diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..6b468b6 --- /dev/null +++ b/.gitignore @@ -0,0 +1 @@ +*.class diff --git a/pathfinding/AbstractNode.java b/pathfinding/AbstractNode.java new file mode 100644 index 0000000..70d2a14 --- /dev/null +++ b/pathfinding/AbstractNode.java @@ -0,0 +1,351 @@ +/* + Copyright (C) 2012 http://software-talk.org/ (developer@software-talk.org) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +package pathfinding; + +/** + * This class represents an AbstractNode. It has all the appropriate fields as well + * as getter and setter to be used by the A* algorithm. + *

+ *

+ * An AbstractNode has x- and y-coordinates and can be walkable or not. + * A previous AbstractNode may be set, as well as the + * fCosts, gCosts and hCosts. + *

+ *

+ * fCosts: gCosts + hCosts + *

+ * gCosts: calculated costs from start AbstractNode to this AbstractNode + *

+ * hCosts: estimated costs to get from this AbstractNode to end AbstractNode + *

+ *

+ * A subclass has to override the heuristic function + *

+ * sethCosts(AbstractNode endAbstractNode) + *

+ * @see ExampleNode#sethCosts(AbstractNode endNode) example Implementation using manhatten method + *

+ * + * @version 1.0 + */ +public abstract class AbstractNode { + + /** costs to move sideways from one square to another. */ + protected static final int BASICMOVEMENTCOST = 10; + /** costs to move diagonally from one square to another. */ + protected static final int DIAGONALMOVEMENTCOST = 14; + + private int xPosition; + private int yPosition; + private boolean walkable; + + // for pathfinding: + + /** the previous AbstractNode of this one on the currently calculated path. */ + private AbstractNode previous; + + /** weather or not the move from previous to this AbstractNode is diagonally. */ + private boolean diagonally; + + /** optional extra penalty. */ + private int movementPanelty; + + //private int fCosts; // g + h costs + + /** calculated costs from start AbstractNode to this AbstractNode. */ + private int gCosts; + + /** estimated costs to get from this AbstractNode to end AbstractNode. */ + private int hCosts; + + /** + * constructs a walkable AbstractNode with given coordinates. + * + * @param xPosition + * @param yPosition + */ + public AbstractNode(int xPosition, int yPosition) { + this.xPosition = xPosition; + this.yPosition = yPosition; + this.walkable = true; + this.movementPanelty = 0; + } + + /** + * returns weather or not the move from the previousAbstractNode was + * diagonally. If it is not diagonal, it is sideways. + * + * @return + */ + public boolean isDiagonaly() { + return diagonally; + } + + /** + * sets weather or not the move from the previousAbstractNode was + * diagonally. If it is not diagonal, it is sideways. + * + * @param isDiagonaly + */ + public void setIsDiagonaly(boolean isDiagonaly) { + this.diagonally = isDiagonaly; + } + + /** + * sets x and y coordinates. + * + * @param x + * @param y + */ + public void setCoordinates(int x, int y) { + this.xPosition = x; + this.yPosition = y; + } + + /** + * @return the xPosition + */ + public int getxPosition() { + return xPosition; + } + + /** + * @return the yPosition + */ + public int getyPosition() { + return yPosition; + } + + /** + * @return the walkable + */ + public boolean isWalkable() { + return walkable; + } + + /** + * @param walkable the walkable to set + */ + public void setWalkable(boolean walkable) { + this.walkable = walkable; + } + + /** + * returns the node set as previous node on the current path. + * + * @return the previous + */ + public AbstractNode getPrevious() { + return previous; + } + + /** + * @param previous the previous to set + */ + public void setPrevious(AbstractNode previous) { + this.previous = previous; + } + + /** + * sets a general penalty for the movement on this node. + * + * @param movementPanelty the movementPanelty to set + */ + public void setMovementPanelty(int movementPanelty) { + this.movementPanelty = movementPanelty; + } + + /** + * returns gCosts + hCosts. + *

+ * + * + * @return the fCosts + */ + public int getfCosts() { + return gCosts + hCosts; + } + + /** + * returns the calculated costs from start AbstractNode to this AbstractNode. + * + * @return the gCosts + */ + public int getgCosts() { + return gCosts; + } + + /** + * sets gCosts to gCosts plus movementPanelty + * for this AbstractNode. + * + * @param gCosts the gCosts to set + */ + private void setgCosts(int gCosts) { + this.gCosts = gCosts + movementPanelty; + } + + /** + * sets gCosts to gCosts plus movementPanelty + * for this AbstractNode given the previous AbstractNode as well as the basic cost + * from it to this AbstractNode. + * + * @param previousAbstractNode + * @param basicCost + */ + public void setgCosts(AbstractNode previousAbstractNode, int basicCost) { + setgCosts(previousAbstractNode.getgCosts() + basicCost); + } + + /** + * sets gCosts to gCosts plus movementPanelty + * for this AbstractNode given the previous AbstractNode. + *

+ * It will assume BASICMOVEMENTCOST as the cost from + * previousAbstractNode to itself if the movement is not diagonally, + * otherwise it will assume DIAGONALMOVEMENTCOST. + * Weather or not it is diagonally is set in the Map class method which + * finds the adjacent AbstractNodes. + * + * @param previousAbstractNode + */ + public void setgCosts(AbstractNode previousAbstractNode) { + if (diagonally) { + setgCosts(previousAbstractNode, DIAGONALMOVEMENTCOST); + } else { + setgCosts(previousAbstractNode, BASICMOVEMENTCOST); + } + } + + /** + * calculates - but does not set - g costs. + *

+ * It will assume BASICMOVEMENTCOST as the cost from + * previousAbstractNode to itself if the movement is not diagonally, + * otherwise it will assume DIAGONALMOVEMENTCOST. + * Weather or not it is diagonally is set in the Map class method which + * finds the adjacent AbstractNodes. + * + * @param previousAbstractNode + * @return gCosts + */ + public int calculategCosts(AbstractNode previousAbstractNode) { + if (diagonally) { + return (previousAbstractNode.getgCosts() + + DIAGONALMOVEMENTCOST + movementPanelty); + } else { + return (previousAbstractNode.getgCosts() + + BASICMOVEMENTCOST + movementPanelty); + } + } + + /** + * calculates - but does not set - g costs, adding a movementPanelty. + * + * @param previousAbstractNode + * @param movementCost costs from previous AbstractNode to this AbstractNode. + * @return gCosts + */ + public int calculategCosts(AbstractNode previousAbstractNode, int movementCost) { + return (previousAbstractNode.getgCosts() + movementCost + movementPanelty); + } + + /** + * returns estimated costs to get from this AbstractNode to end AbstractNode. + * + * @return the hCosts + */ + public int gethCosts() { + return hCosts; + } + + /** + * sets hCosts. + * + * @param hCosts the hCosts to set + */ + protected void sethCosts(int hCosts) { + this.hCosts = hCosts; + } + + /** + * calculates hCosts for this AbstractNode to a given end AbstractNode. + * Uses Manhatten method. + * + * @param endAbstractNode + */ + public abstract void sethCosts(AbstractNode endAbstractNode); + + + /* + * @return the movementPanelty + */ + private int getMovementPanelty() { + return movementPanelty; + } + + /** + * returns a String containing the coordinates, as well as h, f and g + * costs. + * + * @return + */ + @Override + public String toString() { + return "(" + getxPosition() + ", " + getyPosition() + "): h: " + + gethCosts() + " g: " + getgCosts() + " f: " + getfCosts(); + } + + /** + * returns weather the coordinates of AbstractNodes are equal. + * + * @param obj + * @return + */ + @Override + public boolean equals(Object obj) { + if (obj == null) { + return false; + } + if (getClass() != obj.getClass()) { + return false; + } + final AbstractNode other = (AbstractNode) obj; + if (this.xPosition != other.xPosition) { + return false; + } + if (this.yPosition != other.yPosition) { + return false; + } + return true; + } + + /** + * returns hash code calculated with coordinates. + * + * @return + */ + @Override + public int hashCode() { + int hash = 3; + hash = 17 * hash + this.xPosition; + hash = 17 * hash + this.yPosition; + return hash; + } + +} diff --git a/pathfinding/ExampleFactory.java b/pathfinding/ExampleFactory.java new file mode 100644 index 0000000..88edfdc --- /dev/null +++ b/pathfinding/ExampleFactory.java @@ -0,0 +1,30 @@ +/* + Copyright (C) 2012 http://software-talk.org/ (developer@software-talk.org) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +package pathfinding; + +/** + * A simple Factory for example nodes. + */ +public class ExampleFactory implements NodeFactory { + + @Override + public AbstractNode createNode(int x, int y) { + return new ExampleNode(x, y); + } + +} diff --git a/pathfinding/ExampleNode.java b/pathfinding/ExampleNode.java new file mode 100644 index 0000000..8332bf6 --- /dev/null +++ b/pathfinding/ExampleNode.java @@ -0,0 +1,41 @@ +/* + Copyright (C) 2012 http://software-talk.org/ (developer@software-talk.org) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +package pathfinding; + +/** + * A simple Example implementation of a Node only overriding the sethCosts + * method; uses manhatten method. + */ +public class ExampleNode extends AbstractNode { + + public ExampleNode(int xPosition, int yPosition) { + super(xPosition, yPosition); + // do other init stuff + } + + public void sethCosts(AbstractNode endNode) { + this.sethCosts((absolute(this.getxPosition() - endNode.getxPosition()) + + absolute(this.getyPosition() - endNode.getyPosition())) + * BASICMOVEMENTCOST); + } + + private int absolute(int a) { + return a > 0 ? a : -a; + } + +} diff --git a/pathfinding/ExampleUsage.java b/pathfinding/ExampleUsage.java new file mode 100644 index 0000000..b47bd1e --- /dev/null +++ b/pathfinding/ExampleUsage.java @@ -0,0 +1,43 @@ +/* + Copyright (C) 2012 http://software-talk.org/ (developer@software-talk.org) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +package pathfinding; + +import java.util.List; + +/** + * A simple example for the usage of this package. + * + * @see ExampleFactory + * @see ExampleNode + */ +public class ExampleUsage { + + /** + * @param args the command line arguments + */ + public static void main(String[] args) { + Map myMap = new Map(50, 50, new ExampleFactory()); + List path = myMap.findPath(0, 0, 40, 40); + + for (int i = 0; i < path.size(); i++) { + System.out.print("(" + path.get(i).getxPosition() + ", " + path.get(i).getyPosition() + ") -> "); + } + } + + +} diff --git a/pathfinding/LICENSE b/pathfinding/LICENSE new file mode 100644 index 0000000..94a9ed0 --- /dev/null +++ b/pathfinding/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/pathfinding/Map.java b/pathfinding/Map.java new file mode 100644 index 0000000..d06e355 --- /dev/null +++ b/pathfinding/Map.java @@ -0,0 +1,363 @@ +/* + Copyright (C) 2012 http://software-talk.org/ (developer@software-talk.org) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +/* + * // TODO + * possible optimizations: + * - calculate f as soon as g or h are set, so it will not have to be + * calculated each time it is retrieved + * - store nodes in openList sorted by their f value. + */ + +package pathfinding; + +import java.util.LinkedList; +import java.util.List; + +/** + * This class represents a simple map. + *

+ * It's width as well as hight can be set up on construction. + * The map can represent nodes that are walkable or not, it can be printed + * to sto, and it can calculate the shortest path between two nodes avoiding + * walkable nodes. + *

+ *

+ * Usage of this package: + * Create a node class which extends AbstractNode and implements the sethCosts + * method. + * Create a NodeFactory that implements the NodeFactory interface. + * Create Map instance with those created classes. + * @see ExampleUsage ExampleUsage + *

+ * + * @see AbstractNode + * @see NodeFactory + * @version 1.0 + * @param + */ +public class Map { + + /** weather or not it is possible to walk diagonally on the map in general. */ + protected static boolean CANMOVEDIAGONALY = true; + + /** holds nodes. first dim represents x-, second y-axis. */ + private T[][] nodes; + + /** width + 1 is size of first dimension of nodes. */ + protected int width; + /** higth + 1 is size of second dimension of nodes. */ + protected int higth; + + /** a Factory to create instances of specified nodes. */ + private NodeFactory nodeFactory; + + /** + * constructs a squared map with given width and hight. + *

+ * The nodes will be instanciated througth the given nodeFactory. + * + * @param width + * @param higth + * @param nodeFactory + */ + public Map(int width, int higth, NodeFactory nodeFactory) { + // TODO check parameters. width and higth should be > 0. + // TODO: Find the length of the track as the height + this.nodeFactory = nodeFactory; + nodes = (T[][]) new AbstractNode[width][higth]; + this.width = width - 1; + this.higth = higth - 1; + initEmptyNodes(); + } + + /** + * initializes all nodes. Their coordinates will be set correctly. + TODO: Edit this part + */ + private void initEmptyNodes() { + for (int i = 0; i <= width; i++) { + for (int j = 0; j <= higth; j++) { + nodes[i][j] = (T) nodeFactory.createNode(i, j); + } + } + } + + /** + * sets nodes walkable field at given coordinates to given value. + *

+ * x/y must be bigger or equal to 0 and smaller or equal to width/hight. + * + * @param x + * @param y + * @param bool + */ + public void setWalkable(int x, int y, boolean bool) { + // TODO check parameter. + nodes[x][y].setWalkable(bool); + } + + /** + * returns node at given coordinates. + *

+ * x/y must be bigger or equal to 0 and smaller or equal to width/hight. + * + * @param x + * @param y + * @return node + */ + public final T getNode(int x, int y) { + // TODO check parameter. + return nodes[x][y]; + } + + /** + * prints map to sto. Feel free to override this method. + *

+ * a player will be represented as "o", an unwakable terrain as "#". + * Movement penalty will not be displayed. + */ + public void drawMap() { + for (int i = 0; i <= width; i++) { + print(" _"); // boarder of map + } + print("\n"); + + for (int j = higth; j >= 0; j--) { + print("|"); // boarder of map + for (int i = 0; i <= width; i++) { + if (nodes[i][j].isWalkable()) { + print(" "); + } else { + print(" #"); // draw unwakable + } + } + print("|\n"); // boarder of map + } + + for (int i = 0; i <= width; i++) { + print(" _"); // boarder of map + } + } + + /** + * prints something to sto. + */ + private void print(String s) { + System.out.print(s); + } + + + /* Variables and methodes for path finding */ + + + // variables needed for path finding + + /** list containing nodes not visited but adjacent to visited nodes. */ + private List openList; + /** list containing nodes already visited/taken care of. */ + private List closedList; + /** done finding path? */ + private boolean done = false; + + /** + * finds an allowed path from start to goal coordinates on this map. + *

+ * This method uses the A* algorithm. The hCosts value is calculated in + * the given Node implementation. + *

+ * This method will return a LinkedList containing the start node at the + * beginning followed by the calculated shortest allowed path ending + * with the end node. + *

+ * If no allowed path exists, an empty list will be returned. + *

+ *

+ * x/y must be bigger or equal to 0 and smaller or equal to width/hight. + * + * @param oldX + * @param oldY + * @param newX + * @param newY + * @return + */ + public final List findPath(int oldX, int oldY, int newX, int newY) { + // TODO check input + openList = new LinkedList(); + closedList = new LinkedList(); + openList.add(nodes[oldX][oldY]); // add starting node to open list + + done = false; + T current; + while (!done) { + current = lowestFInOpen(); // get node with lowest fCosts from openList + closedList.add(current); // add current node to closed list + openList.remove(current); // delete current node from open list + + if ((current.getxPosition() == newX) + && (current.getyPosition() == newY)) { // found goal + return calcPath(nodes[oldX][oldY], current); + } + + // for all adjacent nodes: + List adjacentNodes = getAdjacent(current); + for (int i = 0; i < adjacentNodes.size(); i++) { + T currentAdj = adjacentNodes.get(i); + if (!openList.contains(currentAdj)) { // node is not in openList + currentAdj.setPrevious(current); // set current node as previous for this node + currentAdj.sethCosts(nodes[newX][newY]); // set h costs of this node (estimated costs to goal) + currentAdj.setgCosts(current); // set g costs of this node (costs from start to this node) + openList.add(currentAdj); // add node to openList + } else { // node is in openList + if (currentAdj.getgCosts() > currentAdj.calculategCosts(current)) { // costs from current node are cheaper than previous costs + currentAdj.setPrevious(current); // set current node as previous for this node + currentAdj.setgCosts(current); // set g costs of this node (costs from start to this node) + } + } + } + + if (openList.isEmpty()) { // no path exists + return new LinkedList(); // return empty list + } + } + return null; // unreachable + } + + /** + * calculates the found path between two points according to + * their given previousNode field. + * + * @param start + * @param goal + * @return + */ + private List calcPath(T start, T goal) { + // TODO if invalid nodes are given (eg cannot find from + // goal to start, this method will result in an infinite loop!) + LinkedList path = new LinkedList(); + + T curr = goal; + boolean done = false; + while (!done) { + path.addFirst(curr); + curr = (T) curr.getPrevious(); + + if (curr.equals(start)) { + done = true; + } + } + return path; + } + + /** + * returns the node with the lowest fCosts. + * + * @return + */ + private T lowestFInOpen() { + // TODO currently, this is done by going through the whole openList! + T cheapest = openList.get(0); + for (int i = 0; i < openList.size(); i++) { + if (openList.get(i).getfCosts() < cheapest.getfCosts()) { + cheapest = openList.get(i); + } + } + return cheapest; + } + + /** + * returns a LinkedList with nodes adjacent to the given node. + * if those exist, are walkable and are not already in the closedList! + */ + private List getAdjacent(T node) { + // TODO make loop + int x = node.getxPosition(); + int y = node.getyPosition(); + List adj = new LinkedList(); + + T temp; + if (x > 0) { + temp = this.getNode((x - 1), y); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(false); + adj.add(temp); + } + } + + if (x < width) { + temp = this.getNode((x + 1), y); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(false); + adj.add(temp); + } + } + + if (y > 0) { + temp = this.getNode(x, (y - 1)); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(false); + adj.add(temp); + } + } + + if (y < higth) { + temp = this.getNode(x, (y + 1)); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(false); + adj.add(temp); + } + } + + + // add nodes that are diagonaly adjacent too: + if (CANMOVEDIAGONALY) { + if (x < width && y < higth) { + temp = this.getNode((x + 1), (y + 1)); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(true); + adj.add(temp); + } + } + + if (x > 0 && y > 0) { + temp = this.getNode((x - 1), (y - 1)); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(true); + adj.add(temp); + } + } + + if (x > 0 && y < higth) { + temp = this.getNode((x - 1), (y + 1)); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(true); + adj.add(temp); + } + } + + if (x < width && y > 0) { + temp = this.getNode((x + 1), (y - 1)); + if (temp.isWalkable() && !closedList.contains(temp)) { + temp.setIsDiagonaly(true); + adj.add(temp); + } + } + } + return adj; + } + +} diff --git a/pathfinding/NodeFactory.java b/pathfinding/NodeFactory.java new file mode 100644 index 0000000..a58c58c --- /dev/null +++ b/pathfinding/NodeFactory.java @@ -0,0 +1,44 @@ +/* + Copyright (C) 2012 http://software-talk.org/ (developer@software-talk.org) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +package pathfinding; + +/** + * A Factory which creates new instances of an implementation of the + * AbstractNode at given coordinates. + *

+ * Must be implemented and given to Map instance on + * construction. + * + * @see AbstractNode + * @version 1.0 + */ +public interface NodeFactory { + + /** + * creates new instances of an implementation of the + * AbstractNode. + * In an implementation, it should return a new node with its position + * set to the given x and y values. + * + * @param x position on the x-axis + * @param y position on the y-axis + * @return + */ + public AbstractNode createNode(int x, int y); + +} diff --git a/pathfinding/package-info.java b/pathfinding/package-info.java new file mode 100644 index 0000000..b0669ed --- /dev/null +++ b/pathfinding/package-info.java @@ -0,0 +1,24 @@ +/* + Copyright (C) 2012 http://software-talk.org/ (developer@software-talk.org) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . +*/ + +/** + * This package may be used for its A* pathfinding algorithm. + * Extend the AbstractNode class as you need, but also implement the gethCosts + * method with a heuristic. + * The Map class may be extended as well. + */ +package pathfinding;