I was going to to write a game (it's called "Qwirkle" if you ever heard of it) in which a 2-dimensional game field stores the position of stones which the players have put into it. The first player puts a stone anywhere and other players can connect to it from any side (left / right / top and bottom). The game field itself is not restricted to a fixed size which would ruin the game idea. However, the number of stones is limited to a value the player can define at start.
Because of the game logic I need to for-loop through the stones with an index. However, since the players can add stones from any side, I'd need a list which is expandable into any direction (e.g. into negative and positive index direction).
Performance is not unimportant since I need to check several stones in one turn.
The best thing would be to access a stone like _stones[-3,5] to access the one at position -3, 5, of course.
I thought a stack which can be pushed and popped from any side (like PushBack / PushFront) would be useful for this, but I'm not quite sure how to realize that in C#.
Are there pre-implemented lists / stacks like the one I'm thinking of, or is my approach completely weird?
The data structure you want is an immutable quadtree. If the board is mostly empty then using an immutable quadree enables you to represent boards that are essentially unlimited in size; a one-trillion-by-one-trillion cell board takes only a few bytes more memory than a 32-by-32 cell board. Immutable quadtrees can easily be indexed in the manner you describe, and computing a new quadtree given an old quadtree and an edit is straightforward.
I've written immutable quadtree algorithms several times over the years and I have been meaning for a long time to do a series of blog articles on them, but I never have. When I do I'll come back and update this answer.
In the meanwhile, this Dr. Dobbs article on Gosper's Algorithm is the one I used to learn how immutable quadtrees work.
http://www.drdobbs.com/jvm/an-algorithm-for-compressing-space-and-t/184406478
What you want is a double ended queue (known as a deque, pronounced "deck"). There is no implementation in the .NET BCL (unfortunately) but there are 3rd party implementations (see Google).
Dictionary could be an option, instead of thinking about indexes of a list, you could think of integer keys of a Dictionary. No matter what's the dimension.
Dictionary<int,Dictionary<int,Stone>> stones = new Dictionary<int,Dictionary<int,Stone>>();
// do some initialisation for the base field size ...
// access it this way
Stone s = stones[-1][-5];
Only issue is when you want to add a 2nd dimension which can get resource consuming (iterating over all 1st dimensions).
I think you will learn more from implementing a custom data structure containing, say, two ArrayLists. One going forward and one going backward. Of course, in your implementation they will both go the same way but your implementation could have the data structure return a negation of the positive index plus one so that you don't get an index of -0 for the first element in the backward ArrayList.
Maybe I've misunderstood the problem, but that's how I would go about implementing a two-way expandable data structure.
Good luck!
You could do something like:
_stones[-(i),i] and/or _stones[i,-(i)]
Just a suggestion.
Related
I am trying to implement a pathfinding algorithm, but I think I'm running into terminology issues, in that I'm not quite sure how to explain what I need the algorithm to do.
I have a regular grid of nodes, and I am trying to find all nodes within a certain "Manhattan Distance".
Finding the nodes within, say, 5, is simple enough.
But I am interested in a "Weighted Manhattan Distance", where certain squares "cost" twice as much (or more) to enter. For instance, if orange squares cost 2 to enter, and purple squares cost 10, the graph I'm interested in looks like this:
Firstly, is there a term for this? It's hard to look up info on things when you're not entirely sure what they're called in the first place.
Secondly, how can I calculate which nodes fall within my parameters? I'm not looking for a full solution, necessarily, just some hints to get started; when I realized my implementation would require three Dictionarys, I began to think there might be an easier way of handling things.
For terminology, you're basically asking for all points within a certain distance on an arbitrary (positive) weighted graph. The use of differing weights means it no longer corresponds to a specific metric such as Manhattan distance.
As for algorithms, Dijkstra's algorithm is probably what you want. The basic idea is to maintain the minimum cost to each square that you've found so far, and a priority queue of the best squares to explore next.
Unlike traditional Dijkstra's where you keep going until you find the minimal path to every square, you'll want to stop adding nodes to the queue if the distance to them is too long. Once you're done, you'll have a list of all squares whose shortest path from the starting square is at most x, which sounds like what you want.
Eric Lippert provides an excellent blog-series on writing an A-* path finding algorithm in C# here:
Part 1:http://blogs.msdn.com/b/ericlippert/archive/2007/10/02/path-finding-using-a-in-c-3-0.aspx
Part 2: http://blogs.msdn.com/b/ericlippert/archive/2007/10/04/path-finding-using-a-in-c-3-0-part-two.aspx
Part 3: http://blogs.msdn.com/b/ericlippert/archive/2007/10/08/path-finding-using-a-in-c-3-0-part-three.aspx
Part 4: http://blogs.msdn.com/b/ericlippert/archive/2007/10/10/path-finding-using-a-in-c-3-0-part-four.aspx
You are probably best to go with Dijkstra's algorithm with weighted graph, like described here:
http://www.csl.mtu.edu/cs2321/www/newLectures/29_Weighted_Graphs_and_Dijkstra's_Algorithm.html
(There is algorithm description near the middle of the page.)
Manhattan distance in your case probably just means you don't want the diagonal paths in the graph.
I'm looking for a data structure similar to T[,,] (a 3D array) except I don't know the dimensions beforehand (nor have a reasonable upper bound) that will expand outwards as time goes on. I'd like to use negative indexes as well.
The only thing that comes to mind is a dictionary, with some kind of Point3 struct as the key. Are there any other alternatives? I'd like to lookups to be as fast as possible. The data will always be clustered around 0,0,0. It can expand in any direction, but there will never be any "gaps" between points.
I think I'm going to go ahead and just use a Dictionary<Point3, T> for now, and see how that performs. If it's a performance issue I'll try building a wrapper around T[,,] such that I can use negative indexes.
Obviously you'll need to store this in a data structure resembling a sparse array, because you have no idea how large your data-set is going to be. So a Dictionary seems reasonable.
I'm going a little crazy here, but I think your indices should be in Spherical Coordinates. It makes sense to me as your data grows outwards. It will also make finding elements at a specific range from (0, 0, 0) extremely easy.
If you may need range queries, KD-Trees comes to mind. They are tree-like structures, at each level seperate the universe into two along one axis. They offer O(logN) lookup time (for constant number of dimensions) which may or may not be fast enough, but they also provide O(logN + S) time for range queries where S is the size of the items found, which usually is very good. They can handle dynamic data (insertions and deletions along with lookups) but the tree may become unbalanced as a result. Also you can do Nearest Neighboor search from a given point, (i.e. get the 10 nearest objects to point (7,8,9)) Wikipedia, as always, is a good starting point: http://en.wikipedia.org/wiki/Kd-tree
If there are huge numbers of things in the world, of if the world is very dynamic (things move, be created/destroyed all the time), kd-trees may not be good enough. If most of the time you will only ask "give me the thing at (7,8,9)" you can either use a hash as you mentioned in your question or something like a List<List<List<T>>>. I'd just implement whichever is easier within an interface and worry about the performance later.
I am kind of assuming you need the dynamic aspect because array could be huge. In that case, what you could try is to allocate your array as a set of 3d 'tiles'. At the top level you have a 3d data structure that stores pointers to your tiles. You expand and allocate this as you go along.
Each individual tile could contain, say, 32x32x32 voxels. Or whatever amount suits your goals.
Looking up you tile is done by dividing your coordinate index by 32 (by bitshifting, of course), and the index in the tile is calculated by masking away the upper bits.
A lookup like this is fairly cheap, possible on par with a .net Dictionary, but it will use less memory, which is good for performance too.
The resulting array will be chunky, though: the array boundaries are multiples of your tile size.
Array access is a very fast linear lookup - if speed of lookup is your priority, then it's probably the way to go, depending on how often you will need to modify your arrays.
If your goal is to maintain the chunks around a player, you might want to arrange a "current world" array structure around the player, such that it is a 3-dimensional array with the centre chunk at 9,9,9 with a size of [20,20,20]. Each time the player leaves the centre chunk for another, you re-index the array to drop the old chunks and move on.
Ultimately, you're asking for options on how to optimize your game engine, but it's nearly impossible to say which is going to be correct for you. Even though games tend to be more optimized for performance than other applications, don't get lured into micro-optimizations; optimize for readability first and then optimize for performance when you find it necessary.
If you suspect this particular data-structure is going to be a bottleneck in your engine, put some performance tracing in so it's easy to be sure one way or the other once you've got the engine running.
Was wondering if anyone has knowledge on implementing pathfinding, but using scent. The stronger the scent in the nodes surrounding, is the way the 'enemy' moves towards.
Thanks
Yes, I did my university final project on the subject.
One of the applications of this idea is for finding the shortest path.
The idea is that the 'scent', as you put it, will decay over time. But the shortest path between two points will have the strongest scent.
Have a look at this paper.
What did you want to know exactly??
Not quite clear what the question is in particular - but this just seems like another way of describing the Ant colony optimization problem:
In computer science and operations
research, the ant colony optimization
algorithm (ACO) is a probabilistic
technique for solving computational
problems which can be reduced to
finding good paths through graphs.
Well, think about it for a minute.
My idea would to divide the game field into sections of 32x32 (or whatever size your character is). Then run some checks every x seconds (so if they stay still the tiles around them will have more 'scent') to figure out how strong a scent is on any given tile. Some examples might be: 1) If you cross over the tile, add 3; 2) if you crossed over an adjacent tile, add 1.
Then add things like degradation over time, reduce every tile by 1 every x seconds until it hits zero.
The last thing you will need to worry about is using AI to track this path. I would recommend just putting the AI somewhere, and telling it to find a node with a scent, then goto an adjacent node with a higher/equal value scent. Also worry about crossing off paths taken. If the player goes up a path, then back down it another direction, make sure the AI does always just take the looped back path.
The last thing to look at with the AI would be to add a bit of error. Make the AI take the wrong path every once in a while. Or lose the trail a little more easily.
Those are the key points, I'm sure you can come up with some more, with some more brainstorming.
Every game update (or some other, less frequent time frame), increase the scent value of nodes near to where the target objects (red blobs) are.
Decrease all node scent values by some fall-off amount to zero.
In the yellow blob's think/move function get available nodes to move to. Move towards the node with the highest scent value.
Depending on the number of nodes the 'decrease all node scent values' could do with optomisation, e.g. maybe maintaining a a list of non-zero nodes to be decreased.
I see a big contradiction between scent model and pathfinding. For a hunter in the nature finding the path by scent means finding exactly the path used by the followed subject. And in games pathfinding means finding the fastest path between two points. It is not the same.
1. While modelling the scent you will count the scent concentration in the point as the SUM of the surrounding concentrations multiplied by different factors. And searching for the fastest path from the point means taking the MINIMUM of the times counted for surrounding points, multiplied by the different parametres.
2. Counting the scent you should use recursive model - scent goes in all directions, including backward. In the case of the pathfinding, if you have found the shortest paths for points surrounding the target, they won't change.
3 Level of scent can rise and fall. In pathfinding, while searching for minimum, the result can never rise.
So, the scent model is really much more complicated than your target. Of course, what I have said, is true only for the standard situation and you can have something very special...
I am working on a project where the game world is irregularly shaped (Think of the shape of a lake). this shape has a grid with coordinates placed over it. The game world is only on the inside of the shape. (Once again, think Lake)
How can I efficiently represent the game world? I know that many worlds are basically square, and work well in a 2 or 3 dimension array. I feel like if I use an array that is square, then I am basically wasting space, and increasing the amount of time that I need to iterate through the array. However, I am not sure how a jagged array would work here either.
Example shape of gameworld
X
XX
XX X XX
XXX XXX
XXXXXXX
XXXXXXXX
XXXXX XX
XX X
X
Edit:
The game world will most likely need each valid location stepped through. So I would a method that makes it easy to do so.
There's computational overhead and complexity associated with sparse representations, so unless the bounding area is much larger than your actual world, it's probably most efficient to simply accept the 'wasted' space. You're essentially trading off additional memory usage for faster access to world contents. More importantly, the 'wasted-space' implementation is easier to understand and maintain, which is always preferable until the point where a more complex implementation is required. If you don't have good evidence that it's required, then it's much better to keep it simple.
You could use a quadtree to minimize the amount of wasted space in your representation. Quad trees are good for partitioning 2-dimensional space with varying granularity - in your case, the finest granularity is a game square. If you had a whole 20x20 area without any game squares, the quad tree representation would allow you to use only one node to represent that whole area, instead of 400 as in the array representation.
Use whatever structure you've come up with---you can always change it later. If you're comfortable with using an array, use it. Stop worrying about the data structure you're going to use and start coding.
As you code, build abstractions away from this underlying array, like wrapping it in a semantic model; then, if you realize (through profiling) that it's waste of space or slow for the operations you need, you can swap it out without causing problems. Don't try to optimize until you know what you need.
Use a data structure like a list or map, and only insert the valid game world coordinates. That way the only thing you are saving are valid locations, and you don't waste memory saving the non-game world locations since you can deduce those from lack of presence in your data structure.
The easiest thing is to just use the array, and just mark the non-gamespace positions with some special marker. A jagged array might work too, but I don't use those much.
You could present the world as an (undirected) graph of land (or water) patches. Each patch then has a regular form and the world is the combination of these patches. Every patch is a node in the graph and has has graph edges to all its neighbours.
That is probably also the most natural representation of any general world (but it might not be the most efficient one). From an efficiency point of view, it will probably beat an array or list for a highly irregular map but not for one that fits well into a rectangle (or other regular shape) with few deviations.
An example of a highly irregular map:
x
x x
x x x
x x
x xxx
x
x
x
x
There’s virtually no way this can be efficiently fitted (both in space ratio and access time) into a regular shape. The following, on the other hand, fits very well into a regular shape by applying basic geometric transformations (it’s a parallelogram with small bits missing):
xxxxxx x
xxxxxxxxx
xxxxxxxxx
xx xxxx
One other option that could allow you to still access game world locations in O(1) time and not waste too much space would be a hashtable, where the keys would be the coordinates.
Another way would be to store an edge list - a line vector along each straight edge. Easy to check for inclusion this way and a quad tree or even a simple location hash on each vertice can speed lookup of info. We did this with a height component per edge to model the walls of a baseball stadium and it worked beautifully.
There is a big issue that nobody here addressed: the huge difference between storing it on disk and storing it in memory.
Assuming you are talking about a game world as you said, this means it's going to be very large. You're not going to store the whole thing in memory in once, but instead you will store the immediate vicinity in memory and update it as the player walks around.
This vicinity area should be as simple, easy and quick to access as possible. It should definitely be an array (or a set of arrays which are swapped out as the player moves). It will be referenced often and by many subsystems of your game engine: graphics and physics will handle loading the models, drawing them, keeping the player on top of the terrain, collisions, etc.; sound will need to know what ground type the player is currently standing on, to play the appropriate footstep sound; and so on. Rather than broadcast and duplicate this data among all the subsystems, if you just keep it in global arrays they can access it at will and at 100% speed and efficiency. This can really simplify things (but be aware of the consequences of global variables!).
However, on disk you definitely want to compress it. Some of the given answers provide good suggestions; you can serialize a data structure such as a hash table, or a list of only filled-in locations. You could certainly store an octree as well. In any case, you don't want to store blank locations on disk; according to your statistic, that would mean 66% of the space is wasted. Sure there is a time to forget about optimization and make it Just Work, but you don't want to distribute a 66%-empty file to end users. Also keep in mind that disks are not perfect random-access machines (except for SSDs); mechanical hard drives should still be around another several years at least, and they work best sequentially. See if you can organize your data structure so that the read operations are sequential, as you stream more vicinity terrain while the player moves, and you'll probably find it to be a noticeable difference. Don't take my word for it though, I haven't actually tested this sort of thing, it just makes sense right?
I'm writing a game in which a character moves around on a randomly generated map in real time (as it's revealed.) This leads me an interesting data structures problem. The map is generated as it comes into view, in a circle around the character (probably 20-60 tiles) so where there is data, it is very dense, and all in a grid. Where there's not data, though, there could be huge, ungenerated spaces. The character could walk in a huge circle, for example, creating a ring of tiles around vast empty space.
A simple matrix would create massive amounts of unneeded overhead, and waste a lot of space. Typical BSPs, though, seem like they would cause a huge performance drop because of the dense, grid-like nature of the data.
What do you suggest? Matrixes - quadtrees - some hybrid of the two?
I am thinking of implementing something similar in my game that I am working on. I'm going to create a custom class that can be accessed like a 2D array ex. map[x][y] but the underlying datatype would be closer to a hashtable. Something like data[x.Value.ToString() + "," + y.Value.ToString()]
My game is fairly basic as my tiles will only ever be walkable, deadly, or unwalkable.
I'm interested in a more elegant solution though :D
I've been tackling this for the past month, and have come up with what I believe is a fairly good solution. It's not as fast as a pure matrix, but has the benefit of being infinitely extensible (within the limits of an int.)
Basically, it's a binary space partition which builds upwards (instead of downwards, like a quadtree.) If you write to a point outside of the currently allocated matrix space, it generates a larger node and expands. If a majority of a node's children nodes are allocated matrices, it will aggregate them into itself and remove their references. This means that the more well-defined boundaries you use, the better performance you get, as the more this structure acts like a matrix.
I've posted my code here, and will try and write some sort of demo in the future, and move to a better hosting site.
Don't hesitate to let me know what you think, or if you have any questions about it.