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• Gradient algororithm produces little white dots

  - by user146780

  I'm working on an algorithm to generate point to point linear gradients. I have a rough, proof of concept implementation done: GLuint OGLENGINEFUNCTIONS::CreateGradient( std::vector<ARGBCOLORF> &input,POINTFLOAT start, POINTFLOAT end, int width, int height,bool radial ) { std::vector<POINT> pol; std::vector<GLubyte> pdata(width * height * 4); std::vector<POINTFLOAT> linearpts; std::vector<float> lookup; float distance = GetDistance(start,end); RoundNumber(distance); POINTFLOAT temp; float incr = 1 / (distance + 1); for(int l = 0; l < 100; l ++) { POINTFLOAT outA; POINTFLOAT OutB; float dirlen; float perplen; POINTFLOAT dir; POINTFLOAT ndir; POINTFLOAT perp; POINTFLOAT nperp; POINTFLOAT perpoffset; POINTFLOAT diroffset; dir.x = end.x - start.x; dir.y = end.y - start.y; dirlen = sqrt((dir.x * dir.x) + (dir.y * dir.y)); ndir.x = static_cast<float>(dir.x * 1.0 / dirlen); ndir.y = static_cast<float>(dir.y * 1.0 / dirlen); perp.x = dir.y; perp.y = -dir.x; perplen = sqrt((perp.x * perp.x) + (perp.y * perp.y)); nperp.x = static_cast<float>(perp.x * 1.0 / perplen); nperp.y = static_cast<float>(perp.y * 1.0 / perplen); perpoffset.x = static_cast<float>(nperp.x * l * 0.5); perpoffset.y = static_cast<float>(nperp.y * l * 0.5); diroffset.x = static_cast<float>(ndir.x * 0 * 0.5); diroffset.y = static_cast<float>(ndir.y * 0 * 0.5); outA.x = end.x + perpoffset.x + diroffset.x; outA.y = end.y + perpoffset.y + diroffset.y; OutB.x = start.x + perpoffset.x - diroffset.x; OutB.y = start.y + perpoffset.y - diroffset.y; for (float i = 0; i < 1; i += incr) { temp = GetLinearBezier(i,outA,OutB); RoundNumber(temp.x); RoundNumber(temp.y); linearpts.push_back(temp); lookup.push_back(i); } for (unsigned int j = 0; j < linearpts.size(); j++) { if(linearpts[j].x < width && linearpts[j].x >= 0 && linearpts[j].y < height && linearpts[j].y >=0) { pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 0] = (GLubyte) j; pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 1] = (GLubyte) j; pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 2] = (GLubyte) j; pdata[linearpts[j].x * 4 * width + linearpts[j].y * 4 + 3] = (GLubyte) 255; } } lookup.clear(); linearpts.clear(); } return CreateTexture(pdata,width,height); } It works as I would expect most of the time, but at certain angles it produces little white dots. I can't figure out what does this. This is what it looks like at most angles (good) http://img9.imageshack.us/img9/5922/goodgradient.png But once in a while it looks like this (bad): http://img155.imageshack.us/img155/760/badgradient.png What could be causing the white dots? Is there maybe also a better way to generate my gradients if no solution is possible for this? Thanks

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• What is wrong with my logic for the divide and conquer algorithm for Closest pair problem?

  - by Programming Noob

  I have been following Coursera's course on Algorithms and came up with a thought about the divide/conquer algorithm for the closest pair problem, that I want clarified. As per Prof Roughgarden's algorithm (which you can see here if you're interested): For a given set of points P, of which we have two copies - sorted in X and Y direction - Px and Py, the algorithm can be given as closestPair(Px,Py): Divide points into left half - Q, and right half - R, and form sorted copies of both halves along x and y directions - Qx,Qy,Rx,Ry Let closestPair(Qx,Qy) be points p1 and q1 Let closestPair(Rx,Ry) be p2,q2 Let delta be minimum of dist(p1,q1) and dist(p2,q2) This is the unfortunate case, let p3,q3 be the closestSplitPair(Px,Py,delta) Return the best result Now, the clarification that I want is related to step 5. I should say this beforehand, that what I'm suggesting, is barely any improvement at all, but if you're still interested, read ahead. Prof R says that since the points are already sorted in X and Y directions, to find the best pair in step 5, we need to iterate over points in the strip of width 2*delta, starting from bottom to up, and in the inner loop we need only 7 comparisions. Can this be bettered to just one? How I think is possible seemed a little difficult to explain in plain text, so I drew a diagram and wrote it on paper and uploaded it here: Since no one else came up with is, I'm pretty sure there's some error in my line of thought. But I have literally been thinking about this for HOURS now, and I just HAD to post this. It's all that is in my head. Can someone point out where I'm going wrong?

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• If your algorithm is correct, does it matter how long it took you to write it?

  - by John Isaacks

  I recently found out that Facebook had a programming challenge that if completed correctly you automatically get a phone interview. There is a sample challenge that asks you to write an algorithm that can solve a Tower of Hanoi type problem. Given a number of pegs and discs, an initial and final configuration; Your algorithm must determine the fewest steps possible to get to the final configuration and output the steps. This sample challenge gives you a 45 minute time limit but allows you to still test your code to see if it passes once your time limit expires. I did not know of any cute math solution that could solve it, and I didn't want to look for one since I think that would be cheating. So I tried to solve the challenge the best I could on my own. I was able to make an algorithm that worked and passed. However, it took me over 4 hours to make, much longer than the 45 minute requirement. Since it took me so much longer than the allotted time, I have not attempted the actual challenge. This got me wondering though, in reality does it really matter that it took me that long? I mean is this a sign that I will not be able to get a job at a place like this (not just Facebook, but Google, Fog Creek, etc.) and need to lower my aspirations, or does the fact that I actually passed on my first attempt even though it took too long be taken as good?

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• questions regarding the use of A* with the 15-square puzzle

  - by Cheeso

  I'm trying to build an A* solver for a 15-square puzzle. The goal is to re-arrange the tiles so that they appear in their natural positions. You can only slide one tile at a time. Each possible state of the puzzle is a node in the search graph. For the h(x) function, I am using an aggregate sum, across all tiles, of the tile's dislocation from the goal state. In the above image, the 5 is at location 0,0, and it belongs at location 1,0, therefore it contributes 1 to the h(x) function. The next tile is the 11, located at 0,1, and belongs at 2,2, therefore it contributes 3 to h(x). And so on. EDIT: I now understand this is what they call "Manhattan distance", or "taxicab distance". I have been using a step count for g(x). In my implementation, for any node in the state graph, g is just +1 from the prior node's g. To find successive nodes, I just examine where I can possibly move the "hole" in the puzzle. There are 3 neighbors for the puzzle state (aka node) that is displayed: the hole can move north, west, or east. My A* search sometimes converges to a solution in 20s, sometimes 180s, and sometimes doesn't converge at all (waited 10 mins or more). I think h is reasonable. I'm wondering if I've modeled g properly. In other words, is it possible that my A* function is reaching a node in the graph via a path that is not the shortest path? Maybe have I not waited long enough? Maybe 10 minutes is not long enough? For a fully random arrangement, (assuming no parity problems), What is the average number of permutations an A* solution will examine? (please show the math) I'm going to look for logic errors in my code, but in the meantime, Any tips? (ps: it's done in Javascript). Also, no, this isn't CompSci homework. It's just a personal exploration thing. I'm just trying to learn Javascript. EDIT: I've found that the run-time is highly depend upon the heuristic. I saw the 10x factor applied to the heuristic from the article someone mentioned, and it made me wonder - why 10x? Why linear? Because this is done in javascript, I could modify the code to dynamically update an html table with the node currently being considered. This allowd me to peek at the algorithm as it was progressing. With a regular taxicab distance heuristic, I watched as it failed to converge. There were 5's and 12's in the top row, and they kept hanging around. I'd see 1,2,3,4 creep into the top row, but then they'd drop out, and other numbers would move up there. What I was hoping to see was 1,2,3,4 sort of creeping up to the top, and then staying there. I thought to myself - this is not the way I solve this personally. Doing this manually, I solve the top row, then the 2ne row, then the 3rd and 4th rows sort of concurrently. So I tweaked the h(x) function to more heavily weight the higher rows and the "lefter" columns. The result was that the A* converged much more quickly. It now runs in 3 minutes instead of "indefinitely". With the "peek" I talked about, I can see the smaller numbers creep up to the higher rows and stay there. Not only does this seem like the right thing, it runs much faster. I'm in the process of trying a bunch of variations. It seems pretty clear that A* runtime is very sensitive to the heuristic. Currently the best heuristic I've found uses the summation of dislocation * ((4-i) + (4-j)) where i and j are the row and column, and dislocation is the taxicab distance. One interesting part of the result I got: with a particular heuristic I find a path very quickly, but it is obviously not the shortest path. I think this is because I am weighting the heuristic. In one case I got a path of 178 steps in 10s. My own manual effort produce a solution in 87 moves. (much more than 10s). More investigation warranted. So the result is I am seeing it converge must faster, and the path is definitely not the shortest. I have to think about this more. Code: var stop = false; function Astar(start, goal, callback) { // start and goal are nodes in the graph, represented by // an array of 16 ints. The goal is: [1,2,3,...14,15,0] // Zero represents the hole. // callback is a method to call when finished. This runs a long time, // therefore we need to use setTimeout() to break it up, to avoid // the browser warning like "Stop running this script?" // g is the actual distance traveled from initial node to current node. // h is the heuristic estimate of distance from current to goal. stop = false; start.g = start.dontgo = 0; // calcHeuristic inserts an .h member into the array calcHeuristicDistance(start); // start the stack with one element var closed = []; // set of nodes already evaluated. var open = [ start ]; // set of nodes to evaluate (start with initial node) var iteration = function() { if (open.length==0) { // no more nodes. Fail. callback(null); return; } var current = open.shift(); // get highest priority node // update the browser with a table representation of the // node being evaluated $("#solution").html(stateToString(current)); // check solution returns true if current == goal if (checkSolution(current,goal)) { // reconstructPath just records the position of the hole // through each node var path= reconstructPath(start,current); callback(path); return; } closed.push(current); // get the set of neighbors. This is 3 or fewer nodes. // (nextStates is optimized to NOT turn directly back on itself) var neighbors = nextStates(current, goal); for (var i=0; i<neighbors.length; i++) { var n = neighbors[i]; // skip this one if we've already visited it if (closed.containsNode(n)) continue; // .g, .h, and .previous get assigned implicitly when // calculating neighbors. n.g is nothing more than // current.g+1 ; // add to the open list if (!open.containsNode(n)) { // slot into the list, in priority order (minimum f first) open.priorityPush(n); n.previous = current; } } if (stop) { callback(null); return; } setTimeout(iteration, 1); }; // kick off the first iteration iteration(); return null; }

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• Need help with fixing Genetic Algorithm that's not evolving correctly

  - by EnderMB

  I am working on a maze solving application that uses a Genetic Algorithm to evolve a set of genes (within Individuals) to evolve a Population of Individuals that power an Agent through a maze. The majority of the code used appears to be working fine but when the code runs it's not selecting the best Individual's to be in the new Population correctly. When I run the application it outputs the following: Total Fitness: 380.0 - Best Fitness: 11.0 Total Fitness: 406.0 - Best Fitness: 15.0 Total Fitness: 344.0 - Best Fitness: 12.0 Total Fitness: 373.0 - Best Fitness: 11.0 Total Fitness: 415.0 - Best Fitness: 12.0 Total Fitness: 359.0 - Best Fitness: 11.0 Total Fitness: 436.0 - Best Fitness: 13.0 Total Fitness: 390.0 - Best Fitness: 12.0 Total Fitness: 379.0 - Best Fitness: 15.0 Total Fitness: 370.0 - Best Fitness: 11.0 Total Fitness: 361.0 - Best Fitness: 11.0 Total Fitness: 413.0 - Best Fitness: 16.0 As you can clearly see the fitnesses are not improving and neither are the best fitnesses. The main code responsible for this problem is here, and I believe the problem to be within the main method, most likely where the selection methods are called: package GeneticAlgorithm; import GeneticAlgorithm.Individual.Action; import Robot.Robot.Direction; import Maze.Maze; import Robot.Robot; import java.util.ArrayList; import java.util.Random; public class RunGA { protected static ArrayList tmp1, tmp2 = new ArrayList(); // Implementation of Elitism protected static int ELITISM_K = 5; // Population size protected static int POPULATION_SIZE = 50 + ELITISM_K; // Max number of Iterations protected static int MAX_ITERATIONS = 200; // Probability of Mutation protected static double MUTATION_PROB = 0.05; // Probability of Crossover protected static double CROSSOVER_PROB = 0.7; // Instantiate Random object private static Random rand = new Random(); // Instantiate Population of Individuals private Individual[] startPopulation; // Total Fitness of Population private double totalFitness; Robot robot = new Robot(); Maze maze; public void setElitism(int result) { ELITISM_K = result; } public void setPopSize(int result) { POPULATION_SIZE = result + ELITISM_K; } public void setMaxIt(int result) { MAX_ITERATIONS = result; } public void setMutProb(double result) { MUTATION_PROB = result; } public void setCrossoverProb(double result) { CROSSOVER_PROB = result; } /** * Constructor for Population */ public RunGA(Maze maze) { // Create a population of population plus elitism startPopulation = new Individual[POPULATION_SIZE]; // For every individual in population fill with x genes from 0 to 1 for (int i = 0; i < POPULATION_SIZE; i++) { startPopulation[i] = new Individual(); startPopulation[i].randGenes(); } // Evaluate the current population's fitness this.evaluate(maze, startPopulation); } /** * Set Population * @param newPop */ public void setPopulation(Individual[] newPop) { System.arraycopy(newPop, 0, this.startPopulation, 0, POPULATION_SIZE); } /** * Get Population * @return */ public Individual[] getPopulation() { return this.startPopulation; } /** * Evaluate fitness * @return */ public double evaluate(Maze maze, Individual[] newPop) { this.totalFitness = 0.0; ArrayList<Double> fitnesses = new ArrayList<Double>(); for (int i = 0; i < POPULATION_SIZE; i++) { maze = new Maze(8, 8); maze.fillMaze(); fitnesses.add(startPopulation[i].evaluate(maze, newPop)); //this.totalFitness += startPopulation[i].evaluate(maze, newPop); } //totalFitness = (Math.round(totalFitness / POPULATION_SIZE)); StringBuilder sb = new StringBuilder(); for(Double tmp : fitnesses) { sb.append(tmp + ", "); totalFitness += tmp; } // Progress of each Individual //System.out.println(sb.toString()); return this.totalFitness; } /** * Roulette Wheel Selection * @return */ public Individual rouletteWheelSelection() { // Calculate sum of all chromosome fitnesses in population - sum S. double randNum = rand.nextDouble() * this.totalFitness; int i; for (i = 0; i < POPULATION_SIZE && randNum > 0; ++i) { randNum -= startPopulation[i].getFitnessValue(); } return startPopulation[i-1]; } /** * Tournament Selection * @return */ public Individual tournamentSelection() { double randNum = rand.nextDouble() * this.totalFitness; // Get random number of population (add 1 to stop nullpointerexception) int k = rand.nextInt(POPULATION_SIZE) + 1; int i; for (i = 1; i < POPULATION_SIZE && i < k && randNum > 0; ++i) { randNum -= startPopulation[i].getFitnessValue(); } return startPopulation[i-1]; } /** * Finds the best individual * @return */ public Individual findBestIndividual() { int idxMax = 0; double currentMax = 0.0; double currentMin = 1.0; double currentVal; for (int idx = 0; idx < POPULATION_SIZE; ++idx) { currentVal = startPopulation[idx].getFitnessValue(); if (currentMax < currentMin) { currentMax = currentMin = currentVal; idxMax = idx; } if (currentVal > currentMax) { currentMax = currentVal; idxMax = idx; } } // Double check to see if this has the right one //System.out.println(startPopulation[idxMax].getFitnessValue()); // Maximisation return startPopulation[idxMax]; } /** * One Point Crossover * @param firstPerson * @param secondPerson * @return */ public static Individual[] onePointCrossover(Individual firstPerson, Individual secondPerson) { Individual[] newPerson = new Individual[2]; newPerson[0] = new Individual(); newPerson[1] = new Individual(); int size = Individual.SIZE; int randPoint = rand.nextInt(size); int i; for (i = 0; i < randPoint; ++i) { newPerson[0].setGene(i, firstPerson.getGene(i)); newPerson[1].setGene(i, secondPerson.getGene(i)); } for (; i < Individual.SIZE; ++i) { newPerson[0].setGene(i, secondPerson.getGene(i)); newPerson[1].setGene(i, firstPerson.getGene(i)); } return newPerson; } /** * Uniform Crossover * @param firstPerson * @param secondPerson * @return */ public static Individual[] uniformCrossover(Individual firstPerson, Individual secondPerson) { Individual[] newPerson = new Individual[2]; newPerson[0] = new Individual(); newPerson[1] = new Individual(); for(int i = 0; i < Individual.SIZE; ++i) { double r = rand.nextDouble(); if (r > 0.5) { newPerson[0].setGene(i, firstPerson.getGene(i)); newPerson[1].setGene(i, secondPerson.getGene(i)); } else { newPerson[0].setGene(i, secondPerson.getGene(i)); newPerson[1].setGene(i, firstPerson.getGene(i)); } } return newPerson; } public double getTotalFitness() { return totalFitness; } public static void main(String[] args) { // Initialise Environment Maze maze = new Maze(8, 8); maze.fillMaze(); // Instantiate Population //Population pop = new Population(); RunGA pop = new RunGA(maze); // Instantiate Individuals for Population Individual[] newPop = new Individual[POPULATION_SIZE]; // Instantiate two individuals to use for selection Individual[] people = new Individual[2]; Action action = null; Direction direction = null; String result = ""; /*result += "Total Fitness: " + pop.getTotalFitness() + " - Best Fitness: " + pop.findBestIndividual().getFitnessValue();*/ // Print Current Population System.out.println("Total Fitness: " + pop.getTotalFitness() + " - Best Fitness: " + pop.findBestIndividual().getFitnessValue()); // Instantiate counter for selection int count; for (int i = 0; i < MAX_ITERATIONS; i++) { count = 0; // Elitism for (int j = 0; j < ELITISM_K; ++j) { // This one has the best fitness newPop[count] = pop.findBestIndividual(); count++; } // Build New Population (Population size = Steps (28)) while (count < POPULATION_SIZE) { // Roulette Wheel Selection people[0] = pop.rouletteWheelSelection(); people[1] = pop.rouletteWheelSelection(); // Tournament Selection //people[0] = pop.tournamentSelection(); //people[1] = pop.tournamentSelection(); // Crossover if (rand.nextDouble() < CROSSOVER_PROB) { // One Point Crossover //people = onePointCrossover(people[0], people[1]); // Uniform Crossover people = uniformCrossover(people[0], people[1]); } // Mutation if (rand.nextDouble() < MUTATION_PROB) { people[0].mutate(); } if (rand.nextDouble() < MUTATION_PROB) { people[1].mutate(); } // Add to New Population newPop[count] = people[0]; newPop[count+1] = people[1]; count += 2; } // Make new population the current population pop.setPopulation(newPop); // Re-evaluate the current population //pop.evaluate(); pop.evaluate(maze, newPop); // Print results to screen System.out.println("Total Fitness: " + pop.totalFitness + " - Best Fitness: " + pop.findBestIndividual().getFitnessValue()); //result += "\nTotal Fitness: " + pop.totalFitness + " - Best Fitness: " + pop.findBestIndividual().getFitnessValue(); } // Best Individual Individual bestIndiv = pop.findBestIndividual(); //return result; } } I have uploaded the full project to RapidShare if you require the extra files, although if needed I can add the code to them here. This problem has been depressing me for days now and if you guys can help me I will forever be in your debt.

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• Invalid algorithm specified on Windows 2003 Server only

  - by JL

  I am decoding a file using the following method: string outFileName = zfoFileName.Replace(".zfo", "_tmp.zfo"); FileStream inFile = null; FileStream outFile = null; inFile = File.Open(zfoFileName, FileMode.Open); outFile = File.Create(outFileName); LargeCMS.CMS cms = new LargeCMS.CMS(); cms.Decode(inFile, outFile); This is working fine on my Win 7 dev machine, but on a Windows 2003 server production machine it fails with the following exception: Exception: System.Exception: CryptMsgUpdate error #-2146893816 --- System.ComponentModel.Win32Exception: Invalid algorithm specified --- End of inner exception stack trace --- at LargeCMS.CMS.Decode(FileStream inFile, FileStream outFile) Here are the classes below which I call to do the decoding, if needed I can upload a sample file for decoding, its just strange it works on Win 7, and not on Win2k3 server: using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.IO; using System.Security.Cryptography; using System.Security.Cryptography.X509Certificates; using System.Runtime.InteropServices; using System.ComponentModel; namespace LargeCMS { class CMS { // File stream to use in callback function private FileStream m_callbackFile; // Streaming callback function for encoding private Boolean StreamOutputCallback(IntPtr pvArg, IntPtr pbData, int cbData, Boolean fFinal) { // Write all bytes to encoded file Byte[] bytes = new Byte[cbData]; Marshal.Copy(pbData, bytes, 0, cbData); m_callbackFile.Write(bytes, 0, cbData); if (fFinal) { // This is the last piece. Close the file m_callbackFile.Flush(); m_callbackFile.Close(); m_callbackFile = null; } return true; } // Encode CMS with streaming to support large data public void Encode(X509Certificate2 cert, FileStream inFile, FileStream outFile) { // Variables Win32.CMSG_SIGNER_ENCODE_INFO SignerInfo; Win32.CMSG_SIGNED_ENCODE_INFO SignedInfo; Win32.CMSG_STREAM_INFO StreamInfo; Win32.CERT_CONTEXT[] CertContexts = null; Win32.BLOB[] CertBlobs; X509Chain chain = null; X509ChainElement[] chainElements = null; X509Certificate2[] certs = null; RSACryptoServiceProvider key = null; BinaryReader stream = null; GCHandle gchandle = new GCHandle(); IntPtr hProv = IntPtr.Zero; IntPtr SignerInfoPtr = IntPtr.Zero; IntPtr CertBlobsPtr = IntPtr.Zero; IntPtr hMsg = IntPtr.Zero; IntPtr pbPtr = IntPtr.Zero; Byte[] pbData; int dwFileSize; int dwRemaining; int dwSize; Boolean bResult = false; try { // Get data to encode dwFileSize = (int)inFile.Length; stream = new BinaryReader(inFile); pbData = stream.ReadBytes(dwFileSize); // Prepare stream for encoded info m_callbackFile = outFile; // Get cert chain chain = new X509Chain(); chain.Build(cert); chainElements = new X509ChainElement[chain.ChainElements.Count]; chain.ChainElements.CopyTo(chainElements, 0); // Get certs in chain certs = new X509Certificate2[chainElements.Length]; for (int i = 0; i < chainElements.Length; i++) { certs[i] = chainElements[i].Certificate; } // Get context of all certs in chain CertContexts = new Win32.CERT_CONTEXT[certs.Length]; for (int i = 0; i < certs.Length; i++) { CertContexts[i] = (Win32.CERT_CONTEXT)Marshal.PtrToStructure(certs[i].Handle, typeof(Win32.CERT_CONTEXT)); } // Get cert blob of all certs CertBlobs = new Win32.BLOB[CertContexts.Length]; for (int i = 0; i < CertContexts.Length; i++) { CertBlobs[i].cbData = CertContexts[i].cbCertEncoded; CertBlobs[i].pbData = CertContexts[i].pbCertEncoded; } // Get CSP of client certificate key = (RSACryptoServiceProvider)certs[0].PrivateKey; bResult = Win32.CryptAcquireContext( ref hProv, key.CspKeyContainerInfo.KeyContainerName, key.CspKeyContainerInfo.ProviderName, key.CspKeyContainerInfo.ProviderType, 0 ); if (!bResult) { throw new Exception("CryptAcquireContext error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Populate Signer Info struct SignerInfo = new Win32.CMSG_SIGNER_ENCODE_INFO(); SignerInfo.cbSize = Marshal.SizeOf(SignerInfo); SignerInfo.pCertInfo = CertContexts[0].pCertInfo; SignerInfo.hCryptProvOrhNCryptKey = hProv; SignerInfo.dwKeySpec = (int)key.CspKeyContainerInfo.KeyNumber; SignerInfo.HashAlgorithm.pszObjId = Win32.szOID_OIWSEC_sha1; // Populate Signed Info struct SignedInfo = new Win32.CMSG_SIGNED_ENCODE_INFO(); SignedInfo.cbSize = Marshal.SizeOf(SignedInfo); SignedInfo.cSigners = 1; SignerInfoPtr = Marshal.AllocHGlobal(Marshal.SizeOf(SignerInfo)); Marshal.StructureToPtr(SignerInfo, SignerInfoPtr, false); SignedInfo.rgSigners = SignerInfoPtr; SignedInfo.cCertEncoded = CertBlobs.Length; CertBlobsPtr = Marshal.AllocHGlobal(Marshal.SizeOf(CertBlobs[0]) * CertBlobs.Length); for (int i = 0; i < CertBlobs.Length; i++) { Marshal.StructureToPtr(CertBlobs[i], new IntPtr(CertBlobsPtr.ToInt64() + (Marshal.SizeOf(CertBlobs[i]) * i)), false); } SignedInfo.rgCertEncoded = CertBlobsPtr; // Populate Stream Info struct StreamInfo = new Win32.CMSG_STREAM_INFO(); StreamInfo.cbContent = dwFileSize; StreamInfo.pfnStreamOutput = new Win32.StreamOutputCallbackDelegate(StreamOutputCallback); // TODO: CMSG_DETACHED_FLAG // Open message to encode hMsg = Win32.CryptMsgOpenToEncode( Win32.X509_ASN_ENCODING | Win32.PKCS_7_ASN_ENCODING, 0, Win32.CMSG_SIGNED, ref SignedInfo, null, ref StreamInfo ); if (hMsg.Equals(IntPtr.Zero)) { throw new Exception("CryptMsgOpenToEncode error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Process the whole message gchandle = GCHandle.Alloc(pbData, GCHandleType.Pinned); pbPtr = gchandle.AddrOfPinnedObject(); dwRemaining = dwFileSize; dwSize = (dwFileSize < 1024 * 1000 * 100) ? dwFileSize : 1024 * 1000 * 100; while (dwRemaining > 0) { // Update message piece by piece bResult = Win32.CryptMsgUpdate( hMsg, pbPtr, dwSize, (dwRemaining <= dwSize) ? true : false ); if (!bResult) { throw new Exception("CryptMsgUpdate error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Move to the next piece pbPtr = new IntPtr(pbPtr.ToInt64() + dwSize); dwRemaining -= dwSize; if (dwRemaining < dwSize) { dwSize = dwRemaining; } } } finally { // Clean up if (gchandle.IsAllocated) { gchandle.Free(); } if (stream != null) { stream.Close(); } if (m_callbackFile != null) { m_callbackFile.Close(); } if (!CertBlobsPtr.Equals(IntPtr.Zero)) { Marshal.FreeHGlobal(CertBlobsPtr); } if (!SignerInfoPtr.Equals(IntPtr.Zero)) { Marshal.FreeHGlobal(SignerInfoPtr); } if (!hProv.Equals(IntPtr.Zero)) { Win32.CryptReleaseContext(hProv, 0); } if (!hMsg.Equals(IntPtr.Zero)) { Win32.CryptMsgClose(hMsg); } } } // Decode CMS with streaming to support large data public void Decode(FileStream inFile, FileStream outFile) { // Variables Win32.CMSG_STREAM_INFO StreamInfo; Win32.CERT_CONTEXT SignerCertContext; BinaryReader stream = null; GCHandle gchandle = new GCHandle(); IntPtr hMsg = IntPtr.Zero; IntPtr pSignerCertInfo = IntPtr.Zero; IntPtr pSignerCertContext = IntPtr.Zero; IntPtr pbPtr = IntPtr.Zero; IntPtr hStore = IntPtr.Zero; Byte[] pbData; Boolean bResult = false; int dwFileSize; int dwRemaining; int dwSize; int cbSignerCertInfo; try { // Get data to decode dwFileSize = (int)inFile.Length; stream = new BinaryReader(inFile); pbData = stream.ReadBytes(dwFileSize); // Prepare stream for decoded info m_callbackFile = outFile; // Populate Stream Info struct StreamInfo = new Win32.CMSG_STREAM_INFO(); StreamInfo.cbContent = dwFileSize; StreamInfo.pfnStreamOutput = new Win32.StreamOutputCallbackDelegate(StreamOutputCallback); // Open message to decode hMsg = Win32.CryptMsgOpenToDecode( Win32.X509_ASN_ENCODING | Win32.PKCS_7_ASN_ENCODING, 0, 0, IntPtr.Zero, IntPtr.Zero, ref StreamInfo ); if (hMsg.Equals(IntPtr.Zero)) { throw new Exception("CryptMsgOpenToDecode error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Process the whole message gchandle = GCHandle.Alloc(pbData, GCHandleType.Pinned); pbPtr = gchandle.AddrOfPinnedObject(); dwRemaining = dwFileSize; dwSize = (dwFileSize < 1024 * 1000 * 100) ? dwFileSize : 1024 * 1000 * 100; while (dwRemaining > 0) { // Update message piece by piece bResult = Win32.CryptMsgUpdate( hMsg, pbPtr, dwSize, (dwRemaining <= dwSize) ? true : false ); if (!bResult) { throw new Exception("CryptMsgUpdate error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Move to the next piece pbPtr = new IntPtr(pbPtr.ToInt64() + dwSize); dwRemaining -= dwSize; if (dwRemaining < dwSize) { dwSize = dwRemaining; } } // Get signer certificate info cbSignerCertInfo = 0; bResult = Win32.CryptMsgGetParam( hMsg, Win32.CMSG_SIGNER_CERT_INFO_PARAM, 0, IntPtr.Zero, ref cbSignerCertInfo ); if (!bResult) { throw new Exception("CryptMsgGetParam error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } pSignerCertInfo = Marshal.AllocHGlobal(cbSignerCertInfo); bResult = Win32.CryptMsgGetParam( hMsg, Win32.CMSG_SIGNER_CERT_INFO_PARAM, 0, pSignerCertInfo, ref cbSignerCertInfo ); if (!bResult) { throw new Exception("CryptMsgGetParam error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Open a cert store in memory with the certs from the message hStore = Win32.CertOpenStore( Win32.CERT_STORE_PROV_MSG, Win32.X509_ASN_ENCODING | Win32.PKCS_7_ASN_ENCODING, IntPtr.Zero, 0, hMsg ); if (hStore.Equals(IntPtr.Zero)) { throw new Exception("CertOpenStore error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Find the signer's cert in the store pSignerCertContext = Win32.CertGetSubjectCertificateFromStore( hStore, Win32.X509_ASN_ENCODING | Win32.PKCS_7_ASN_ENCODING, pSignerCertInfo ); if (pSignerCertContext.Equals(IntPtr.Zero)) { throw new Exception("CertGetSubjectCertificateFromStore error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } // Set message for verifying SignerCertContext = (Win32.CERT_CONTEXT)Marshal.PtrToStructure(pSignerCertContext, typeof(Win32.CERT_CONTEXT)); bResult = Win32.CryptMsgControl( hMsg, 0, Win32.CMSG_CTRL_VERIFY_SIGNATURE, SignerCertContext.pCertInfo ); if (!bResult) { throw new Exception("CryptMsgControl error #" + Marshal.GetLastWin32Error().ToString(), new Win32Exception(Marshal.GetLastWin32Error())); } } finally { // Clean up if (gchandle.IsAllocated) { gchandle.Free(); } if (!pSignerCertContext.Equals(IntPtr.Zero)) { Win32.CertFreeCertificateContext(pSignerCertContext); } if (!pSignerCertInfo.Equals(IntPtr.Zero)) { Marshal.FreeHGlobal(pSignerCertInfo); } if (!hStore.Equals(IntPtr.Zero)) { Win32.CertCloseStore(hStore, Win32.CERT_CLOSE_STORE_FORCE_FLAG); } if (stream != null) { stream.Close(); } if (m_callbackFile != null) { m_callbackFile.Close(); } if (!hMsg.Equals(IntPtr.Zero)) { Win32.CryptMsgClose(hMsg); } } } } } and using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Runtime.InteropServices; using System.Security.Cryptography.X509Certificates; using System.ComponentModel; using System.Security.Cryptography; namespace LargeCMS { class Win32 { #region "CONSTS" public const int X509_ASN_ENCODING = 0x00000001; public const int PKCS_7_ASN_ENCODING = 0x00010000; public const int CMSG_SIGNED = 2; public const int CMSG_DETACHED_FLAG = 0x00000004; public const int AT_KEYEXCHANGE = 1; public const int AT_SIGNATURE = 2; public const String szOID_OIWSEC_sha1 = "1.3.14.3.2.26"; public const int CMSG_CTRL_VERIFY_SIGNATURE = 1; public const int CMSG_CERT_PARAM = 12; public const int CMSG_SIGNER_CERT_INFO_PARAM = 7; public const int CERT_STORE_PROV_MSG = 1; public const int CERT_CLOSE_STORE_FORCE_FLAG = 1; #endregion #region "STRUCTS" [StructLayout(LayoutKind.Sequential)] public struct CRYPT_ALGORITHM_IDENTIFIER { public String pszObjId; BLOB Parameters; } [StructLayout(LayoutKind.Sequential)] public struct CERT_ID { public int dwIdChoice; public BLOB IssuerSerialNumberOrKeyIdOrHashId; } [StructLayout(LayoutKind.Sequential)] public struct CMSG_SIGNER_ENCODE_INFO { public int cbSize; public IntPtr pCertInfo; public IntPtr hCryptProvOrhNCryptKey; public int dwKeySpec; public CRYPT_ALGORITHM_IDENTIFIER HashAlgorithm; public IntPtr pvHashAuxInfo; public int cAuthAttr; public IntPtr rgAuthAttr; public int cUnauthAttr; public IntPtr rgUnauthAttr; public CERT_ID SignerId; public CRYPT_ALGORITHM_IDENTIFIER HashEncryptionAlgorithm; public IntPtr pvHashEncryptionAuxInfo; } [StructLayout(LayoutKind.Sequential)] public struct CERT_CONTEXT { public int dwCertEncodingType; public IntPtr pbCertEncoded; public int cbCertEncoded; public IntPtr pCertInfo; public IntPtr hCertStore; } [StructLayout(LayoutKind.Sequential)] public struct BLOB { public int cbData; public IntPtr pbData; } [StructLayout(LayoutKind.Sequential)] public struct CMSG_SIGNED_ENCODE_INFO { public int cbSize; public int cSigners; public IntPtr rgSigners; public int cCertEncoded; public IntPtr rgCertEncoded; public int cCrlEncoded; public IntPtr rgCrlEncoded; public int cAttrCertEncoded; public IntPtr rgAttrCertEncoded; } [StructLayout(LayoutKind.Sequential)] public struct CMSG_STREAM_INFO { public int cbContent; public StreamOutputCallbackDelegate pfnStreamOutput; public IntPtr pvArg; } #endregion #region "DELEGATES" public delegate Boolean StreamOutputCallbackDelegate(IntPtr pvArg, IntPtr pbData, int cbData, Boolean fFinal); #endregion #region "API" [DllImport("advapi32.dll", CharSet = CharSet.Auto, SetLastError = true)] public static extern Boolean CryptAcquireContext( ref IntPtr hProv, String pszContainer, String pszProvider, int dwProvType, int dwFlags ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern IntPtr CryptMsgOpenToEncode( int dwMsgEncodingType, int dwFlags, int dwMsgType, ref CMSG_SIGNED_ENCODE_INFO pvMsgEncodeInfo, String pszInnerContentObjID, ref CMSG_STREAM_INFO pStreamInfo ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern IntPtr CryptMsgOpenToDecode( int dwMsgEncodingType, int dwFlags, int dwMsgType, IntPtr hCryptProv, IntPtr pRecipientInfo, ref CMSG_STREAM_INFO pStreamInfo ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern Boolean CryptMsgClose( IntPtr hCryptMsg ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern Boolean CryptMsgUpdate( IntPtr hCryptMsg, Byte[] pbData, int cbData, Boolean fFinal ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern Boolean CryptMsgUpdate( IntPtr hCryptMsg, IntPtr pbData, int cbData, Boolean fFinal ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern Boolean CryptMsgGetParam( IntPtr hCryptMsg, int dwParamType, int dwIndex, IntPtr pvData, ref int pcbData ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern Boolean CryptMsgControl( IntPtr hCryptMsg, int dwFlags, int dwCtrlType, IntPtr pvCtrlPara ); [DllImport("advapi32.dll", SetLastError = true)] public static extern Boolean CryptReleaseContext( IntPtr hProv, int dwFlags ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern IntPtr CertCreateCertificateContext( int dwCertEncodingType, IntPtr pbCertEncoded, int cbCertEncoded ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern Boolean CertFreeCertificateContext( IntPtr pCertContext ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern IntPtr CertOpenStore( int lpszStoreProvider, int dwMsgAndCertEncodingType, IntPtr hCryptProv, int dwFlags, IntPtr pvPara ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern IntPtr CertGetSubjectCertificateFromStore( IntPtr hCertStore, int dwCertEncodingType, IntPtr pCertId ); [DllImport("Crypt32.dll", SetLastError = true)] public static extern IntPtr CertCloseStore( IntPtr hCertStore, int dwFlags ); #endregion } }

  Read the article

• How to optimize dynamic programming?

  - by Chan

  Problem A number is called lucky if the sum of its digits, as well as the sum of the squares of its digits is a prime number. How many numbers between A and B are lucky? Input: The first line contains the number of test cases T. Each of the next T lines contains two integers, A and B. Output: Output T lines, one for each case containing the required answer for the corresponding case. Constraints: 1 <= T <= 10000 1 <= A <= B <= 10^18 Sample Input: 2 1 20 120 130 Sample Output: 4 1 Explanation: For the first case, the lucky numbers are 11, 12, 14, 16. For the second case, the only lucky number is 120. The problem is quite simple if we use brute force, however the running time is so critical that my program failed most test cases. My current idea is to use dynamic programming by storing the previous sum in a temporary array, so for example: sum_digits(10) = 1 -> sum_digits(11) = sum_digits(10) + 1 The same idea is applied for sum square but with counter equals to odd numbers. Unfortunately, it still failed 9 of 10 test cases which makes me think there must be a better way to solve it. Any idea would be greatly appreciated. #include <iostream> #include <vector> #include <string> #include <algorithm> #include <unordered_map> #include <unordered_set> #include <cmath> #include <cassert> #include <bitset> using namespace std; bool prime_table[1540] = { 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 }; unsigned num_digits(long long i) { return i > 0 ? (long) log10 ((double) i) + 1 : 1; } void get_sum_and_sum_square_digits(long long n, int& sum, int& sum_square) { sum = 0; sum_square = 0; int digit; while (n) { digit = n % 10; sum += digit; sum_square += digit * digit; n /= 10; } } void init_digits(long long n, long long previous_sum[], const int size = 18) { int current_no_digits = num_digits(n); int digit; for (int i = 0; i < current_no_digits; ++i) { digit = n % 10; previous_sum[i] = digit; n /= 10; } for (int i = current_no_digits; i <= size; ++i) { previous_sum[i] = 0; } } void display_previous(long long previous[]) { for (int i = 0; i < 18; ++i) { cout << previous[i] << ","; } } int count_lucky_number(long long A, long long B) { long long n = A; long long end = B; int sum = 0; int sum_square = 0; int lucky_counter = 0; get_sum_and_sum_square_digits(n, sum, sum_square); long long sum_counter = sum; long long sum_square_counter = sum_square; if (prime_table[sum_counter] && prime_table[sum_square_counter]) { lucky_counter++; } long long previous_sum[19] = {1}; init_digits(n, previous_sum); while (n < end) { n++; if (n % 100000000000000000 == 0) { previous_sum[17]++; sum_counter = previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[16] = 0; previous_sum[15] = 0; previous_sum[14] = 0; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000000000000 == 0) { previous_sum[16]++; sum_counter = previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[15] = 0; previous_sum[14] = 0; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000000000000 == 0) { previous_sum[15]++; sum_counter = previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[14] = 0; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000000000000 == 0) { previous_sum[14]++; sum_counter = previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[13] = 0; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000000000 == 0) { previous_sum[13]++; sum_counter = previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[12] = 0; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000000000 == 0) { previous_sum[12]++; sum_counter = previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[11] = 0; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000000000 == 0) { previous_sum[11]++; sum_counter = previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[10] = 0; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000000 == 0) { previous_sum[10]++; sum_counter = previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[9] = 0; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000000 == 0) { previous_sum[9]++; sum_counter = previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[8] = 0; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000000 == 0) { previous_sum[8]++; sum_counter = previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[7] = 0; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000000 == 0) { previous_sum[7]++; sum_counter = previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[6] = 0; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000000 == 0) { previous_sum[6]++; sum_counter = previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[5] = 0; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100000 == 0) { previous_sum[5]++; sum_counter = previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[4] = 0; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10000 == 0) { previous_sum[4]++; sum_counter = previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[3] = 0; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 1000 == 0) { previous_sum[3]++; sum_counter = previous_sum[3] + previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[3] * previous_sum[3] + previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[2] = 0; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 100 == 0) { previous_sum[2]++; sum_counter = previous_sum[2] + previous_sum[3] + previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[2] * previous_sum[2] + previous_sum[3] * previous_sum[3] + previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[1] = 0; previous_sum[0] = 0; } else if (n % 10 == 0) { previous_sum[1]++; sum_counter = previous_sum[1] + previous_sum[2] + previous_sum[3] + previous_sum[4] + previous_sum[5] + previous_sum[6] + previous_sum[7] + previous_sum[8] + previous_sum[9] + previous_sum[10] + previous_sum[11] + previous_sum[12] + previous_sum[13] + previous_sum[14] + previous_sum[15] + previous_sum[16] + previous_sum[17] + previous_sum[18]; sum_square_counter = previous_sum[1] * previous_sum[1] + previous_sum[2] * previous_sum[2] + previous_sum[3] * previous_sum[3] + previous_sum[4] * previous_sum[4] + previous_sum[5] * previous_sum[5] + previous_sum[6] * previous_sum[6] + previous_sum[7] * previous_sum[7] + previous_sum[8] * previous_sum[8] + previous_sum[9] * previous_sum[9] + previous_sum[10] * previous_sum[10] + previous_sum[11] * previous_sum[11] + previous_sum[12] * previous_sum[12] + previous_sum[13] * previous_sum[13] + previous_sum[14] * previous_sum[14] + previous_sum[15] * previous_sum[15] + previous_sum[16] * previous_sum[16] + previous_sum[17] * previous_sum[17] + previous_sum[18] * previous_sum[18]; previous_sum[0] = 0; } else { sum_counter++; sum_square_counter += ((n - 1) % 10) * 2 + 1; } // get_sum_and_sum_square_digits(n, sum, sum_square); // assert(sum == sum_counter && sum_square == sum_square_counter); if (prime_table[sum_counter] && prime_table[sum_square_counter]) { lucky_counter++; } } return lucky_counter; } void inout_lucky_numbers() { int n; cin >> n; long long a; long long b; while (n--) { cin >> a >> b; cout << count_lucky_number(a, b) << endl; } } int main() { inout_lucky_numbers(); return 0; }

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• Find kth smallest element in a binary search tree in Optimum way

  - by Bragaadeesh

  Hi, I need to find the kth smallest element in the binary search tree without using any static/global variable. How to achieve it efficiently? The solution that I have in my mind is doing the operation in O(n), the worst case since I am planning to do an inorder traversal of the entire tree. But deep down I feel that I am not using the BST property here. Is my assumptive solution correct or is there a better one available ?

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• Write a function that compares two strings and returns a third string containing only the letters th

  - by Pritam

  Hi All, I got this homework. And have solved it in following way. I need your comments whether it is a good approach or I need to use any other data sturcture to solve it in better way. public string ReturnCommon(string firstString, string scndString) { StringBuilder newStb = new StringBuilder(); if (firstString != null && scndString != null) { foreach (char ichar in firstString) { if (!newStb.ToString().Contains(ichar) && scndString.Contains(ichar)) newStb.Append(ichar); } } return newStb.ToString(); }

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• Point in polygon OR point on polygon using LINQ

  - by wageoghe

  As noted in an earlier question, How to Zip enumerable with itself, I am working on some math algorithms based on lists of points. I am currently working on point in polygon. I have the code for how to do that and have found several good references here on SO, such as this link Hit test. So, I can figure out whether or not a point is in a polygon. As part of determining that, I want to determine if the point is actually on the polygon. This I can also do. If I can do all of that, what is my question you might ask? Can I do it efficiently using LINQ? I can already do something like the following (assuming a Pairwise extension method as described in my earlier question as well as in links to which my question/answers links, and assuming a Position type that has X and Y members). I have not tested much, so the lambda might not be 100% correct. Also, it does not take very small differences into account. public static PointInPolygonLocation PointInPolygon(IEnumerable<Position> pts, Position pt) { int numIntersections = pts.Pairwise( (p1, p2) => { if (p1.Y != p2.Y) { if ((p1.Y >= pt.Y && p2.Y < pt.Y) || (p1.Y < pt.Y && p2.Y >= pt.Y)) { if (p1.X < p1.X && p2.X < pt.X) { return 1; } if (p1.X < pt.X || p2.X < pt.X) { if (((pt.Y - p1.Y) * ((p1.X - p2.X) / (p1.Y - p2.Y)) * p1.X) < pt.X) { return 1; } } } } return 0; }).Sum(); if (numIntersections % 2 == 0) { return PointInPolygonLocation.Outside; } else { return PointInPolygonLocation.Inside; } } This function, PointInPolygon, takes the input Position, pt, iterates over the input sequence of position values, and uses the Jordan Curve method to determine how many times a ray extended from pt to the left intersects the polygon. The lambda expression will yield, into the "zipped" list, 1 for every segment that is crossed, and 0 for the rest. The sum of these values determines if pt is inside or outside of the polygon (odd == inside, even == outside). So far, so good. Now, for any consecutive pairs of position values in the sequence (i.e. in any execution of the lambda), we can also determine if pt is ON the segment p1, p2. If that is the case, we can stop the calculation because we have our answer. Ultimately, my question is this: Can I perform this calculation (maybe using Aggregate?) such that we will only iterate over the sequence no more than 1 time AND can we stop the iteration if we encounter a segment that pt is ON? In other words, if pt is ON the very first segment, there is no need to examine the rest of the segments because we have the answer. It might very well be that this operation (particularly the requirement/desire to possibly stop the iteration early) does not really lend itself well to the LINQ approach. It just occurred to me that maybe the lambda expression could yield a tuple, the intersection value (1 or 0 or maybe true or false) and the "on" value (true or false). Maybe then I could use TakeWhile(anontype.PointOnPolygon == false). If I Sum the tuples and if ON == 1, then the point is ON the polygon. Otherwise, the oddness or evenness of the sum of the other part of the tuple tells if the point is inside or outside.

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• Best practice to calculate the average speed from GPS coordinates

  - by Sebi

  i have here a device which can give me gps coordinates. the time intervall i can define. i want to use it to calculate the average speed during driving or travelling by car. actually i used a orthodrome formula to calculate the distance between two points and then divided it by the given time intervall. by the implemenation i followed this term (http://de.wikipedia.org/wiki/Orthodrome#Genauere_Formel_zur_Abstandsberechnung_auf_der_Erde). Unfortunately i could only find a german link, but i think the formula should be understandable in any language ;) Unfortunately, using this formula and a time intverall of 1 seconds gives very unprecises results. the speed while walking is between 1 km/h and 20km/h. So i wonder if there is a general reference how to implement distance calculation between two gps coordinates (i found something similar on SO) and particulary, which is the best time intervall to update the GPS coordiantes.

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• How do I detect overflow while multiplying two 2's complement integers?

  - by eSKay

  I want to multiply two numbers, and detect if there was an overflow. What is the simplest way to do that?

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• Dynamic programming - Coin change decision problem?

  - by Tony

  I'm reviewing some old notes from my algorithms course and the dynamic programming problems are seeming a bit tricky to me. I have a problem where we have an unlimited supply of coins, with some denominations x1, x2, ... xn and we want to make change for some value X. We are trying to design a dynamic program to decide whether change for X can be made or not (not minimizing the number of coins, or returning which coins, just true or false). I've done some thinking about this problem, and I can see a recursive method of doing this where it's something like... MakeChange(X, x[1..n this is the coins]) for (int i = 1; i < n; i++) { if ( (X - x[i] ==0) || MakeChange(X - x[i]) ) return true; } return false; Converting this a dynamic program is not coming so easily to me. How might I approach this?

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• Finding anagaram(s) of dictionary words

  - by Codenotguru

  How can I take an input word (or sequence of letters) and output a word from a dictionary that contains exactly those letters? Does java has an English dictionary class (list of words) that I can use, or are there open source implementations of this? How can I optimize my code if this needs to be done repeatedly?

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• Find the "largest" dense sub matrix in a large sparse matrix

  - by BCS

  Given a large sparse matrix (say 10k+ by 1M+) I need to find a subset, not necessarily continuous, of the rows and columns that form a dense matrix (all non-zero elements). I want this sub matrix to be as large as possible (not the largest sum, but the largest number of elements) within some aspect ratio constraints. Are there any known exact or aproxamate solutions to this problem? A quick scan on Google seems to give a lot of close-but-not-exactly results. What terms should I be looking for? edit: Just to clarify; the sub matrix need not be continuous. In fact the row and column order is completely arbitrary so adjacency is completely irrelevant. A thought based on Chad Okere's idea Order the rows from largest count to smallest count (not necessary but might help perf) Select two rows that have a "large" overlap Add all other rows that won't reduce the overlap Record that set Add whatever row reduces the overlap by the least Repeat at #3 until the result gets to small Start over at #2 with a different starting pair Continue until you decide the result is good enough

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• How to Zip one IEnumerable with itself

  - by wageoghe

  I am implementing some math algorithms based on lists of points, like Distance, Area, Centroid, etc. Just like in this post: http://stackoverflow.com/questions/2227828/find-the-distance-required-to-navigate-a-list-of-points-using-linq That post describes how to calculate the total distance of a sequence of points (taken in order) by essentially zipping the sequence "with itself", generating the sequence for Zip by offsetting the start position of the original IEnumerable by 1. So, given the Zip extension in .Net 4.0, assuming Point for the point type, and a reasonable Distance formula, you can make calls like this to generate a sequence of distances from one point to the next and then to sum the distances: var distances = points.Zip(points.Skip(1),Distance); double totalDistance = distances.Sum(); Area and Centroid calculations are similar in that they need to iterate over the sequence, processing each pair of points (points[i] and points[i+1]). I thought of making a generic IEnumerable extension suitable for implementing these (and possibly other) algorithms that operate over sequences, taking two items at a time (points[0] and points[1], points[1] and points[2], ..., points[n-1] and points[n] (or is it n-2 and n-1 ...) and applying a function. My generic iterator would have a similar signature to Zip, but it would not receive a second sequence to zip with as it is really just going to zip with itself. My first try looks like this: public static IEnumerable<TResult> ZipMyself<TSequence, TResult>(this IEnumerable<TSequence> seq, Func<TSequence, TSequence, TResult> resultSelector) { return seq.Zip(seq.Skip(1),resultSelector); } With my generic iterator in place, I can write functions like this: public static double Length(this IEnumerable<Point> points) { return points.ZipMyself(Distance).Sum(); } and call it like this: double d = points.Length(); and double GreensTheorem(Point p1, Point p1) { return p1.X * p2.Y - p1.Y * p2.X; } public static double SignedArea(this IEnumerable<Point> points) { return points.ZipMyself(GreensTheorem).Sum() / 2.0 } public static double Area(this IEnumerable<Point> points) { return Math.Abs(points.SignedArea()); } public static bool IsClockwise(this IEnumerable<Point> points) { return SignedArea(points) < 0; } and call them like this: double a = points.Area(); bool isClockwise = points.IsClockwise(); In this case, is there any reason NOT to implement "ZipMyself" in terms of Zip and Skip(1)? Is there already something in LINQ that automates this (zipping a list with itself) - not that it needs to be made that much easier ;-) Also, is there better name for the extension that might reflect that it is a well-known pattern (if, indeed it is a well-known pattern)? Had a link here for a StackOverflow question about area calculation. It is question 2432428. Also had a link to Wikipedia article on Centroid. Just go to Wikipedia and search for Centroid if interested. Just starting out, so don't have enough rep to post more than one link,

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• Looking for more details about "Group varint encoding/decoding" presented in Jeff's slides

  - by Mickey Shine

  I noticed that in Jeff's slides "Challenges in Building Large-Scale Information Retrieval Systems", which can also be downloaded here: http://research.google.com/people/jeff/WSDM09-keynote.pdf, a method of integers compression called "group varint encoding" was mentioned. It was said much faster than 7 bits per byte integer encoding (2X more). I am very interested in this and looking for an implementation of this, or any more details that could help me implement this by myself. I am not a pro and new to this, and any help is welcome!

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• Find largest rectangle containing all zero's in an N X N binary matrix

  - by Rajendra

  Given an N X N binary matrix (containing only 0's or 1's). How can we go about finding largest rectangle containing all 0's? Example: I 0 0 0 0 1 0 0 0 1 0 0 1 II->0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 <--IV 0 0 1 0 0 0 IV is a 6 X 6 binary matrix, return value in this case will be Cell 1: (2, 1) and Cell 2: (4, 4). Resulting sub-matrix can be square or rectangle. Return value can be size of the largest sub-matrix of all 0's also, for example, here 3 X 4.

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• commands&creating pointer [closed]

  - by gcc

  input 23 3 4 4 42 n 23 0 9 9 n n n 3 9 9 x //according to input,i should create int pointer arrays. pointer arrays // starting from 1 (that is initial arrays is arrays[1].when program sees n ,it // must be jumb to arrays 2 // the first int input 23 is num_arrays which used in malloc(sizeof(int)*num_arrays expected output: elements of arrays[1] 3 4 5 42 elements of arrays[2] 23 0 9 9 elements of arrays[5] 3 9 9 another input 12 2 3 4 n n 2 3 4 n 12 3 x expected output elements of arrays[1] 2 3 4 elements of arrays[3] 2 3 4 elements of arrays[4] 12 3 specification: x is stopper n is comman to create new pointer array i am new in this site anyone help me how can i write

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• How is counting sort a stable sort?

  - by eSKay

  Suppose my input is (a,b and c to distinguish between equal keys) 1 6a 8 3 6b 0 6c 4 My counting sort will save as (discarding the a,b and c info!!) 0(1) 1(1) 3(1) 4(1) 6(3) 8(1) which will give me the result 0 1 3 4 6 6 6 8 So, how is this stable sort? I am not sure how it is "maintaining the relative order of records with equal keys." Please explain.

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• Sha or Md5 algorithm i need to encrypt and decrypt in flex

  - by praveen

  Hi I am developing my application in flex and JSP, so when I am passing values through HTTP Service Post method with request object but these values are tracing and modifying by testing team so I am planning to encrypt values in flex and decrypt it in jsp.so is there any algorithms like SHA or MD5 more secure algorithms, so please send any code or related links it is very useful to me. I am using like httpService = new HTTPService; httpService.request = new Object; httpService.request.task = "doInvite"; httpService.request.email = emailInput.text; httpService.request.firstName = firstNameInput.text; httpService.request.lastName = lastNameInput.text; httpService.send(); So is there any other way to give more secure ,please help me in this,Thanks in Advance.

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• C# average function for large numbers without overflow exception

  - by Ron Klein

  .NET Framework 3.5. I'm trying to calculate the average of some pretty large numbers. For instance: using System; using System.Linq; class Program { static void Main(string[] args) { var items = new long[] { long.MaxValue - 100, long.MaxValue - 200, long.MaxValue - 300 }; try { var avg = items.Average(); Console.WriteLine(avg); } catch (OverflowException ex) { Console.WriteLine("can't calculate that!"); } Console.ReadLine(); } } Obviously, the mathematical result is 9223372036854775607 (long.MaxValue - 200), but I get an exception there. This is because the implementation (on my machine) to the Average extension method, as inspected by .NET Reflector is: public static double Average(this IEnumerable<long> source) { if (source == null) { throw Error.ArgumentNull("source"); } long num = 0L; long num2 = 0L; foreach (long num3 in source) { num += num3; num2 += 1L; } if (num2 <= 0L) { throw Error.NoElements(); } return (((double) num) / ((double) num2)); } I know I can use a BigInt library (yes, I know that it is included in .NET Framework 4.0, but I'm tied to 3.5). But I still wonder if there's a pretty straight forward implementation of calculating the average of integers without an external library. Do you happen to know about such implementation? Thanks!!

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• n & x commands&creating pointer&with using malloc [closed]

  - by gcc

  input 23 3 4 4 42 n 23 0 9 9 n n n 3 9 9 x //according to input,i should create int pointer arrays. pointer arrays // starting from 1 (that is initial arrays is arrays[1].when program sees n ,it // must be jumb to arrays 2 // the first int input 23 is num_arrays which used in malloc(sizeof(int)*num_arrays expected output arrays[1] 3 4 5 42 arrays[2] 23 0 9 9 arrays[5] 3 9 9 another input 12 2 3 4 n n 2 3 4 n 12 3 x expected output arrays[1] 2 3 4 arrays[3] 2 3 4 arrays[4] 12 3 x is stopper n is comman to create new pointer array i am new in this site anyone help me how can i write

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• C# rounding DateTime objects

  - by grenade

  I want to round dates/times to the nearest interval for a charting application. I'd like an extension method signature like follows so that the rounding can be acheived for any level of accuracy: static DateTime Round(this DateTime date, TimeSpan span); The idea is that if I pass in a timespan of ten minutes, it will round to the nearest ten minute interval. I can't get my head around the implementation and am hoping one of you will have written or used something similar before. I think either a floor, ceiling or nearest implementation is fine. Any ideas? Edit: Thanks to @tvanfosson & @ShuggyCoUk, the implementation looks like this: public static class DateExtensions { public static DateTime Round(this DateTime date, TimeSpan span) { long ticks = (date.Ticks / span.Ticks) + (span.Ticks / 2) + 1; return new DateTime(ticks * span.Ticks); } public static DateTime Floor(this DateTime date, TimeSpan span) { long ticks = (date.Ticks / span.Ticks); return new DateTime(ticks * span.Ticks); } public static DateTime Ceil(this DateTime date, TimeSpan span) { long ticks = (date.Ticks + span.Ticks - 1) / span.Ticks; return new DateTime(ticks * span.Ticks); } } And is called like so: DateTime nearestHour = DateTime.Now.Round(new TimeSpan(1,0,0)); DateTime minuteCeiling = DateTime.Now.Ceil(new TimeSpan(0,1,0)); DateTime weekFloor = DateTime.Now.Floor(new TimeSpan(7,0,0,0)); ... Cheers!

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• reopen or read and say why not reopened [closed]

  - by gcc

  input 23 3 4 4 42 n 23 0 9 9 n n n 3 9 9 x //according to input,i should create int pointer arrays. pointer arrays // starting from 1 (that is initial arrays is arrays[1].when program sees n ,it // must be jumb to arrays 2 // the first int input 23 is num_arrays which used in malloc(sizeof(int)*num_arrays expected output: elements of arrays[1] 3 4 5 42 elements of arrays[2] 23 0 9 9 elements of arrays[5] 3 9 9 another input 12 2 3 4 n n 2 3 4 n 12 3 x expected output elements of arrays[1] 2 3 4 elements of arrays[3] 2 3 4 elements of arrays[4] 12 3 specification: x is stopper n is comman to create new pointer array i am new in this site anyone help me how can i write

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