 0 1 0 0 0 2 If I turn left I'm facing the wrong way and the agent will move completely off the maze if it moves forward. I assume that the first generation of the string will be completely random and it will evolve as the fitness grows but I don't get how the string will work within a maze. So, to get this straight... The fitness is the result of when the agent is able to move and is by a wall. The genes are a string of 32 bits, split into 16 sets of 2 bits to show the available actions and for the robot to move the two bits need to be passed with four bits from the agent showings its position near the walls. If the move is to go past a wall the move isn't made and it is deemed invalid and if the move is made and if a new wall is found then the fitness goes up. Is that right?

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  • How to change Matlab program for solving equation with finite element method?

    - by DSblizzard
    I don't know is this question more related to mathematics or programming and I'm absolute newbie in Matlab. Program FEM_50 applies the finite element method to Laplace's equation -Uxx(x, y) - Uyy(x, y) = F(x, y) in Omega. How to change it to apply FEM to equation -Uxx(x, y) - Uyy(x, y) + U(x, y) = F(x, y)? At this page: http://sc.fsu.edu/~burkardt/m_src/fem_50/fem_50.html additional code files in case you need them. function fem_50 ( ) %% FEM_50 applies the finite element method to Laplace's equation. % % Discussion: % % FEM_50 is a set of MATLAB routines to apply the finite % element method to solving Laplace's equation in an arbitrary % region, using about 50 lines of MATLAB code. % % FEM_50 is partly a demonstration, to show how little it % takes to implement the finite element method (at least using % every possible MATLAB shortcut.) The user supplies datafiles % that specify the geometry of the region and its arrangement % into triangular and quadrilateral elements, and the location % and type of the boundary conditions, which can be any mixture % of Neumann and Dirichlet. % % The unknown state variable U(x,y) is assumed to satisfy % Laplace's equation: % -Uxx(x,y) - Uyy(x,y) = F(x,y) in Omega % with Dirichlet boundary conditions % U(x,y) = U_D(x,y) on Gamma_D % and Neumann boundary conditions on the outward normal derivative: % Un(x,y) = G(x,y) on Gamma_N % If Gamma designates the boundary of the region Omega, % then we presume that % Gamma = Gamma_D + Gamma_N % but the user is free to determine which boundary conditions to % apply. Note, however, that the problem will generally be singular % unless at least one Dirichlet boundary condition is specified. % % The code uses piecewise linear basis functions for triangular elements, % and piecewise isoparametric bilinear basis functions for quadrilateral % elements. % % The user is required to supply a number of data files and MATLAB % functions that specify the location of nodes, the grouping of nodes % into elements, the location and value of boundary conditions, and % the right hand side function in Laplace's equation. Note that the % fact that the geometry is completely up to the user means that % just about any two dimensional region can be handled, with arbitrary % shape, including holes and islands. % clear % % Read the nodal coordinate data file. % load coordinates.dat; % % Read the triangular element data file. % load elements3.dat; % % Read the quadrilateral element data file. % load elements4.dat; % % Read the Neumann boundary condition data file. % I THINK the purpose of the EVAL command is to create an empty NEUMANN array % if no Neumann file is found. % eval ( 'load neumann.dat;', 'neumann=[];' ); % % Read the Dirichlet boundary condition data file. % load dirichlet.dat; A = sparse ( size(coordinates,1), size(coordinates,1) ); b = sparse ( size(coordinates,1), 1 ); % % Assembly. % for j = 1 : size(elements3,1) A(elements3(j,:),elements3(j,:)) = A(elements3(j,:),elements3(j,:)) ... + stima3(coordinates(elements3(j,:),:)); end for j = 1 : size(elements4,1) A(elements4(j,:),elements4(j,:)) = A(elements4(j,:),elements4(j,:)) ... + stima4(coordinates(elements4(j,:),:)); end % % Volume Forces. % for j = 1 : size(elements3,1) b(elements3(j,:)) = b(elements3(j,:)) ... + det( [1,1,1; coordinates(elements3(j,:),:)'] ) * ... f(sum(coordinates(elements3(j,:),:))/3)/6; end for j = 1 : size(elements4,1) b(elements4(j,:)) = b(elements4(j,:)) ... + det([1,1,1; coordinates(elements4(j,1:3),:)'] ) * ... f(sum(coordinates(elements4(j,:),:))/4)/4; end % % Neumann conditions. % if ( ~isempty(neumann) ) for j = 1 : size(neumann,1) b(neumann(j,:)) = b(neumann(j,:)) + ... norm(coordinates(neumann(j,1),:) - coordinates(neumann(j,2),:)) * ... g(sum(coordinates(neumann(j,:),:))/2)/2; end end % % Determine which nodes are associated with Dirichlet conditions. % Assign the corresponding entries of U, and adjust the right hand side. % u = sparse ( size(coordinates,1), 1 ); BoundNodes = unique ( dirichlet ); u(BoundNodes) = u_d ( coordinates(BoundNodes,:) ); b = b - A * u; % % Compute the solution by solving A * U = B for the remaining unknown values of U. % FreeNodes = setdiff ( 1:size(coordinates,1), BoundNodes ); u(FreeNodes) = A(FreeNodes,FreeNodes) \ b(FreeNodes); % % Graphic representation. % show ( elements3, elements4, coordinates, full ( u ) ); return end

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  • A Taxonomy of Numerical Methods v1

    - by JoshReuben
    Numerical Analysis – When, What, (but not how) Once you understand the Math & know C++, Numerical Methods are basically blocks of iterative & conditional math code. I found the real trick was seeing the forest for the trees – knowing which method to use for which situation. Its pretty easy to get lost in the details – so I’ve tried to organize these methods in a way that I can quickly look this up. I’ve included links to detailed explanations and to C++ code examples. I’ve tried to classify Numerical methods in the following broad categories: Solving Systems of Linear Equations Solving Non-Linear Equations Iteratively Interpolation Curve Fitting Optimization Numerical Differentiation & Integration Solving ODEs Boundary Problems Solving EigenValue problems Enjoy – I did ! Solving Systems of Linear Equations Overview Solve sets of algebraic equations with x unknowns The set is commonly in matrix form Gauss-Jordan Elimination http://en.wikipedia.org/wiki/Gauss%E2%80%93Jordan_elimination C++: http://www.codekeep.net/snippets/623f1923-e03c-4636-8c92-c9dc7aa0d3c0.aspx Produces solution of the equations & the coefficient matrix Efficient, stable 2 steps: · Forward Elimination – matrix decomposition: reduce set to triangular form (0s below the diagonal) or row echelon form. If degenerate, then there is no solution · Backward Elimination –write the original matrix as the product of ints inverse matrix & its reduced row-echelon matrix à reduce set to row canonical form & use back-substitution to find the solution to the set Elementary ops for matrix decomposition: · Row multiplication · Row switching · Add multiples of rows to other rows Use pivoting to ensure rows are ordered for achieving triangular form LU Decomposition http://en.wikipedia.org/wiki/LU_decomposition C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-lu-decomposition-for-solving.html Represent the matrix as a product of lower & upper triangular matrices A modified version of GJ Elimination Advantage – can easily apply forward & backward elimination to solve triangular matrices Techniques: · Doolittle Method – sets the L matrix diagonal to unity · Crout Method - sets the U matrix diagonal to unity Note: both the L & U matrices share the same unity diagonal & can be stored compactly in the same matrix Gauss-Seidel Iteration http://en.wikipedia.org/wiki/Gauss%E2%80%93Seidel_method C++: http://www.nr.com/forum/showthread.php?t=722 Transform the linear set of equations into a single equation & then use numerical integration (as integration formulas have Sums, it is implemented iteratively). an optimization of Gauss-Jacobi: 1.5 times faster, requires 0.25 iterations to achieve the same tolerance Solving Non-Linear Equations Iteratively find roots of polynomials – there may be 0, 1 or n solutions for an n order polynomial use iterative techniques Iterative methods · used when there are no known analytical techniques · Requires set functions to be continuous & differentiable · Requires an initial seed value – choice is critical to convergence à conduct multiple runs with different starting points & then select best result · Systematic - iterate until diminishing returns, tolerance or max iteration conditions are met · bracketing techniques will always yield convergent solutions, non-bracketing methods may fail to converge Incremental method if a nonlinear function has opposite signs at 2 ends of a small interval x1 & x2, then there is likely to be a solution in their interval – solutions are detected by evaluating a function over interval steps, for a change in sign, adjusting the step size dynamically. Limitations – can miss closely spaced solutions in large intervals, cannot detect degenerate (coinciding) solutions, limited to functions that cross the x-axis, gives false positives for singularities Fixed point method http://en.wikipedia.org/wiki/Fixed-point_iteration C++: http://books.google.co.il/books?id=weYj75E_t6MC&pg=PA79&lpg=PA79&dq=fixed+point+method++c%2B%2B&source=bl&ots=LQ-5P_taoC&sig=lENUUIYBK53tZtTwNfHLy5PEWDk&hl=en&sa=X&ei=wezDUPW1J5DptQaMsIHQCw&redir_esc=y#v=onepage&q=fixed%20point%20method%20%20c%2B%2B&f=false Algebraically rearrange a solution to isolate a variable then apply incremental method Bisection method http://en.wikipedia.org/wiki/Bisection_method C++: http://numericalcomputing.wordpress.com/category/algorithms/ Bracketed - Select an initial interval, keep bisecting it ad midpoint into sub-intervals and then apply incremental method on smaller & smaller intervals – zoom in Adv: unaffected by function gradient à reliable Disadv: slow convergence False Position Method http://en.wikipedia.org/wiki/False_position_method C++: http://www.dreamincode.net/forums/topic/126100-bisection-and-false-position-methods/ Bracketed - Select an initial interval , & use the relative value of function at interval end points to select next sub-intervals (estimate how far between the end points the solution might be & subdivide based on this) Newton-Raphson method http://en.wikipedia.org/wiki/Newton's_method C++: http://www-users.cselabs.umn.edu/classes/Summer-2012/csci1113/index.php?page=./newt3 Also known as Newton's method Convenient, efficient Not bracketed – only a single initial guess is required to start iteration – requires an analytical expression for the first derivative of the function as input. Evaluates the function & its derivative at each step. Can be extended to the Newton MutiRoot method for solving multiple roots Can be easily applied to an of n-coupled set of non-linear equations – conduct a Taylor Series expansion of a function, dropping terms of order n, rewrite as a Jacobian matrix of PDs & convert to simultaneous linear equations !!! Secant Method http://en.wikipedia.org/wiki/Secant_method C++: http://forum.vcoderz.com/showthread.php?p=205230 Unlike N-R, can estimate first derivative from an initial interval (does not require root to be bracketed) instead of inputting it Since derivative is approximated, may converge slower. Is fast in practice as it does not have to evaluate the derivative at each step. Similar implementation to False Positive method Birge-Vieta Method http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/bv%20method.html C++: http://books.google.co.il/books?id=cL1boM2uyQwC&pg=SA3-PA51&lpg=SA3-PA51&dq=Birge-Vieta+Method+c%2B%2B&source=bl&ots=QZmnDTK3rC&sig=BPNcHHbpR_DKVoZXrLi4nVXD-gg&hl=en&sa=X&ei=R-_DUK2iNIjzsgbE5ID4Dg&redir_esc=y#v=onepage&q=Birge-Vieta%20Method%20c%2B%2B&f=false combines Horner's method of polynomial evaluation (transforming into lesser degree polynomials that are more computationally efficient to process) with Newton-Raphson to provide a computational speed-up Interpolation Overview Construct new data points for as close as possible fit within range of a discrete set of known points (that were obtained via sampling, experimentation) Use Taylor Series Expansion of a function f(x) around a specific value for x Linear Interpolation http://en.wikipedia.org/wiki/Linear_interpolation C++: http://www.hamaluik.com/?p=289 Straight line between 2 points à concatenate interpolants between each pair of data points Bilinear Interpolation http://en.wikipedia.org/wiki/Bilinear_interpolation C++: http://supercomputingblog.com/graphics/coding-bilinear-interpolation/2/ Extension of the linear function for interpolating functions of 2 variables – perform linear interpolation first in 1 direction, then in another. Used in image processing – e.g. texture mapping filter. Uses 4 vertices to interpolate a value within a unit cell. Lagrange Interpolation http://en.wikipedia.org/wiki/Lagrange_polynomial C++: http://www.codecogs.com/code/maths/approximation/interpolation/lagrange.php For polynomials Requires recomputation for all terms for each distinct x value – can only be applied for small number of nodes Numerically unstable Barycentric Interpolation http://epubs.siam.org/doi/pdf/10.1137/S0036144502417715 C++: http://www.gamedev.net/topic/621445-barycentric-coordinates-c-code-check/ Rearrange the terms in the equation of the Legrange interpolation by defining weight functions that are independent of the interpolated value of x Newton Divided Difference Interpolation http://en.wikipedia.org/wiki/Newton_polynomial C++: http://jee-appy.blogspot.co.il/2011/12/newton-divided-difference-interpolation.html Hermite Divided Differences: Interpolation polynomial approximation for a given set of data points in the NR form - divided differences are used to approximately calculate the various differences. For a given set of 3 data points , fit a quadratic interpolant through the data Bracketed functions allow Newton divided differences to be calculated recursively Difference table Cubic Spline Interpolation http://en.wikipedia.org/wiki/Spline_interpolation C++: https://www.marcusbannerman.co.uk/index.php/home/latestarticles/42-articles/96-cubic-spline-class.html Spline is a piecewise polynomial Provides smoothness – for interpolations with significantly varying data Use weighted coefficients to bend the function to be smooth & its 1st & 2nd derivatives are continuous through the edge points in the interval Curve Fitting A generalization of interpolating whereby given data points may contain noise à the curve does not necessarily pass through all the points Least Squares Fit http://en.wikipedia.org/wiki/Least_squares C++: http://www.ccas.ru/mmes/educat/lab04k/02/least-squares.c Residual – difference between observed value & expected value Model function is often chosen as a linear combination of the specified functions Determines: A) The model instance in which the sum of squared residuals has the least value B) param values for which model best fits data Straight Line Fit Linear correlation between independent variable and dependent variable Linear Regression http://en.wikipedia.org/wiki/Linear_regression C++: http://www.oocities.org/david_swaim/cpp/linregc.htm Special case of statistically exact extrapolation Leverage least squares Given a basis function, the sum of the residuals is determined and the corresponding gradient equation is expressed as a set of normal linear equations in matrix form that can be solved (e.g. using LU Decomposition) Can be weighted - Drop the assumption that all errors have the same significance –-> confidence of accuracy is different for each data point. Fit the function closer to points with higher weights Polynomial Fit - use a polynomial basis function Moving Average http://en.wikipedia.org/wiki/Moving_average C++: http://www.codeproject.com/Articles/17860/A-Simple-Moving-Average-Algorithm Used for smoothing (cancel fluctuations to highlight longer-term trends & cycles), time series data analysis, signal processing filters Replace each data point with average of neighbors. Can be simple (SMA), weighted (WMA), exponential (EMA). Lags behind latest data points – extra weight can be given to more recent data points. Weights can decrease arithmetically or exponentially according to distance from point. Parameters: smoothing factor, period, weight basis Optimization Overview Given function with multiple variables, find Min (or max by minimizing –f(x)) Iterative approach Efficient, but not necessarily reliable Conditions: noisy data, constraints, non-linear models Detection via sign of first derivative - Derivative of saddle points will be 0 Local minima Bisection method Similar method for finding a root for a non-linear equation Start with an interval that contains a minimum Golden Search method http://en.wikipedia.org/wiki/Golden_section_search C++: http://www.codecogs.com/code/maths/optimization/golden.php Bisect intervals according to golden ratio 0.618.. Achieves reduction by evaluating a single function instead of 2 Newton-Raphson Method Brent method http://en.wikipedia.org/wiki/Brent's_method C++: http://people.sc.fsu.edu/~jburkardt/cpp_src/brent/brent.cpp Based on quadratic or parabolic interpolation – if the function is smooth & parabolic near to the minimum, then a parabola fitted through any 3 points should approximate the minima – fails when the 3 points are collinear , in which case the denominator is 0 Simplex Method http://en.wikipedia.org/wiki/Simplex_algorithm C++: http://www.codeguru.com/cpp/article.php/c17505/Simplex-Optimization-Algorithm-and-Implemetation-in-C-Programming.htm Find the global minima of any multi-variable function Direct search – no derivatives required At each step it maintains a non-degenerative simplex – a convex hull of n+1 vertices. Obtains the minimum for a function with n variables by evaluating the function at n-1 points, iteratively replacing the point of worst result with the point of best result, shrinking the multidimensional simplex around the best point. Point replacement involves expanding & contracting the simplex near the worst value point to determine a better replacement point Oscillation can be avoided by choosing the 2nd worst result Restart if it gets stuck Parameters: contraction & expansion factors Simulated Annealing http://en.wikipedia.org/wiki/Simulated_annealing C++: http://code.google.com/p/cppsimulatedannealing/ Analogy to heating & cooling metal to strengthen its structure Stochastic method – apply random permutation search for global minima - Avoid entrapment in local minima via hill climbing Heating schedule - Annealing schedule params: temperature, iterations at each temp, temperature delta Cooling schedule – can be linear, step-wise or exponential Differential Evolution http://en.wikipedia.org/wiki/Differential_evolution C++: http://www.amichel.com/de/doc/html/ More advanced stochastic methods analogous to biological processes: Genetic algorithms, evolution strategies Parallel direct search method against multiple discrete or continuous variables Initial population of variable vectors chosen randomly – if weighted difference vector of 2 vectors yields a lower objective function value then it replaces the comparison vector Many params: #parents, #variables, step size, crossover constant etc Convergence is slow – many more function evaluations than simulated annealing Numerical Differentiation Overview 2 approaches to finite difference methods: · A) approximate function via polynomial interpolation then differentiate · B) Taylor series approximation – additionally provides error estimate Finite Difference methods http://en.wikipedia.org/wiki/Finite_difference_method C++: http://www.wpi.edu/Pubs/ETD/Available/etd-051807-164436/unrestricted/EAMPADU.pdf Find differences between high order derivative values - Approximate differential equations by finite differences at evenly spaced data points Based on forward & backward Taylor series expansion of f(x) about x plus or minus multiples of delta h. Forward / backward difference - the sums of the series contains even derivatives and the difference of the series contains odd derivatives – coupled equations that can be solved. Provide an approximation of the derivative within a O(h^2) accuracy There is also central difference & extended central difference which has a O(h^4) accuracy Richardson Extrapolation http://en.wikipedia.org/wiki/Richardson_extrapolation C++: http://mathscoding.blogspot.co.il/2012/02/introduction-richardson-extrapolation.html A sequence acceleration method applied to finite differences Fast convergence, high accuracy O(h^4) Derivatives via Interpolation Cannot apply Finite Difference method to discrete data points at uneven intervals – so need to approximate the derivative of f(x) using the derivative of the interpolant via 3 point Lagrange Interpolation Note: the higher the order of the derivative, the lower the approximation precision Numerical Integration Estimate finite & infinite integrals of functions More accurate procedure than numerical differentiation Use when it is not possible to obtain an integral of a function analytically or when the function is not given, only the data points are Newton Cotes Methods http://en.wikipedia.org/wiki/Newton%E2%80%93Cotes_formulas C++: http://www.siafoo.net/snippet/324 For equally spaced data points Computationally easy – based on local interpolation of n rectangular strip areas that is piecewise fitted to a polynomial to get the sum total area Evaluate the integrand at n+1 evenly spaced points – approximate definite integral by Sum Weights are derived from Lagrange Basis polynomials Leverage Trapezoidal Rule for default 2nd formulas, Simpson 1/3 Rule for substituting 3 point formulas, Simpson 3/8 Rule for 4 point formulas. For 4 point formulas use Bodes Rule. Higher orders obtain more accurate results Trapezoidal Rule uses simple area, Simpsons Rule replaces the integrand f(x) with a quadratic polynomial p(x) that uses the same values as f(x) for its end points, but adds a midpoint Romberg Integration http://en.wikipedia.org/wiki/Romberg's_method C++: http://code.google.com/p/romberg-integration/downloads/detail?name=romberg.cpp&can=2&q= Combines trapezoidal rule with Richardson Extrapolation Evaluates the integrand at equally spaced points The integrand must have continuous derivatives Each R(n,m) extrapolation uses a higher order integrand polynomial replacement rule (zeroth starts with trapezoidal) à a lower triangular matrix set of equation coefficients where the bottom right term has the most accurate approximation. The process continues until the difference between 2 successive diagonal terms becomes sufficiently small. Gaussian Quadrature http://en.wikipedia.org/wiki/Gaussian_quadrature C++: http://www.alglib.net/integration/gaussianquadratures.php Data points are chosen to yield best possible accuracy – requires fewer evaluations Ability to handle singularities, functions that are difficult to evaluate The integrand can include a weighting function determined by a set of orthogonal polynomials. Points & weights are selected so that the integrand yields the exact integral if f(x) is a polynomial of degree <= 2n+1 Techniques (basically different weighting functions): · Gauss-Legendre Integration w(x)=1 · Gauss-Laguerre Integration w(x)=e^-x · Gauss-Hermite Integration w(x)=e^-x^2 · Gauss-Chebyshev Integration w(x)= 1 / Sqrt(1-x^2) Solving ODEs Use when high order differential equations cannot be solved analytically Evaluated under boundary conditions RK for systems – a high order differential equation can always be transformed into a coupled first order system of equations Euler method http://en.wikipedia.org/wiki/Euler_method C++: http://rosettacode.org/wiki/Euler_method First order Runge–Kutta method. Simple recursive method – given an initial value, calculate derivative deltas. Unstable & not very accurate (O(h) error) – not used in practice A first-order method - the local error (truncation error per step) is proportional to the square of the step size, and the global error (error at a given time) is proportional to the step size In evolving solution between data points xn & xn+1, only evaluates derivatives at beginning of interval xn à asymmetric at boundaries Higher order Runge Kutta http://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods C++: http://www.dreamincode.net/code/snippet1441.htm 2nd & 4th order RK - Introduces parameterized midpoints for more symmetric solutions à accuracy at higher computational cost Adaptive RK – RK-Fehlberg – estimate the truncation at each integration step & automatically adjust the step size to keep error within prescribed limits. At each step 2 approximations are compared – if in disagreement to a specific accuracy, the step size is reduced Boundary Value Problems Where solution of differential equations are located at 2 different values of the independent variable x à more difficult, because cannot just start at point of initial value – there may not be enough starting conditions available at the end points to produce a unique solution An n-order equation will require n boundary conditions – need to determine the missing n-1 conditions which cause the given conditions at the other boundary to be satisfied Shooting Method http://en.wikipedia.org/wiki/Shooting_method C++: http://ganeshtiwaridotcomdotnp.blogspot.co.il/2009/12/c-c-code-shooting-method-for-solving.html Iteratively guess the missing values for one end & integrate, then inspect the discrepancy with the boundary values of the other end to adjust the estimate Given the starting boundary values u1 & u2 which contain the root u, solve u given the false position method (solving the differential equation as an initial value problem via 4th order RK), then use u to solve the differential equations. Finite Difference Method For linear & non-linear systems Higher order derivatives require more computational steps – some combinations for boundary conditions may not work though Improve the accuracy by increasing the number of mesh points Solving EigenValue Problems An eigenvalue can substitute a matrix when doing matrix multiplication à convert matrix multiplication into a polynomial EigenValue For a given set of equations in matrix form, determine what are the solution eigenvalue & eigenvectors Similar Matrices - have same eigenvalues. Use orthogonal similarity transforms to reduce a matrix to diagonal form from which eigenvalue(s) & eigenvectors can be computed iteratively Jacobi method http://en.wikipedia.org/wiki/Jacobi_method C++: http://people.sc.fsu.edu/~jburkardt/classes/acs2_2008/openmp/jacobi/jacobi.html Robust but Computationally intense – use for small matrices < 10x10 Power Iteration http://en.wikipedia.org/wiki/Power_iteration For any given real symmetric matrix, generate the largest single eigenvalue & its eigenvectors Simplest method – does not compute matrix decomposition à suitable for large, sparse matrices Inverse Iteration Variation of power iteration method – generates the smallest eigenvalue from the inverse matrix Rayleigh Method http://en.wikipedia.org/wiki/Rayleigh's_method_of_dimensional_analysis Variation of power iteration method Rayleigh Quotient Method Variation of inverse iteration method Matrix Tri-diagonalization Method Use householder algorithm to reduce an NxN symmetric matrix to a tridiagonal real symmetric matrix vua N-2 orthogonal transforms     Whats Next Outside of Numerical Methods there are lots of different types of algorithms that I’ve learned over the decades: Data Mining – (I covered this briefly in a previous post: http://geekswithblogs.net/JoshReuben/archive/2007/12/31/ssas-dm-algorithms.aspx ) Search & Sort Routing Problem Solving Logical Theorem Proving Planning Probabilistic Reasoning Machine Learning Solvers (eg MIP) Bioinformatics (Sequence Alignment, Protein Folding) Quant Finance (I read Wilmott’s books – interesting) Sooner or later, I’ll cover the above topics as well.

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  • GRAPH PROBLEM: find an algorithm to determine the shortest path from one point to another in a recta

    - by newba
    I'm getting such an headache trying to elaborate an appropriate algorithm to go from a START position to a EXIT position in a maze. For what is worth, the maze is rectangular, maxsize 500x500 and, in theory, is resolvable by DFS with some branch and bound techniques ... 10 3 4 7 6 3 3 1 2 2 1 0 2 2 2 4 2 2 5 2 2 1 3 0 2 2 2 2 1 3 3 4 2 3 4 4 3 1 1 3 1 2 2 4 2 2 1 Output: 5 1 4 2 Explanation: Our agent looses energy every time he gives a step and he can only move UP, DOWN, LEFT and RIGHT. Also, if the agent arrives with a remaining energy of zero or less, he dies, so we print something like "Impossible". So, in the input 10 is the initial agent's energy, 3 4 is the START position (i.e. column 3, line 4) and we have a maze 7x6. Think this as a kind of labyrinth, in which I want to find the exit that gives the agent a better remaining energy (shortest path). In case there are paths which lead to the same remaining energy, we choose the one which has the small number of steps, of course. I need to know if a DFS to a maze 500x500 in the worst case is feasible with these limitations and how to do it, storing the remaining energy in each step and the number of steps taken so far. The output means the agent arrived with remaining energy= 5 to the exit pos 1 4 in 2 steps. If we look carefully, in this maze it's also possible to exit at pos 3 1 (column 3, row 1) with the same energy but with 3 steps, so we choose the better one. With these in mind, can someone help me some code or pseudo-code? I have troubles working this around with a 2D array and how to store the remaining energy, the path (or number of steps taken)....

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  • Street-Fighting Mathematics

    Sanjoy Mahajan's new book lays out practical tools for educated guessing and down-and-dirty problem-solving Problem solving - Math - Recreations - Competitions - Methods and Theories

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  • Anyone have ideas for solving the "n items remaining" problem on Internet Explorer?

    - by CMPalmer
    In my ASP.Net app, which is javascript and jQuery heavy, but also uses master pages and .Net Ajax pieces, I am consistently seeing on the status bar of IE 6 (and occasionally IE 7) the message "2 items remaining" or "15 items remaining" followed by "loading somegraphicsfile.png|gif ." This message never goes away and may or may not prevent some page functionality from running (it certainly seems to bog down, but I'm not positive). I can cause this to happen 99% of the time by just refreshing an .aspx age, but the number of items and, sometimes, the file it mentions varies. Usually it is 2, 3, 12, 13, or 15. I've Googled for answers and there are several suggestions or explanations. Some of them haven't worked for us, and others aren't practical for us to implement or try. Here are some of the ideas/theories: IE isn't caching images right, so it repeatedly asks for the same image if the image is repeated on the page and the server assumes that it should be cached locally since it's already served it in that page context. IE displays the images correctly, but sits and waits for a server response that never comes. Typically the file it says it is waiting on is repeated on the page. The page is using PNG graphics with transparency. Indeed it is, but they are jQuery-UI Themeroller generated graphics which, according to the jQuery-UI folks, are IE safe. The jQuery-UI components are the only things using PNGs. All of our PNG references are in CSS, if that helps. I've changed some of the graphics from PNG to GIF, but it is just as likely to say it's waiting for somegraphicsfile.png as it is for somegraphicsfile.gif Images are being specified in CSS and/or JavaScript but are on things that aren't currently being displayed (display: none items for example). This may be true, but if it is, then I would think preloading images would work, but so far, adding a preloader doesn't do any good. IIS's caching policy is confusing the browser. If this is true, it is only Microsoft server SW having problems with Microsoft's browser (which doesn't surprise me at all). Unfortunately, I don't have much control over the IIS configuration that will be hosting the app. Has anyone seen this and found a way to combat it? Particularly on ASP.Net apps with jQuery and jQuery-UI? UPDATE One other data point: on at least one of the pages, just commenting out the jQuery-UI Datepicker component setup causes the problem to go away, but I don't think (or at least I'm not sure) if that fixes all of the pages. If it does "fix" them, I'll have to swap out plug-ins because that functionality needs to be there. There doesn't seem to be any open issues against jQuery-UI on IE6/7 currently... UPDATE 2 I checked the IIS settings and "enable content expiration" was not set on any of my folders. Unchecking that setting was a common suggestion for fixing this problem. I have another, simpler, page that I can consistently create the error on. I'm using the jQuery-UI 1.6rc6 file (although I've also tried jQuery-UI 1.7.1 with the same results). The problem only occurs when I refresh the page that contains the jQuery-UI Datepicker. If I comment out the Datepicker setup, the problem goes away. Here are a few things I notice when I do this: This page always says "(1 item remaining) Downloading picture http:///images/Calendar_scheduleHS.gif", but only when reloading. When I look at HTTP logging, I see that it requests that image from the server every time it is dynamically turned on, without regard to caching. All of the requests for that graphic are complete and return the graphic correctly. None are marked code 200 or 304 (indicating that the server is telling IE to use the cached version). Why it says waiting on that graphic when all of the requests have completed I have no idea. There is a single other graphic on the page (one of the UI PNG files) that has a code 304 (Not Modified). On another page where I managed to log HTTP traffic with "2 items remaining", two different graphic files (both UI PNGs) had a 304 as well (but neither was the one listed as "Downloading". This error is not innocuous - the page is not fully responsive. For example, if I click on one of the buttons which should execute a client-side action, the page refreshes. Going away from the page and coming back does not produce the error. I have moved the script and script references to the bottom of the content and this doesn't affect this problem. The script is still running in the $(document).ready() though (it's too hairy to divide out unless I absolutely have to). FINAL UPDATE AND ANSWER There were a lot of good answers and suggestions below, but none of them were exactly our problem. The closest one (and the one that led me to the solution) was the one about long running JavaScript, so I awarded the bounty there (I guess I could have answered it myself, but I'd rather reward info that leads to solutions). Here was our solution: We had multiple jQueryUI datepickers that were created on the $(document).ready event in script included from the ASP.Net master page. On this client page, a local script's $(document).ready event had script that destroyed the datepickers under certain conditions. We had to use "destroy" because the previous version of datepicker had a problem with "disable". When we upgraded to the latest version of jQuery UI (1.7.1) and replaced the "destroy"s with "disable"s for the datepickers, the problem went away (or mostly went away - if you do things too fast while the page is loading, it is still possible to get the "n items remaining" status). My theory as to what was happening goes like this: The page content loads and has 12 or so text boxes with the datepicker class. The master page script creates datepickers on those text boxes. IE queues up requests for each calendar graphic independently because IE doesn't know how to properly cache dynamic image requests. Before the requests get processed, the client area script destroys those datepickers so the graphics are no longer needed. IE is left with some number of orphaned requests that it doesn't know what to do with.

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  • What are the differences between GIT and SVN when it comes to merge conflicts solving.

    - by chalup
    I keep hearing that branching in git is so much easier than in SVN, because it's easier to merge the branch back to trunk/master. I've read some tutorials, but they only covered basic merge conflicts ("Alice changed line 8 of code.cpp and at the same time Bob changed line 8 of code.cpp...") and there are no differences between SVN and all other distributed source control systems. Can you give me the examples of changes in branch that would cause troubles in SVN repository, but would be handled gracefully by git?

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  • Calculus? Need help solving for a time-dependent variable given some other variables.

    - by user451527
    Long story short, I'm making a platform game. I'm not old enough to have taken Calculus yet, so I know not of derivatives or integrals, but I know of them. The desired behavior is for my character to automagically jump when there is a block to either side of him that is above the one he's standing on; for instance, stairs. This way the player can just hold left / right to climb stairs, instead of having to spam the jump key too. The issue is with the way I've implemented jumping; I've decided to go mario-style, and allow the player to hold 'jump' longer to jump higher. To do so, I have a 'jump' variable which is added to the player's Y velocity. The jump variable increases to a set value when the 'jump' key is pressed, and decreases very quickly once the 'jump' key is released, but decreases less quickly so long as you hold the 'jump' key down, thus providing continuous acceleration up as long as you hold 'jump.' This also makes for a nice, flowing jump, rather than a visually jarring, abrupt acceleration. So, in order to account for variable stair height, I want to be able to calculate exactly what value the 'jump' variable should get in order to jump exactly to the height of the stair; preferably no more, no less, though slightly more is permissible. This way the character can jump up steep or shallow flights of stairs without it looking weird or being slow. There are essentially 5 variables in play: h -the height the character needs to jump to reach the stair top<br> j -the jump acceleration variable<br> v -the vertical velocity of the character<br> p -the vertical position of the character<br> d -initial vertical position of the player minus final position<br> Each timestep:<br> j -= 1.5; //the jump variable's deceleration<br> v -= j; //the jump value's influence on vertical speed<br> v *= 0.95; //friction on the vertical speed<br> v += 1; //gravity<br> p += v; //add the vertical speed to the vertical position<br> v-initial is known to be zero<br> v-final is known to be zero<br> p-initial is known<br> p-final is known<br> d is known to be p-initial minus p-final<br> j-final is known to be zero<br> j-initial is unknown<br> Given all of these facts, how can I make an equation that will solve for j? tl;dr How do I Calculus? Much thanks to anyone who's made it this far and decides to plow through this problem.

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  • XCode, error: '_object' undeclared. Need some help solving this problem

    - by user309030
    I've got this code in my viewController.m file - (void)viewDidLoad { [super viewDidLoad]; GameLogic *_game = [[GameLogic alloc] init]; [_game initGame]; ....... } GameLogic is another class which I created. in the same viewController.m file, I have got another function - (void)test { if([_game returnElecFence]) { NSLog(@"YES"); } else { NSLog(@"NO"); } } Problem is, whenever the test function is called, I get an error saying '_game' undeclared. I tried putting the GameLogic init code in the .h file and on top of the @implementation to make it global but every method I tried resulted in a worse error. TIA to anyone who can suggest some ideas to clear this error up

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  • I need help solving a rather weird error in a WCF service.

    - by Moulde
    Hi.. I have a solution that contains three projects. A main project with my MVC app, a silverlight application and a (silverlight enabled) WCF service project. In my silverlight project i have made a Service Reference to my WCF service. And i pretty much got that working. In my WCF service i have a method that returns an Book object, which got some random fields like title, date etc. In the book class, i have a ICollection field that contains a list of events. The book class is generated using entity framework 4.0, and Lazy Loading is enabled. If i in my getBook(int id) method return a book with the events field not initialized, it works as a charm. But if i initialize the field, i'm getting this error. The server did not provide a meaningful reply; this might be caused by a contract mismatch, a premature session shutdown or an internal server error. I have a few ideas why that is happening, and while writing this i just got another one. The wcf service somehow threw away the reference to the event class. That would be very weird since i have a reference between my main mvc app (with the models) and my WCF service. Since i have enabled lazy loading in EF 4.0, i suspect that it may be the thing generating the error. But i'm not sure why that would be, because i'm not in any way accessing that field. I could understand that i may not be able to access the events field after i recive the object in my silverlight application since the connection between the book object and the entity framework is like broken. Did i mention that Lazy Loading is enabled on my EF instance? And there is no inner exception in the thrown exception. Thanks in advance. Malte Baden Hansen

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  • How to use TestAndSet() for solving the critical section problem?

    - by Dan Mantyla
    I'm studying for an exam and I'm having difficulty with a concept. This is the pseudo code I am given: int mutex = 0; do { while (TestAndSet(&mutex)); // critical section mutiex = 0; // remainder section } while (TRUE); My instructor says that only two of the three necessary conditions (mutual exclusion, progress, and bounded waiting) are met with this code, but I don't understand which one isn't being met...?? How should the code be modified to support the missing condition to solve the critical region problem? Thanks in advance for any insight!

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