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| /*
===========================================================================
======================== A* (A Star) algorithm ============================
===========================================================================
====== INFORMATIONS:
======
====== Version 1.0b - August 2008
====== By Mael Nison (nison_m@epitech.net), for the Kyria Project
======
====== The main comments (functions descriptions, readme, ...) are in
====== english, but single-line comments are in french.
===========================================================================
====== NOTES:
======
====== #1: The lists are under a special shape, because we need to destroy
====== elements by their keys.
======
====== #2: The response of the getBetterNode() function is under the shape:
====== [ID of the best node, content of the best node]
====== The best node is directly put in the black list.
===========================================================================
====== CONFIGURATION OPTIONS (second parameter of the constructor):
======
====== -- iterations --
====== Maximal number of nodes which will be read. Usefull for big maps.
====== Default value is the width of the map by its height (width*height).
====== You don't have to use an upper value, but you can use a lowest. As
====== you want ...
======
====== -- debug --
====== If set on 'true', display some information on the screen. You can use it
====== if you want to know how A* works. Default value is false.
======
====== -- ondbg --
====== Function called when a debug text must be displayed
======
====== -- diagonal --
====== If set on 'true', A* will check diagonal nodes (a). If set on 'false',
====== it will only check the closest nodes (b).
====== a. + + + b. X + X
====== + O + + 0 +
====== + + + X + X
====== Default value is false. If you want to use it, you may need
====== to change the heuristic (look underneath).
======
====== -- cost --
====== It's a function which is called to get the cost of the current node.
====== Default is: function(obj, fromX, fromY, toX, toY) { return obj.map[toY][toX]; }
====== (obj is the Pathfinder object)
======
====== -- heuristic --
====== It's a function called to get an approximative value from the current
====== node to the end of the path. Default value is the Manhattan heuristic.
======
====== -- wall --
====== Function called to check if the current node is a wall. It return a boolean.
===========================================================================
*/
/*
===========================================================================
====== [Object] Astar(map, [, configuration]);
======
====== It's the constructor of the class. It don't return anything else
====== than itself.
======
====== @map must be an array which contain other arrays. These arrays must
====== have the same length.
======
====== @configuration is an optionnal argument. It's an object. All pairs
====== of key/value will be copied in the configuration array. See the main
====== documentation for more information.
===========================================================================
*/
function AStar(map) {
this.map = map;
this.height = map.length;
this.width = map[0].length;
this.configuration.iterations = this.height*this.width;
if(arguments.length > 1) {
for(var key in arguments[1]) {
this.configuration[key] = arguments[1][key];
}
}
}
AStar.prototype.configuration = {iterations:Number.MAX_VALUE,debug:false,diagonal:false,cost:function(obj, fromX, fromY, toX, toY) { return obj.map[toY][toX]; },heuristic:function(obj, x, y) { return ( Math.abs(obj.endX - x) + Math.abs(obj.endY - y) ); },wall:function(obj, fromX, fromY, toX, toY) { return false; },ondbg:function(text) { document.write(text); }};
AStar.prototype.black = new Array();
AStar.prototype.white = new Array();
AStar.prototype.startX = 0;
AStar.prototype.startY = 0;
AStar.prototype.endX = 0;
AStar.prototype.endY = 0;
/*
===========================================================================
====== [Array] AStar.process(startX, startY, endX, endY);
======
====== Use this function to get the best path between two nodes. Its
====== response will be an array. The first item will be the global
====== deplacement cost, the second will be the path used, and the third
====== will be the error number. This last item is in the array only if none
====== paths has been found.
====== 1 = The maximal number of iterations has been reach (often, if you
====== had put a low iteration number in the configuration)
====== 2 = All nodes have been checked, and there is no path to go to the
====== end node. (you can have this error if the start or the end nodes
====== are outside the map)
======
====== @startX and @startY are the cartesians positions of the start node.
====== @endX and @endY are the cartesians positions of the end node.
===========================================================================
*/
AStar.prototype.process = function(startX,startY,endX,endY){
// On convertis les valeur entrées en paramètre afin qu'elles soient de type INT (sinon, erreurs avec les chaînes de caractères)
startX = parseInt(startX);
startY = parseInt(startY);
endX = parseInt(endX);
endY = parseInt(endY);
// Au cas où la position de départ est la même que celle d'arrivée on ne lance PAS l'algorithme (sinon, bug) et on calcule directement le chemin
if(startX == endX && startY == endY) return [this.cost(startX, startY, startX, startY, true), [[startX,startY]]];
// On met à zéro le nombre d'itérations
var iters = 0;
// On nettoie les listes (#1)
this.white = {length:0,id:0,array:{},push:function(element){this.array[this.id]=element; this.id++; this.length++; return this.id-1; },remove:function(id){delete this.array[id]; this.length--;}};
this.black = {length:0,id:0,array:{},push:function(element){this.array[this.id]=element; this.id++; this.length++; return this.id-1; },remove:function(id){delete this.array[id]; this.length--;}};
// On enregistre les paramètres du parcours
this.startX = startX;
this.startY = startY;
this.endX = endX;
this.endY = endY;
// On ajoute la case de départ à la liste ouverte
this.white.push(this.node(-1, startX, startY));
// On boucle tant qu'il y a des éléments dans la liste ouverte
while(iters < this.configuration.iterations && this.white.length > 0) {
// On incrémente le nombre d'itérations (ne fait pas partie de l'algorithme en lui-même...il s'agit juste d'une protection pour éviter les boucles infinies)
iters++;
// On récupère la case avec le plus petit coût F et on la transfère dans la liste noire (#2)
var node = this.getBetterNode();
if(this.configuration.debug) this.configuration.ondbg("Noeud lu: X:"+node[1].x+" Y:"+node[1].y+" F:"+node[1].F+" G:"+node[1].G+" H:"+node[1].H+" PARENT:"+node[1].parent+"<br />");
// On vérifie que cette case ne soit pas la case finale (auquel cas on quitte la boucle)
if(node[1].x == endX && node[1].y == endY) {
if(this.configuration.debug) this.configuration.ondbg('<br />Chemin trouvé !<br />');
var parent = node[0];
var path = new Array();
do {
if(this.configuration.debug) this.configuration.ondbg(' Passage par #'+parent+', X:'+this.black.array[parent].x+' Y:'+this.black.array[parent].y+' (parent: #'+this.black.array[parent].parent+')<br>');
path[path.length] = [this.black.array[parent].x, this.black.array[parent].y];
parent = this.black.array[parent].parent;
} while(parent >= 0);
var reversePath = new Array();
for(var t=0; t<path.length; t++) {
reversePath[t] = path[path.length-1-t];
}
return [node[1].G+this.cost(this.black.array[node[1].parent].x, this.black.array[node[1].parent].y, endX, endY, true), reversePath];
}
// On vérifie les quatres cases alentours
this.check(node[0], node[1].x+0, node[1].y-1); // En haut
this.check(node[0], node[1].x+0, node[1].y+1); // En bas
this.check(node[0], node[1].x-1, node[1].y+0); // A gauche
this.check(node[0], node[1].x+1, node[1].y+0); // A droite
// Plus les quatres cases diagonale, si l'option à été activée
if(this.configuration.diagonal) {
this.check(node[0], node[1].x+1, node[1].y-1); // En haut à droite
this.check(node[0], node[1].x-1, node[1].y+1); // En bas à gauche
this.check(node[0], node[1].x+1, node[1].y+1); // En bas à droite
this.check(node[0], node[1].x-1, node[1].y-1); // En haut à gauche
}
if(this.configuration.debug) this.configuration.ondbg('<br>');
}
// On calcule le code d'erreur
if(iters == this.configuration.iterations) {
var errCode = 1;
} else if(this.white.length == 0) {
var errCode = 2;
} else {
var errCode = -1;
}
// Si aucun chemin n'a été trouvé, on renvois un triplet contenant false et le code d'erreur de l'algorithme
return [false, false, errCode];
}
/*
===========================================================================
====== *** PRIVATE FUNCTION, YOU DON'T HAVE TO USE IT ***
======
====== [Void] AStar.check(parent, x, y);
======
====== If necessary, add the checked node to the white list.
======
====== @parent is the parent node of the checked node.
====== @x and @y are the cartesians positions of the checked node.
===========================================================================
*/
AStar.prototype.check = function(parent, x, y){
// On vérifie que la case existe dans la carte (qu'elle ne soit pas en dehors de la zone) et qu'elle ne soit pas un bloc
if(x>=0 && x<this.width && y>=0 && y<this.height && !this.configuration.wall(this, this.black.array[parent].x, this.black.array[parent].y, x, y)) {
var id = this.exist("white", x, y);
if(typeof(id) != "boolean") {
if(this.white.array[id].G > this.black.array[parent].G+this.cost(this.black.array[parent].x, this.black.array[parent].y, x, y, false)){
this.white.array[id].G = this.black.array[parent].G+this.cost(this.black.array[parent].x, this.black.array[parent].y, x, y, false);
this.white.array[id].F = this.white.array[id].G + this.white.array[id].H;
this.white.array[id].parent = parent;
if(this.configuration.debug) this.configuration.ondbg(" Noeud modifié ("+id+"): X:"+x+" Y:"+y+" F:"+this.white.array[id].F+" G:"+this.white.array[id].G+" H:"+this.white.array[id].H+" PARENT:"+parent+"<br />");
}
} else if(typeof(this.exist("black", x, y))=="boolean") {
var node = this.node(parent, x, y);
var id = this.white.push(node);
if(this.configuration.debug) this.configuration.ondbg(" Noeud ajouté ("+id+"): X:"+x+" Y:"+y+" F:"+node.F+" G:"+node.G+" H:"+node.H+" PARENT:"+parent+"<br />");
}
} else if(this.configuration.debug) this.configuration.ondbg(' Refus d\'accèder à la case '+x+', '+y+'<br>');
}
/*
===========================================================================
====== *** PRIVATE FUNCTION, YOU DON'T HAVE TO USE IT ***
======
====== [Integer/Boolean] AStar.exist(type, x, y);
======
====== Return 'false' if a node with specified positions exist in the @type
====== list. Else, return the ID of the node matched. You may need a typeof
====== to get the real response of this function (it can return 0 or 'false').
======
====== @type is the list where the search will be perform (can be "white"
====== or "black").
===========================================================================
*/
AStar.prototype.exist = function(type, x, y) {
var test = (type=="white") ? this.white : this.black;
var result = false;
for(var tmp in test.array) {
if(test.array[tmp].x == x && test.array[tmp].y == y){
result = tmp;
break;
}
}
return result;
}
/*
===========================================================================
====== *** PRIVATE FUNCTION, YOU DON'T HAVE TO USE IT ***
======
====== [Array] AStar.node(parent, x, y);
======
====== Build a node.
======
====== @parent is the parent node of the node to build
====== @x and @y are the cartesians positions of the node to build.
===========================================================================
*/
AStar.prototype.node = function(parent, x, y){
if(parent >= 0) {
var oldCost = this.black.array[parent].G;
var oldx = this.black.array[parent].x;
var oldy = this.black.array[parent].y;
} else {
var oldCost = 0;
var oldx = x;
var oldy = y;
}
var node = {}
node.x = x;
node.y = y;
node.G = oldCost + this.cost(oldx, oldy, x, y, false);
node.H = this.heuristic(x, y);
node.F = node.G + node.H;
node.parent = parent;
return node;
}
/*
===========================================================================
====== *** PRIVATE FUNCTION, YOU DON'T HAVE TO USE IT ***
======
====== [Integer] AStar.cost(fromX, fromY, toX, toY [, real=false]);
======
====== Return the cost to go onto the targeted node (use the cost
====== configuration callback).
======
====== @fromX and @fromY are the cartesians positions of the parent of the
====== node looked.
====== @toX and @toY are the cartesians positions of the node looked.
====== @real is egal to 'false' if the end node of the path must always
====== return 0.
===========================================================================
*/
AStar.prototype.cost = function(fromX, fromY, toX, toY, real) {
if(typeof(real)=="undefined") var real = false;
return (toX!=this.endX || toY!=this.endY || real) ? this.configuration.cost(this, fromX, fromY, toX, toY) : 0;
}
/*
===========================================================================
====== *** PRIVATE FUNCTION, YOU DON'T HAVE TO USE IT ***
======
====== [Array] AStar.heuristic(x, y);
======
====== Call the heuristic configuration callback.
======
====== @x and @y are the cartesians positions of the node looked.
===========================================================================
*/
AStar.prototype.heuristic = function(x, y) {
return this.configuration.heuristic(this, x, y);
}
/*
===========================================================================
====== *** PRIVATE FUNCTION, YOU DON'T HAVE TO USE IT ***
======
====== [Array] AStar.getBetterNode( [Void] );
======
====== Return the node with the lowest F cost in the white list, and move it
====== into the black list. If you need to make references to this node
====== after, you must call it in the black list, not in the white.
===========================================================================
*/
AStar.prototype.getBetterNode = function(){
var min = Number.MAX_VALUE;
var id = false;
for(var tmp in this.white.array) {
if(this.white.array[tmp].F <= min) {
min = this.white.array[tmp].F;
id = tmp;
}
}
this.black.array[id] = this.white.array[id];
this.white.remove(id);
return new Array(id, this.black.array[id]);
} |
A* (aka Astar)
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