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• Regulating how much to draw based on how much was drawn last frame.

  - by Mike Howard

  I have a 3D game world on an iPhone (limited graphics speed), and I'm already regulating whether I draw each shape on the screen based on it's size and distance from the camera. Something like... if (how_big_it_looks_from_the_camera > constant) then draw What I want to do now is also take into account how many shapes are being drawn, so that in busier areas of the game world I can draw less than I otherwise would. I tried to do this by dividing how_big_it_looks by the number of shapes that were drawn last frame (well, the square root of this but I'm simplifying - the problem is the same). if (how_big_it_looks / shapes_drawn > constant2) then draw But the check happens at the level of objects which represent many drawn shapes, and if an object containing many shapes is switched on, it increases shapes_drawn lots and switches itself back off the next frame. It flickers on and off. I tried keeping a kind of weighted average of previous values, by each frame doing something like shapes_drawn_recently = 0.9 * shapes_drawn_recently + 0.1 * shapes_just_drawn, but of course it only slows the flickering down because of the nature of the feedback loop. Is there a good way of solving this? My project is in Objective-C, but a general algorithm or pseudo-code is good too. Thanks.

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• Algorithm to reduce calls to mapping API

  - by aidan

  A random distribution of points lies on a map. This data lies behind an API, and I want to grab the complete set of points within a given bounding box. I can query the API with the bounding box and the API will return the set of points that fall within that box. The problem is that the API will limit the result set to 10 items, with no pagination and no indication if there are more points that have been omitted. So I made a recursive algorithm that takes a bounding box and requests the points that lie within it. If the result set is exactly 10 items, then I split the bounding box into four quadrants and recurse. It works fine but my question is this: if want to minimize the number of API calls, what is the optimal way to split the bounding box? Splitting it into quadrants was just an arbitrary decision. When there are a lot of points on the map, I have to drill down many levels before I start getting meaningful results. So I imagine it might be faster to split the box into, say, 9, 16, or more sections. But if I do that, then I eventually get to a point where a lot of requests are returning 0 results which isn't so efficient. Also, does the size of the limit on the results set affect the answer? (This is all assuming that I have no prior knowledge of nominal point density in the bounding box)

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• XNA: How to make the Vaus Spacecraft move left and right on directional keys pressed?

  - by Will Marcouiller

  I'm currently learning XNA per suggestion from this question's accepted answer: Where to start writing games, any tutorials or the like? I have then installed everything to get ready to work with XNA Game Studio 4.0. General Objective Writing an Arkanoid-like game. I want to make my ship move when I press either left or right keys. Code Sample protected override void Update(GameTime gameTime) { // Allows the game to exit if (GamePad.GetState(PlayerIndex.One).Buttons.Back == ButtonState.Pressed) this.Exit(); // TODO: Add your update logic here #if WINDOWS if (Keyboard.GetState().IsKeyDown(Keys.Escape)) this.Exit(); else { if (Keyboard.GetState().IsKeyDown(Keys.Left)) MoveLeft(gameTime); } #endif // Move the sprite around. BounceEnergyBall(gameTime); base.Update(gameTime); } void MoveLeft(GameTime gameTime) { // I'm not sure how to play with the Vector2 object and its position here!... _vausSpacecraftPos /= _vausSpacecraftSpeed.X; // This line makes the spacecraft move diagnol-top-left. } Question What formula shall I use, or what algorithm shall I consider to make my spaceship move as expected left and right properly? Thanks for your thoughts! Any clue will be appreciated. I am on my learning curve though I have years of development behind me (already)!

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• Optimized algorithm for line-sphere intersection in GLSL

  - by fernacolo

  Well, hello then! I need to find intersection between line and sphere in GLSL. Right now my solution is based on Paul Bourke's page and was ported to GLSL this way: // The line passes through p1 and p2: vec3 p1 = (...); vec3 p2 = (...); // Sphere center is p3, radius is r: vec3 p3 = (...); float r = ...; float x1 = p1.x; float y1 = p1.y; float z1 = p1.z; float x2 = p2.x; float y2 = p2.y; float z2 = p2.z; float x3 = p3.x; float y3 = p3.y; float z3 = p3.z; float dx = x2 - x1; float dy = y2 - y1; float dz = z2 - z1; float a = dx*dx + dy*dy + dz*dz; float b = 2.0 * (dx * (x1 - x3) + dy * (y1 - y3) + dz * (z1 - z3)); float c = x3*x3 + y3*y3 + z3*z3 + x1*x1 + y1*y1 + z1*z1 - 2.0 * (x3*x1 + y3*y1 + z3*z1) - r*r; float test = b*b - 4.0*a*c; if (test >= 0.0) { // Hit (according to Treebeard, "a fine hit"). float u = (-b - sqrt(test)) / (2.0 * a); vec3 hitp = p1 + u * (p2 - p1); // Now use hitp. } It works perfectly! But it seems slow... I'm new at GLSL. You can answer this questions in two ways: Tell me there is no solution, showing some proof or strong evidence. Tell me about GLSL features (vector APIs, primitive operations) that makes the above algorithm faster, showing some example. Thanks a lot!

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• questions on a particular algorithm

  - by paul smith

  Upon searching for a fast primr algorithm, I stumbled upon this: public static boolean isP(long n) { if (n==2 || n==3) return true; if ((n&0x1)==0 || n%3==0 || n<2) return false; long root=(long)Math.sqrt(n)+1L; // we check just numbers of the form 6*k+1 and 6*k-1 for (long k=6;k<=root;k+=6) { if (n%(k-1)==0) return false; if (n%(k+1)==0) return false; } return true; } My questions are: Why is long being used everywhere instead of int? Because with a long type the argument could be much larger than Integer.MAX thus making the method more flexible? In the second 'if', is n&0x1 the same as n%2? If so why didn't the author just use n%2? To me it's more readable. The line that sets the 'root' variable, why add the 1L? What is the run-time complexity? Is it O(sqrt(n/6)) or O(sqrt(n)/6)? Or would we just say O(n)?

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• Triangulating a partially triangulated mesh (2D)

  - by teodron

  Referring to the above exhibits, this is the scenario I am working with: starting with a planar graph (in my case, a 2D mesh) with a given triangulation, based on a certain criterion, the graph nodes are labeled as RED and BLACK. (A) a subgraph containing all the RED nodes (with edges between only the directly connected neighbours) is formed (note: although this figure shows a tree forming, it may well happen that the subgraph contain loops) (B) Problem: I need to quickly build a triangulation around the subgraph (e.g. as shown in figure C), but under the constraint that I have to keep the already present edges in the final result. Question: Is there a fast way of achieving this given a partially triangulated mesh? Ideally, the complexity should be in the O(n) class. Some side-remarks: it would be nice for the triangulation algorithm to take into account a certain vertex priority when adding edges (e.g. it should always try to build a "1-ring" structure around the most important nodes first - I can implement iteratively such a routine, but it's O(n^2) ). it would also be nice to reflect somehow the "hop distance" when adding edges: add edges first between the nodes that were "closer" to each other given the start topology. Nevertheless, disregarding the remarks, is there an already known scenario similar to this one where a triangulation is built upon a partially given set of triangles/edges?

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• algorithm for Virtual Machine(VM) Consolidation in Cloud

  - by devansh dalal

  PROBLEM: We have N physical machines(PMs) each with ram Ri, cpu Ci and a set of currently scheduled VMs each with ram requirement ri and ci respectively Moving(Migrating) any VM from one PM to other has a cost associated which depends on its ram ri. A PM with no VMs is shut down to save power. Our target is to minimize the weighted sum of (N,migration cost) by migrating some VMs i.e. minimize the number of working PMs as well as not to degrade the service level due to excessive migrations. My Approach: Brute Force approach is choosing the minimum loaded PM and try to fit its VMs to other PMs by First Fit Decreasing algorithm or we can select the victim PMs and target PMs based on their loading level and shut down victims if possible by moving their VMs to targets. I tried this Greedy approach on the Data of Baadal(IIT-D cloud) but It isn't giving promising results. I have also tried to study the Ant colony optimization for dynamic VM consolidating but was unable to understand very much. I used the links. http://dumas.ccsd.cnrs.fr/docs/00/72/52/15/PDF/Esnault.pdf http://hal.archives-ouvertes.fr/docs/00/72/38/56/PDF/RR-8032.pdf Would anyone please explain the solution or suggest any new approach for better performance soon. Thanks in advance.

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• Algorithm to shoot at a target in a 3d game

  - by Sebastian Bugiu

  For those of you remembering Descent Freespace it had a nice feature to help you aim at the enemy when shooting non-homing missiles or lasers: it showed a crosshair in front of the ship you chased telling you where to shoot in order to hit the moving target. I tried using the answer from http://stackoverflow.com/questions/4107403/ai-algorithm-to-shoot-at-a-target-in-a-2d-game?lq=1 but it's for 2D so I tried adapting it. I first decomposed the calculation to solve the intersection point for XoZ plane and saved the x and z coordinates and then solving the intersection point for XoY plane and adding the y coordinate to a final xyz that I then transformed to clipspace and put a texture at those coordinates. But of course it doesn't work as it should or else I wouldn't have posted the question. From what I notice the after finding x in XoZ plane and the in XoY the x is not the same so something must be wrong. float a = ENG_Math.sqr(targetVelocity.x) + ENG_Math.sqr(targetVelocity.y) - ENG_Math.sqr(projectileSpeed); float b = 2.0f * (targetVelocity.x * targetPos.x + targetVelocity.y * targetPos.y); float c = ENG_Math.sqr(targetPos.x) + ENG_Math.sqr(targetPos.y); ENG_Math.solveQuadraticEquation(a, b, c, collisionTime); First time targetVelocity.y is actually targetVelocity.z (the same for targetPos) and the second time it's actually targetVelocity.y. The final position after XoZ is crossPosition.set(minTime * finalEntityVelocity.x + finalTargetPos4D.x, 0.0f, minTime * finalEntityVelocity.z + finalTargetPos4D.z); and after XoY crossPosition.y = minTime * finalEntityVelocity.y + finalTargetPos4D.y; Is my approach of separating into 2 planes and calculating any good? Or for 3D there is a whole different approach? sqr() is square not sqrt - avoiding a confusion.

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• Grid Based Lighting in XNA/Monogame

  - by sm81095

  I know that questions like this have been asked many times, but I have not found one exactly like this yes. I have implemented a top-down grid based world in Monogame, and am starting on the lighting system soon. How I want to do lighting is to have a grid that is 4 times wider and higher, basically splitting each world tile into a 4x4 system of "subtiles". I would like to use a flow like system to spread light across the tiles by reducing the light by a small amount each time. This is kind of the effect I was going for: http://i.imgur.com/rv8LCxZ.png The black grid lines are the light grid, and the red lines are the actual tile grid, and the light drop-off is very exaggerated. I plan to render the world by drawing the unlit grid to a separate RenderTarget2D, then rendering the lighting grid to a separate target and overlaying the two. Basically, my questions are: What would be the algorithm for a flow style lighting system like this? Would there be a more efficient way of rendering this? How would I handle the darkening of the light with colors, reducing the RGB values in each grid, or reducing the alpha in each grid, assuming that I render the light map over the grid using blending? Even assuming the former are possible, what BlendState would I use for that?

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• Genetic Algorithm new generation exponentially increasing

  - by Rdz

  I'm programming Genetic Algorithm in C++ and after searching all kind of ways of doing GA'a operators (selection, crossover, mutation) I came up with a doubt. Let's say I have an initial population of 500. My selection will consist in getting the top 20% of 500(based on best fitness). So I get 100 individuals to mate. When I do the crossover I'll get 2 children where both together have 50% of surviving. So far so good. I start the mutation, and everything's ok.. Now when I start choosing the Next generation, I see that I have a big number of children (in this case, 4950 if you wanna know). Now the thing is, every time I run GA, if I send all the children to the next generation, the number of individuals per generation will increase exponentially. So there must be a way of choosing the children to fulfill a new generation without getting out of this range of the initial population. What I'm asking here is if there is anyway of choosing the children to fill the new generations OR should I choose somehow (and maybe reduce) the parents to mate so I don't get so many children in the end. Thanks :)

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• Algorithm to match timestamped events from two sources

  - by urza.cc

  I have two different physical devices (one is camera, one is other device) that observe the same scene and mark when a specified event occures. (record timestamp) So they each produce a serie of timestamps "when the event was observed". Theoretically the recorded timestamps should be very well aligned: Visualized ideal situation on two time lines "s" and "r" as recorded from the two devices: but more likely they will not be so nicely aligned and there might be missing events from timeline s or r: I am looking for algorithm to match events from "s" and "r" like this: So that the result will be something like: (s1,null); (s2,r1); (s3,null); (s4,r2); (s5,r3); (null,r4); (s6,r5); Or something similar. Maybe with some "confidence" rating. I have some ideas, but I feel that this might be probably a well known problem, that has some good known solutions, but I don't know the right terminology. I am a little bit out of my element here, this is not my primary area of programming.. Any helps, suggestions etc will be appreciated.

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• Algorithm for rating books: Relative perception

  - by suneet

  So I am developing this application for rating books (think like IMDB for books) using relational database. Problem statement : Let's say book "A" deserves 8.5 in absolute sense. In case if A is the best book I have ever seen, I'll most probably rate it 9.5 whereas for someone else, it might be just an average book, so he/they will rate it less (say around 8). Let's assume 4 such guys rate it 8. If there are 10 guys who are like me (who haven't ever read great literature) and they all rate it 9.5-10. This will effectively make it's cumulative rating greater than 9 (9.5*10 + 8*4) / 14 = 9.1 whereas we needed the result to be 8.5 ... How can I take care of(normalize) this bias due to incorrect perception of individuals. MyProposedSolution : Here's one of the ways how I think it could be solved. We can have a variable Lit_coefficient which tells us how much knowledge a user has about literature. If I rate "A"(the book) 9.5 and person "X" rates it 8, then he must have read books much better than "A" and thus his Lit_coefficient should be higher. And then we can normalize the ratings according to the Lit_coefficient of user. Could there be a better algorithm/solution for the same?

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• Hash Algorithm Randomness Visualization

  - by clstroud

  I'm curious if anyone here has any idea how the images were generated as shown in this response: Which hashing algorithm is best for uniqueness and speed? Ian posted a very well-received response but I can't seem to understand how he went about making the images. I hate to make a new question dedicated to this, but I can't find any means to ask him more directly. On the other hand, perhaps someone has an alternative perspective. The best I can personally come up with would be to have it almost like a bar graph, which would illustrate how evenly the buckets of the hash table are being generated. I have a working Cocoa program that does this, but it can't generate anything like what he showed there. So the question is two fold I suppose: A) How does one truly interpret the data he shows? Is it more than "less whitespace = better"? B) How does one generate such an image based on some set of inputs, a hash, and an index? Perhaps I'm misunderstanding entirely, but I really would like to know more about this particular visualization technique. Or maybe I'm mis-applying this to hash tables rather than just hashes in general, but in that case I don't know how it would be "bounded" for the image.

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• Turn Based Event Algorithm

  - by GamersIncoming

  I'm currently working on a small roguelike in XNA, which sees the player in a randomly generated series of dungeons fending off creeps, as you might expect. As with most roguelikes, the player makes a move, and then each of the creeps currently active on screen will make a move in turns, until all creeps have updated, and it return's to the player's go. On paper, the simple algorithm is straightforward: Player takes turn Turn Number increments For each active creep, update Position Once all active creeps have updated, allow player to take next turn However, when it comes to actually writing this in more detail, the concept becomes a bit more tricky for me. So my question comes as this: what is the best way to handle events taking turns to trigger, where the completion of each last event triggers the next, when dealing with a large number of creeps (probably stored as an array of an enemy object), and is there an easier way to create some kind of engine that just takes all objects that need updating and chains them together so their updates follow suit? I'm not asking for code, just algorithms and theory in the direction of objects triggering updates one after the other, in a turn based manner. Thanks in advance. Edited: Here's the code I currently have that is horrible :/ if (player.getTurnOver() && updateWait == 0) { if (creep[creepToUpdate].getActive()) { creep[creepToUpdate].moveObject(player, map1); updateWait = 10; } if (creepToUpdate < creep.Length -1) { creepToUpdate++; } else { creepToUpdate = 0; player.setTurnOver(false); } } if (updateWait > 0) { updateWait--; }

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• Pros and cons of PHP vs C,C++ as language in a programming interview ?

  - by DhruvPathak

  Hi All, Though this is a matter of personal choice and comfort. I would want your views on a situation like this. Programmer A has been working on PHP for some years, and has had prior experience in C.C++ during algorithm courses in university. The current fluency is good is PHP,but C,C++ can also be brushed up. So for interviews with major companies who put lot of emphasis on algorithms and data structures in programming interview e.g. binary trees, linked lists, arrays , strings . What should programmer A do ? Try to implement those things in PHP ( which is generally more suited for web development rather than programming contests/interviews ) or Or brush up the C,C++ skills and keep them as primary tool for tackling interview questions. What are advantages/ disadvantages of each language for an environment like programming contest or an interview ? Why would you recommend,not recommend Programmer A to participate in a contest like google code Jam/ ACM ICPC using PHP instead of C++ ? ( assuming PHP is allowed as a language there)

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• Problem with SAT collision detection overlap checking code

  - by handyface

  I'm trying to implement a script that detects whether two rotated rectangles collide for my game, using SAT (Separating Axis Theorem). I used the method explained in the following article for my implementation in Google Dart. 2D Rotated Rectangle Collision I tried to implement this code into my game. Basically from what I understood was that I have two rectangles, these two rectangles can produce four axis (two per rectangle) by subtracting adjacent corner coordinates. Then all the corners from both rectangles need to be projected onto each axis, then multiplying the coordinates of the projection by the axis coordinates (point.x*axis.x+point.y*axis.y) to make a scalar value and checking whether the range of both the rectangle's projections overlap. When all the axis have overlapping projections, there's a collision. First of all, I'm wondering whether my comprehension about this algorithm is correct. If so I'd like to get some pointers in where my implementation (written in Dart, which is very readable for people comfortable with C-syntax) goes wrong. Thanks! EDIT: The question has been solved. For those interested in the working implementation: Click here

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• Prevent collisions between mobs/npcs/units piloted by computer AI : How to avoid mobile obstacles?

  - by Arthur Wulf White

  Lets says we have character a starting at point A and character b starting at point B. character a is headed to point B and character b is headed to point A. There are several simple ways to find the path(I will be using Dijkstra). The question is, how do I take preventative action in the code to stop the two from colliding with one another? case2: Characters a and b start from the same point in different times. Character b starts later and is the faster of the two. How do I make character b walk around character a without going through it? case3:Lets say we have m such characters in each side and there is sufficient room to pass through without the characters overlapping with one another. How do I stop the two groups of characters from "walking on top of one another" and allow them pass around one another in a natural organic way. A correct answer would be any algorithm, that given the path to the destination and a list of mobile objects that block the path, finds an alternative path or stops without stopping all units when there is sufficient room to traverse.

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• Algorithm for grouping friends at the cinema [closed]

  - by Tim Skauge

  I got a brain teaser for you - it's not as simple as it sounds so please read and try to solve the issue. Before you ask if it's homework - it's not! I just wish to see if there's an elegant way of solving this. Here's the issue: X-number of friends want's to go to the cinema and wish to be seated in the best available groups. Best case is that everyone sits together and worst case is that everyone sits alone. Fewer groups are preferred over more groups. Sitting alone is least preferred. Input is the number of people going to the cinema and output should be an array of integer arrays that contains: Ordered combinations (most preferred are first) Number of people in each group Below are some examples of number of people going to the cinema and a list of preferred combinations these people can be seated: 1 person: 1 2 persons: 2, 1+1 3 persons: 3, 2+1, 1+1+1 4 persons: 4, 2+2, 3+1, 2+1+1, 1+1+1+1 5 persons: 5, 3+2, 4+1, 2+2+1, 3+1+1, 2+1+1+1, 1+1+1+1+1 6 persons: 6, 3+3, 4+2, 2+2+2, 5+1, 3+2+1, 2+2+1+1, 2+1+1+1+1, 1+1+1+1+1+1 Example with more than 7 persons explodes in combinations but I think you get the point by now. Question is: What does an algorithm look like that solves this problem? My language by choice is C# so if you could give an answer in C# it would be fantastic!

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• Generating random tunnels

  - by IVlad

  What methods could we use to generate a random tunnel, similar to the one in this classic helicopter game? Other than that it should be smooth and allow you to navigate through it, while looking as natural as possible (not too symmetric but not overly distorted either), it should also: Most importantly - be infinite and allow me to control its thickness in time - make it narrower or wider as I see fit, when I see fit; Ideally, it should be possible to efficiently generate it with smooth curves, not rectangles as in the above game; I should be able to know in advance what its bounds are, so I can detect collisions and generate powerups inside the tunnel; Any other properties that let you have more control over it or offer optimization possibilities are welcome. Note: I'm not asking for which is best or what that game uses, which could spark extended discussion and would be subjective, I'm just asking for some methods that others know about or have used before or even think they might work. That is all, I can take it from there. Also asked on stackoverflow, where someone suggested I should ask here too. I think it fits in both places, since it's as much an algorithm question as it is a gamedev question, IMO.

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• Efficient Algorithm for Recording gameplay's objects positions

  - by Scorch

  So, I have a game idea in mind, and for that I need to record the game around the player. I'me not talking about recording it as video, but rather recording the scene objects, and their positions within the game, and then render them, giving the player the ability to go back and forth, to stop time and move around. I've made a prototype with some data structures in C#, since this is going to be the programming language we'll be using in our game, but if we want the player to be able to go back just five minutes back with the data of just 100 NPC's, it takes almost 1GB of RAM. Right now, I'm just storing a Doubly linked list, each item with the object position. In the game, I'll need to store even more data in each node, so I need something even more ligher. Of course, this algorithm is zero optimized, but still, that is a lot. The alternatives would be create the NPC's that aren't really important to the game when the user is viewing the past, but I don't really like it very much for the sake of realism. I wonder if there is a better way to store this? Thanks in advance, Scorch

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• Efficient algorithm for Virtual Machine(VM) Consolidation in Cloud

  - by devansh dalal

  PROBLEM: We have N physical machines(PMs) each with ram Ri, cpu Ci and a set of currently scheduled VMs each with ram requirement ri and ci respectively Moving(Migrating) any VM from one PM to other has a cost associated which depends on its ram ri. A PM with no VMs is shut down to save power. Our target is to minimize the weighted sum of (N,migration cost) by migrating some VMs i.e. minimize the number of working PMs as well as not to degrade the service level due to excessive migrations. My Approach: Brute Force approach is choosing the minimum loaded PM and try to fit its VMs to other PMs by First Fit Decreasing algorithm or we can select the victim PMs and target PMs based on their loading level and shut down victims if possible by moving their VMs to targets. I tried this Greedy approach on the Data of Baadal(IIT-D cloud) but It isn't giving promising results. I have also tried to study the Ant colony optimization for dynamic VM consolidating but was unable to understand very much. I used the links. http://dumas.ccsd.cnrs.fr/docs/00/72/52/15/PDF/Esnault.pdf http://hal.archives-ouvertes.fr/docs/00/72/38/56/PDF/RR-8032.pdf Would anyone please clarify the solution or suggest any new approach/resources for better performance. I am basically searching for the algorithms not the physical optimizations and I also know that many commercial organizations have provided these solution but I just wanted to know more the underlying algorithms. Thanks in advance.

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• Finding which tiles are intersected by a line, without looping through all of them or skipping any

  - by JustSuds

  I've been staring at this problem for a few days now. I rigged up this graphic to help me visualise the issue: http://i.stack.imgur.com/HxyP9.png (from the graph, we know that the line intersects [1, 1], [1, 2], [2, 2], [2, 3], ending in [3,3]) I want to step along the line to each grid space and check to see if the material of the grid space is solid. I feel like I already know the math involved, but I haven't been able to string it together yet. I'm using this to test line of sight and eliminate nodes after a path is found via my pathfinding algorithms - my agents cant see through a solid block, therefore they cant move through one, therefore the node is not eliminated from the path because it is required to navigate a corner. So, I need an algorithm that will step along the line to each grid space that it intersects. Any ideas? I've taken a look at a lot of common algorithms, like Bresenham's, and one that steps at predefined intervals along the line (unfortunately, this method skips tiles if they're intersecting with a smaller wedge than the step size). I'm populating my whiteboard now with a mass of floor() and ceil() functions - but its getting overly complicated and I'm afraid it might cause a slowdown.

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• Finding the heaviest length-constrained path in a weighted Binary Tree

  - by Hristo

  UPDATE I worked out an algorithm that I think runs in O(n*k) running time. Below is the pseudo-code: routine heaviestKPath( T, k ) // create 2D matrix with n rows and k columns with each element = -8 // we make it size k+1 because the 0th column must be all 0s for a later // function to work properly and simplicity in our algorithm matrix = new array[ T.getVertexCount() ][ k + 1 ] (-8); // set all elements in the first column of this matrix = 0 matrix[ n ][ 0 ] = 0; // fill our matrix by traversing the tree traverseToFillMatrix( T.root, k ); // consider a path that would arc over a node globalMaxWeight = -8; findArcs( T.root, k ); return globalMaxWeight end routine // node = the current node; k = the path length; node.lc = node’s left child; // node.rc = node’s right child; node.idx = node’s index (row) in the matrix; // node.lc.wt/node.rc.wt = weight of the edge to left/right child; routine traverseToFillMatrix( node, k ) if (node == null) return; traverseToFillMatrix(node.lc, k ); // recurse left traverseToFillMatrix(node.rc, k ); // recurse right // in the case that a left/right child doesn’t exist, or both, // let’s assume the code is smart enough to handle these cases matrix[ node.idx ][ 1 ] = max( node.lc.wt, node.rc.wt ); for i = 2 to k { // max returns the heavier of the 2 paths matrix[node.idx][i] = max( matrix[node.lc.idx][i-1] + node.lc.wt, matrix[node.rc.idx][i-1] + node.rc.wt); } end routine // node = the current node, k = the path length routine findArcs( node, k ) if (node == null) return; nodeMax = matrix[node.idx][k]; longPath = path[node.idx][k]; i = 1; j = k-1; while ( i+j == k AND i < k ) { left = node.lc.wt + matrix[node.lc.idx][i-1]; right = node.rc.wt + matrix[node.rc.idx][j-1]; if ( left + right > nodeMax ) { nodeMax = left + right; } i++; j--; } // if this node’s max weight is larger than the global max weight, update if ( globalMaxWeight < nodeMax ) { globalMaxWeight = nodeMax; } findArcs( node.lc, k ); // recurse left findArcs( node.rc, k ); // recurse right end routine Let me know what you think. Feedback is welcome. I think have come up with two naive algorithms that find the heaviest length-constrained path in a weighted Binary Tree. Firstly, the description of the algorithm is as follows: given an n-vertex Binary Tree with weighted edges and some value k, find the heaviest path of length k. For both algorithms, I'll need a reference to all vertices so I'll just do a simple traversal of the Tree to have a reference to all vertices, with each vertex having a reference to its left, right, and parent nodes in the tree. Algorithm 1 For this algorithm, I'm basically planning on running DFS from each node in the Tree, with consideration to the fixed path length. In addition, since the path I'm looking for has the potential of going from left subtree to root to right subtree, I will have to consider 3 choices at each node. But this will result in a O(n*3^k) algorithm and I don't like that. Algorithm 2 I'm essentially thinking about using a modified version of Dijkstra's Algorithm in order to consider a fixed path length. Since I'm looking for heaviest and Dijkstra's Algorithm finds the lightest, I'm planning on negating all edge weights before starting the traversal. Actually... this doesn't make sense since I'd have to run Dijkstra's on each node and that doesn't seem very efficient much better than the above algorithm. So I guess my main questions are several. Firstly, do the algorithms I've described above solve the problem at hand? I'm not totally certain the Dijkstra's version will work as Dijkstra's is meant for positive edge values. Now, I am sure there exist more clever/efficient algorithms for this... what is a better algorithm? I've read about "Using spine decompositions to efficiently solve the length-constrained heaviest path problem for trees" but that is really complicated and I don't understand it at all. Are there other algorithms that tackle this problem, maybe not as efficiently as spine decomposition but easier to understand? Thanks.

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• Implement Negascout Algorithm with stack

  - by Dan

  I'm not familiar with how these stack exchange accounts work so if this is double posting I apologize. I asked the same thing on stackoverflow. I have added an AI routine to a game I am working on using the Negascout algorithm. It works great, but when I set a higher maximum depth it can take a few seconds to complete. The problem is it blocks the main thread, and the framework I am using does not have a way to deal with multi-threading properly across platforms. So I am trying to change this routine from recursively calling itself, to just managing a stack (vector) so that I can progress through the routine at a controlled pace and not lock up the application while the AI is thinking. I am getting hung up on the second recursive call in the loop. It relies on a returned value from the first call, so I don't know how to add these to a stack. My Working c++ Recursive Code: MoveScore abNegascout(vector<vector<char> > &board, int ply, int alpha, int beta, char piece) { if (ply==mMaxPly) { return MoveScore(evaluation.evaluateBoard(board, piece, oppPiece)); } int currentScore; int bestScore = -INFINITY; MoveCoord bestMove; int adaptiveBeta = beta; vector<MoveCoord> moveList = evaluation.genPriorityMoves(board, piece, findValidMove(board, piece, false)); if (moveList.empty()) { return MoveScore(bestScore); } bestMove = moveList[0]; for(int i=0;i<moveList.size();i++) { MoveCoord move = moveList[i]; vector<vector<char> > newBoard; newBoard.insert( newBoard.end(), board.begin(), board.end() ); effectMove(newBoard, piece, move.getRow(), move.getCol()); // First Call ****** MoveScore current = abNegascout(newBoard, ply+1, -adaptiveBeta, -max(alpha,bestScore), oppPiece); currentScore = - current.getScore(); if (currentScore>bestScore){ if (adaptiveBeta == beta || ply>=(mMaxPly-2)){ bestScore = currentScore; bestMove = move; }else { // Second Call ****** current = abNegascout(newBoard, ply+1, -beta, -currentScore, oppPiece); bestScore = - current.getScore(); bestMove = move; } if(bestScore>=beta){ return MoveScore(bestMove,bestScore); } adaptiveBeta = max(alpha, bestScore) + 1; } } return MoveScore(bestMove,bestScore); } If someone can please help by explaining how to get this to work with a simple stack. Example code would be much appreciated. While c++ would be perfect, any language that demonstrates how would be great. Thank You.

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• Equal Gifts Algorithm Problem

  - by 7Aces

  Problem Link - http://opc.iarcs.org.in/index.php/problems/EQGIFTS It is Lavanya's birthday and several families have been invited for the birthday party. As is customary, all of them have brought gifts for Lavanya as well as her brother Nikhil. Since their friends are all of the erudite kind, everyone has brought a pair of books. Unfortunately, the gift givers did not clearly indicate which book in the pair is for Lavanya and which one is for Nikhil. Now it is up to their father to divide up these books between them. He has decided that from each of these pairs, one book will go to Lavanya and one to Nikhil. Moreover, since Nikhil is quite a keen observer of the value of gifts, the books have to be divided in such a manner that the total value of the books for Lavanya is as close as possible to total value of the books for Nikhil. Since Lavanya and Nikhil are kids, no book that has been gifted will have a value higher than 300 Rupees... For the problem, I couldn't think of anything except recursion. The code I wrote is given below. But the problem is that the code is time-inefficient and gives TLE (Time Limit Exceeded) for 9 out of 10 test cases! What would be a better approach to the problem? Code - #include<cstdio> #include<climits> #include<algorithm> using namespace std; int n,g[150][2]; int diff(int a,int b,int f) { ++f; if(f==n) { if(a>b) { return a-b; } else { return b-a; } } return min(diff(a+g[f][0],b+g[f][1],f),diff(a+g[f][1],b+g[f][0],f)); } int main() { int i; scanf("%d",&n); for(i=0;i<n;++i) { scanf("%d%d",&g[i][0],&g[i][1]); } printf("%d",diff(g[0][0],g[0][1],0)); } Note - It is just a practice question, & is not part of a competition.

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