I need to implement an intelligent agent to play Abalone game, for this kind of game the best way to proceed seems a min-max strategy with alpha beta pruning.
I have already implemented a naive search algorithm that use min-max with pruning,
my problem is...
How to generate the nodes of the tree where perform the search?
I have no idea of the right way to do this, and how assign the weigh to each node.
For generating the tree nodes: You need to implement a method that returns a collection of all possible legal moves given the current board position and the player whose turn it is. All these moves will become children of the node representing the current board position. Repeat until memory is exhausted to generate the game tree ;) or rather until you reach a reasonable tree depth.
For alpha-beta search you also need an evaluation function which calculates the weight for each board position/node. You can do some research or think about such a function yourself, maybe considering the number of stones still on the board. However a bad evaluation function can seriously screw up your results, so take care and run a lot of tests.
If you have trouble coming up with a reasonable evaluation function, I recommend you take a look into Monte-Carlo techniques such as UCT.
http://en.wikipedia.org/wiki/Monte_Carlo_tree_search
These tackle the problem using a probabilistic approach and have some nice advantages over alpha-beta. Also they don't require an evaluation function so you could skip this step.
Good luck!
I have published two libraries for move generation in Abalone. You didn't mention the programming language used for your search implementation, but you can easily port the functions.
For C++, https://sourceforge.net/projects/abnet/
For Python, https://gitlab.com/peer.sommerlund/haliotis
For an evaluation function, distance between all your marbles, or distance to their gravity center (same thing), works nicely. Tino Werner used this with a twist for his program that won ICGA 2003.
For understanding distance when using hex coordinates, I can recommend Amit Patel's page: https://www.redblobgames.com/grids/hexagons/
I am working on a basic graph implementation(Adj List based) in C so that I can re-use the basic structure to solve all graph related problems.
To map a graph I draw on a paper,I want the best and easiest way.
Talking of the way I take the input rather then how should I go about implementing it! :)
Should I make an input routine which asks for all the nodes label first and then asks for what all edges are to be connected based on two labels?
What could be a good and quick way out? I want an easy way out which lets me spend less amount of energy on the "Input".
Best is to go for input of an edge list,
that is triplets of,
Source, Destination, Cost
This routine can be used to fill Adj List and Adj Matrix.
With the latter, you would need to properly initialize the Matrix though and setup a convention to determine non existent edges.
Here you find details about representation of graph:
Graph-internal-representaion
However here some codes in c++ and java are also given,which you can easily convert to C codes.
The prof gave us an assigment to finish in the next couple of months, we have to write a web app that is basically a mapping system for a floor of a building. Like a very very simple version of google maps, people need to be able to look up a room and be able to get directions from one part of the floor to another. I have never done any major web programming and don't even know how to start. Is there a google maps or mapquest API that I can use or do I have to start it from scratch? I'm not asking anyone to solve it for me, just nudge me in the right direction so as where to start.
I would suggest thinking of the task as three parts:
Displaying the image of the map
(probably, for best efficiency, as
lazily-loaded tiles like Google Maps
does)
Representing the rooms and the
connections between them, probably
as a graph. Using a graph
allows you to easily use a
well-documented algorithm like
A* or Dijkstra's to find
the shortest route from point A to
point B.
Converting from a click on the image
to a node on the graph, and from a
node on the graph to a point in the
image. Probably each node should
just store a pair of (x,y)
coordinates.
With an arrangement like this, all your code has to do is:
The first time the user clicks
{
Identify the nearest node to their click as node A;
}
The second time the user clicks
{
Identify the nearest node to their click as node B;
Use Dijkstras Algorithm or A* to find the shortest route from node A to node B;
For each edge in the resulting route
{
Add a line to the image of the map;
}
Mark node A with a green dot and node B with a red dot (or something);
}
I found a lot of references to the AI of the ghosts in Pacman, but none of them mentioned how the eyes find their way back to the central ghost hole after a ghost is eaten by Pacman.
In my implementation I implemented a simple but awful solution. I just hard coded on every corner which direction should be taken.
Are there any better/or the best solution? Maybe a generic one that works with different level designs?
Actually, I'd say your approach is a pretty awesome solution, with almost zero-run time cost compared to any sort of pathfinding.
If you need it to generalise to arbitrary maps, you could use any pathfinding algorithm - breadth-first search is simple to implement, for example - and use that to calculate which directions to encode at each of the corners, before the game is run.
EDIT (11th August 2010): I was just referred to a very detailed page on the Pacman system: The Pac-Man Dossier, and since I have the accepted answer here, I felt I should update it. The article doesn't seem to cover the act of returning to the monster house explicitly but it states that the direct pathfinding in Pac-Man is a case of the following:
continue moving towards the next intersection (although this is essentially a special case of 'when given a choice, choose the direction that doesn't involve reversing your direction, as seen in the next step);
at the intersection, look at the adjacent exit squares, except the one you just came from;
picking one which is nearest the goal. If more than one is equally near the goal, pick the first valid direction in this order: up, left, down, right.
I've solved this problem for generic levels that way: Before the level starts, I do some kind of "flood fill" from the monster hole; every tile of the maze that isn't a wall gets a number that says how far it is away from the hole. So when the eyes are on a tile with a distance of 68, they look which of the neighbouring tiles has a distance of 67; that's the way to go then.
For an alternative to more traditional pathfinding algorithms, you could take a look at the (appropriately-named!) Pac-Man Scent Antiobject pattern.
You could diffuse monster-hole-scent around the maze at startup and have the eyes follow it home.
Once the smell is set up, runtime cost is very low.
Edit: sadly the wikipedia article has been deleted, so WayBack Machine to the rescue...
You should take a look a pathfindings algorithm, like Dijsktra's Algorithm or A* algorithm. This is what your problem is : a graph/path problem.
Any simple solution that works is maintainable, reliable and performs well enough is a good solution. It sounds to me like you have already found a good solution ...
An path-finding solution is likely to be more complicated than your current solution, and hence more likely to require debugging. It will probably also be slower.
IMO, if it ain't broken, don't fix it.
EDIT
IMO, if the maze is fixed then your current solution is good / elegant code. Don't make the mistake of equating "good" or "elegant" with "clever". Simple code can also be "good" and "elegant".
If you have configurable maze levels, then maybe you should just do the pathfinding when you initially configure the mazes. Simplest would be to get the maze designer to do it by hand. I'd only bother automating this if you have a bazillion mazes ... or users can design them.
(Aside: if the routes are configured by hand, the maze designer could make a level more interesting by using suboptimal routes ... )
In the original Pacman the Ghost found the yellow pill eater by his "smell" he would leave a trace on the map, the ghost would wander around randomly until they found the smell, then they would simply follow the smell path which lead them directly to the player. Each time Pacman moved, the "smell values" would get decreased by 1.
Now, a simple way to reverse the whole process would be to have a "pyramid of ghost smell", which has its highest point at the center of the map, then the ghost just move in the direction of this smell.
Assuming you already have the logic required for chasing pacman why not reuse that? Just change the target. Seems like it would be a lot less work than trying to create a whole new routine using the exact same logic.
It's a pathfinding problem. For a popular algorithm, see http://wiki.gamedev.net/index.php/A*.
How about each square having a value of distance to the center? This way for each given square you can get values of immediate neighbor squares in all possible directions. You pick the square with the lowest value and move to that square.
Values would be pre-calculated using any available algorithm.
This was the best source that I could find on how it actually worked.
http://gameai.com/wiki/index.php?title=Pac-Man#Respawn
When the ghosts are killed, their disembodied eyes return to their starting location. This is simply accomplished by setting the ghost's target tile to that location. The navigation uses the same rules.
It actually makes sense. Maybe not the most efficient in the world but a pretty nice way to not have to worry about another state or anything along those lines you are just changing the target.
Side note: I did not realize how awesome those pac-man programmers were they basically made an entire message system in a very small space with very limited memory ... that is amazing.
I think your solution is right for the problem, simpler than that, is to make a new version more "realistic" where ghost eyes can go through walls =)
Here's an analog and pseudocode to ammoQ's flood fill idea.
queue q
enqueue q, ghost_origin
set visited
while q has squares
p <= dequeue q
for each square s adjacent to p
if ( s not in visited ) then
add s to visited
s.returndirection <= direction from s to p
enqueue q, s
end if
next
next
The idea is that it's a breadth-first search, so each time you encounter a new adjacent square s, the best path is through p. It's O(N) I do believe.
I don't know much on how you implemented your game but, you could do the following:
Determine the eyes location relative position to the gate. i.e. Is it left above? Right below?
Then move the eyes opposite one of the two directions (such as make it move left if it is right of the gate, and below the gate) and check if there are and walls preventing you from doing so.
If there are walls preventing you from doing so then make it move opposite the other direction (for example, if the coordinates of the eyes relative to the pin is right north and it was currently moving left but there is a wall in the way make it move south.
Remember to keep checking each time to move to keep checking where the eyes are in relative to the gate and check to see when there is no latitudinal coordinate. i.e. it is only above the gate.
In the case it is only above the gate move down if there is a wall, move either left or right and keep doing this number 1 - 4 until the eyes are in the den.
I've never seen a dead end in Pacman this code will not account for dead ends.
Also, I have included a solution to when the eyes would "wobble" between a wall that spans across the origin in my pseudocode.
Some pseudocode:
x = getRelativeOppositeLatitudinalCoord()
y
origX = x
while(eyesNotInPen())
x = getRelativeOppositeLatitudinalCoordofGate()
y = getRelativeOppositeLongitudinalCoordofGate()
if (getRelativeOppositeLatitudinalCoordofGate() == 0 && move(y) == false/*assume zero is neither left or right of the the gate and false means wall is in the way */)
while (move(y) == false)
move(origX)
x = getRelativeOppositeLatitudinalCoordofGate()
else if (move(x) == false) {
move(y)
endWhile
dtb23's suggestion of just picking a random direction at each corner, and eventually you'll find the monster-hole sounds horribly ineficient.
However you could make use of its inefficient return-to-home algorithm to make the game more fun by introducing more variation in the game difficulty. You'd do this by applying one of the above approaches such as your waypoints or the flood fill, but doing so non-deterministically. So at every corner, you could generate a random number to decide whether to take the optimal way, or a random direction.
As the player progresses levels, you reduce the likelihood that a random direction is taken. This would add another lever on the overall difficulty level in addition to the level speed, ghost speed, pill-eating pause (etc). You've got more time to relax while the ghosts are just harmless eyes, but that time becomes shorter and shorter as you progress.
Short answer, not very well. :) If you alter the Pac-man maze the eyes won't necessarily come back. Some of the hacks floating around have that problem. So it's dependent on having a cooperative maze.
I would propose that the ghost stores the path he has taken from the hole to the Pacman. So as soon as the ghost dies, he can follow this stored path in the reverse direction.
Knowing that pacman paths are non-random (ie, each specific level 0-255, inky, blinky, pinky, and clyde will work the exact same path for that level).
I would take this and then guess there are a few master paths that wraps around the entire
maze as a "return path" that an eyeball object takes pending where it is when pac man ate the ghost.
The ghosts in pacman follow more or less predictable patterns in terms of trying to match on X or Y first until the goal was met. I always assumed that this was exactly the same for eyes finding their way back.
Before the game begins save the nodes (intersections) in the map
When the monster dies take the point (coordinates) and find the
nearest node in your node list
Calculate all the paths beginning from that node to the hole
Take the shortest path by length
Add the length of the space between the point and the nearest node
Draw and move on the path
Enjoy!
My approach is a little memory intensive (from the perspective of Pacman era), but you only need to compute once and it works for any level design (including jumps).
Label Nodes Once
When you first load a level, label all the monster lair nodes 0 (representing the distance from the lair). Proceed outward labelling connected nodes 1, nodes connected to them 2, and so on, until all nodes are labelled. (note: this even works if the lair has multiple entrances)
I'm assuming you already have objects representing each node and connections to their neighbours. Pseudo code might look something like this:
public void fillMap(List<Node> nodes) { // call passing lairNodes
int i = 0;
while(nodes.count > 0) {
// Label with distance from lair
nodes.labelAll(i++);
// Find connected unlabelled nodes
nodes = nodes
.flatMap(n -> n.neighbours)
.filter(!n.isDistanceAssigned());
}
}
Eyes Move to Neighbour with Lowest Distance Label
Once all the nodes are labelled, routing the eyes is trivial... just pick the neighbouring node with the lowest distance label (note: if multiple nodes have equal distance, it doesn't matter which is picked). Pseudo code:
public Node moveEyes(final Node current) {
return current.neighbours.min((n1, n2) -> n1.distance - n2.distance);
}
Fully Labelled Example
For my PacMan game I made a somewhat "shortest multiple path home" algorithm which works for what ever labyrinth I provide it with (within my set of rules). It also works across them tunnels.
When the level is loaded, all the path home data in every crossroad is empty (default) and once the ghosts start to explore the labyrinth, them crossroad path home information keeps getting updated every time they run into a "new" crossroad or from a different path stumble again upon their known crossroad.
The original pac-man didn't use path-finding or fancy AI. It just made gamers believe there is more depth to it than it actually was, but in fact it was random. As stated in Artificial Intelligence for Games/Ian Millington, John Funge.
Not sure if it's true or not, but it makes a lot of sense to me. Honestly, I don't see these behaviors that people are talking about. Red/Blinky for ex is not following the player at all times, as they say. Nobody seems to be consistently following the player, on purpose. The chance that they will follow you looks random to me. And it's just very tempting to see behavior in randomness, especially when the chances of getting chased are very high, with 4 enemies and very limited turning options, in a small space. At least in its initial implementation, the game was extremely simple. Check out the book, it's in one of the first chapters.
I've got a manually created NavGraph in a 3D environment. I understand (and have implemented previously) an A* routine to find my way through the graph once you've 'got on the graph'.
What I'm interested in, is the most optimal way to get onto and 'off' the Graph.
Ex:
So the routine go's something like this:
Shoot a ray from the source to the destination, if theres nothing in the way, go ahead and just walk it.
if theres something in the way, we need to use the graph, so to get onto the graph, we need to find the closest visible node on the graph. (to do this, I previously sorted the graph based on the distance from the source, then fired rays from closet to furthest till i found one that didn't have an obstacle. )
Then run the standard A*...
Then 'exit' the graph, through the same method as we got on the graph (used to calculate the endpoint for the above A*) so I take and fire rays from the endpoint to the closest navgraph node.
so by the time this is all said and done, unless my navgraph is very dense, I've spent more time getting on/off the graph than I have calculating the path...
There has to be a better/faster way? (is there some kind of spacial subdivision trick?)
You could build a Quadtree of all the nodes, to quickly find the closest node from a given position.
It is very common to have a spatial subdivision of the world. Something like a quadtree or octree is common in 3D worlds, although you could overlay a grid too, or track arbitrary regions, etc. Basically it's a simple data-structures problem of giving yourself some sort of access to N navgraph nodes without needing an O(N) search to find where you are, and your choices tend to come down to some sort of tree or some sort of hash table.