Path Finder in a 2D Grid Map With Different Terrain Types

Question

     I have been thinking for a while on path finding game algoritms and I can up with one idea witch I want to publish. The goal of my project is when I have a 2 dimensional grid map where squares can have different movement cost, like in Civilization II, to find the shortest way from one point in the map to another. I've used the Breathed First Search Engine. If you are not familiar to this search engine it is better to read about it first because I am not fcusing on it and I assume that you now how it works. You can read about it at the book "Practical Artificial Intelligence Programming in Java" writen by Mark Watson, witch is freely distributed at www.markwatson.com.
     Actually the idea of this 2D grid path finder is to use a third dimension witch have a size equal to the highest movement cost among all terrain types. This helps solving the problem with the different movement cost of the squates. By adding this abstract third dimension it is posible to use the Breadth First Search Engine.
     I this example the movementcost of a terrain type is always the same, no matter from witch square to with are you going (like in Civilization II but I haven't included roads or railroads). For example if you want to go from one square A to another square B with movement cost X (A and B are attached) you must go "up stairs" in the third dimension X - 1 times and then move to square B. But when you step on square B you are again at the lowest floor. So if you want to come back to the previous square A and it have movement cost Y first you must go floor Y and then jump in square A. And now you are again at the lowest floor at square A. When you move from one square to another you go always at the lowest floor. This is the way I handle with different movement costs.
     When you find the path to the goal point it is in 3 dimensions. So you must just project it in the 2D map and that's all you have the shortest path.
     I am sure this is not the best way to code this search engine but this is just the first scratch with no optimisation and so on. If I make a 100x100 randomly generated map it takes on my configuration(400Mhz Pentium II CPU with ASUS P2B MotherBoard on 100 MHz and 256 MB SD RAM on 133 MHz but because of my MB on 100MHz) around 1000 miliseconds (1000 miliseconds = 1 second) to find the shortest path from (1, 1) to (100, 100) witch is pretty good compare to the goTo function in Civilization II witch does not finds the shortest path at all and have made hundrets of gamers angry. This is amazing that nowadays there are so many games with bad path finding.
     This project includes:
1. The PathFinder class witch does the jub.
2. The Map class witch has a generator for a random map in it.
3. The class TerrainType, every square on the map is based on this class.
4. The class TerrainTypes witch is the set of all terrain types used in the map.
5. The class PathFinderTest witch just test the path finder.
To test this project put all files in one directory and run PathFinderTest.java.
Map.java:
import java.util.Vector;
import java.util.Random;
//This class just creates a random map and keeps it. I will not comment on this.
class Map {
  //here is kept the information about the terrain types placed in the map. Where
  //every terrain type has a specific movement cost.
  private int[][] terrain;
  public TerrainTypes terrainTypes;
  private int landMass;
  private int width;
  private int height;
  private int highestMovementCost;
  public Map(int aWidth, int aHeight) {
    width = aWidth;
    height = aHeight;
    terrainTypes = new TerrainTypes();
    highestMovementCost = terrainTypes.getHighestMovementCost();
    terrain = new int[width][height];
    landMass = 0;
    generateRandomMap();
  public void clearGoalAndStartLocFromWater(int sx, int sy, int gx, int gy) {
    terrain[gx][gy] = 0;
    terrain[sx][sy] = 0;
  private void expandWater() {
    int waterConstant = 40;
    int waterExpansion = 2;
    int[][] moreWater = new int[width][height];
    Random randomizer = new Random();
    for (int t = 0; waterExpansion > t; t++) {
      for (int i = 0; i < width; i++) {
        for (int j = 0; j < height; j++) {
          if (i + 1 >= 0 && j >= 0 && i + 1 < width && j < height) {
            if (terrain[i + 1][j] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i + 1][j] = 1;
          if (i + 1 >= 0 && j - 1 >= 0 && i + 1 < width && j - 1 < height) {
            if (terrain[i + 1][j - 1] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i + 1][j - 1] = 1;
          if (i >= 0 && j - 1 >= 0 && i < width && j - 1 < height) {
            if (terrain[i][j - 1] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i][j - 1] = 1;
          if (i - 1 >= 0 && j - 1 >= 0 && i - 1 < width && j - 1 < height) {
            if (terrain[i - 1][j - 1] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i - 1][j - 1] = 1;
          if (i - 1 >= 0 && j >= 0 && i - 1 < width && j < height) {
            if (terrain[i - 1][j] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i - 1][j] = 1;
          if (i - 1 >= 0 && j + 1 >= 0 && i - 1 < width && j + 1 < height) {
            if (terrain[i - 1][j + 1] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i - 1][j + 1] = 1;
          if (i >= 0 && j + 1 >= 0 && i < width && j + 1 < height) {
            if (terrain[i][j + 1] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i][j + 1] = 1;
          if (i + 1 >= 0 && j + 1 >= 0 && i + 1 < width && j + 1 < height) {
            if (terrain[i + 1][j + 1] != 4) {
              if (randomizer.nextInt(waterConstant) == 0)
                moreWater[i + 1][j + 1] = 1;
    for (int i = 0; i < width; i++) {
      for (int j = 0; j < height; j++) {
        if (moreWater[i][j] == 1) {
          terrain[i][j] = 4;
  private void generateRandomMap() {
    Random randomizer = new Random();
    for (int i = 0; i < width; i++) {
      for (int j = 0; j < height; j++) {
        if (randomizer.nextInt(3) == 1)
          terrain[i][j] = 0;
        else if (randomizer.nextInt(2) == 1)
          terrain[i][j] = 1;
        else if (randomizer.nextInt(2) == 1)
          terrain[i][j] = 3;
        else if (randomizer.nextInt(2) == 1)
          terrain[i][j] = 2;
        else if (randomizer.nextInt(2) == 1)
          terrain[i][j] = 2;
        else if (randomizer.nextInt(2) == 1)
          terrain[i][j] = 1;
        else if (randomizer.nextInt(2) == 1)
          terrain[i][j] = 3;
        else
          terrain[i][j] = randomizer.nextInt(5);
    expandWater();
    for (int i = 0; i < width; i++) {
      for (int j = 0; j < height; j++) {
        if (terrain[i][j] != 0)
          landMass++;
  public int getMapHeight() {
    return height;
  public int getMapWidth() {
    return width;
  public int getSquareID(int x, int y) {
    return terrain[x][y];
  public int getSquareMovementCost(int x, int y) {
    return terrainTypes.getMovementCost(terrain[x][y]);
}PathFinder.java:
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Vector;
public class PathFinder {
  private BufferedReader consoleReader = new BufferedReader(new InputStreamReader(System.in));
  //The array t3D[][] represents the 2D square map where t3D.leght = map width
  //and t3D[x].lenght = map width (-1 < x < t3D.leght). The third dimension
  //is refered to the square's movement cost, witch is definite by terrain.
  //The fourth dimension will be with lenght = 3. When running the search engine
  //(expanding the explored squares) this 3 values will keep the position of
  //the previous square in 3 dimension, witch are width, height and the maximum
  //movement cost among all squares.
  private int[][][][] squares3DReference;
  //Keeps information witch squares are visited.
  private boolean[][][] visitedSquares;
  private Map map;
  //this is the queue used in the Breathed First Seatch.
  private Vector queue3D;
  //Here is saved the shortest path
  private Vector path2D;
  private int highestMovementCost;
  public PathFinder(Map aMap) {
    map = aMap;
    queue3D = new Vector();
    path2D = new Vector();
    squares3DReference = new int[map.getMapWidth()][map.getMapHeight()][][];
    visitedSquares = new boolean[map.getMapWidth()][map.getMapHeight()][];
    highestMovementCost = map.terrainTypes.getHighestMovementCost();
    buildAbstract3DTerrain();
  private void buildAbstract3DTerrain() {
    for (int x = 0; x < map.getMapWidth(); x++) {
      for (int y = 0; y <map.getMapHeight(); y++) {
        int movementCost = map.terrainTypes.getMovementCost(map.getSquareID(x, y));
        if ( movementCost > 0) {
          visitedSquares[x][y] = new boolean[highestMovementCost];
          squares3DReference[x][y] = new int[highestMovementCost][3];
          for (int z = 0; z < highestMovementCost; z++) {
            for (int t = 0; t < 3; t++) {
              squares3DReference[x][y][z][t] = -1;
  private boolean isMoveValid(int x, int y, int z, int x2, int y2, int z2) {
    if ( x < 0 || y < 0 || z < 0 || x2 < 0 || y2 < 0 || z2 < 0 || x >= map.getMapWidth() || y >= map.getMapHeight() || z >= highestMovementCost ||  x2 >= map.getMapWidth() || y2 >= map.getMapHeight() || z2 >= highestMovementCost)
      return false;
    if (map.terrainTypes.getMovementCost(map.getSquareID(x2, y2)) < 1)
      return false;
    if (visitedSquares[x2][y2][z2])
      return false;
    if (x == x2 && y == y2)
      return true;
    else {
      if (z == map.terrainTypes.getMovementCost(map.getSquareID(x2, y2)) - 1)
        return true;
      else
        return false;
  private void clearPreviousSearchData() {
    queue3D.clear();
    path2D.clear();
    for (int x = 0; x < map.getMapWidth(); x++) {
      for (int y = 0; y < map.getMapHeight(); y++) {
        if (squares3DReference[x][y] != null) {
          for (int z = 0; z < highestMovementCost; z++) {
            visitedSquares[x][y][z] = false;
            for (int t = 0; t < 3; t++) {
              squares3DReference[x][y][z][t] = -1;
  private Vector copyPath2D() {
    Vector path = new Vector();
    for (int i = 0; i < path2D.size(); i++) {
      path.add(path2D.get(i));
    return path;
  public Vector findPath(int sX, int sY, int gX, int gY) {
    int head = 0;
    int tail = 0;
    int x = sX;
    int y = sY;
    int z = 0;
    visitedSquares[x][y][z] = true;
    mainLoop: {
      while (tail <= head) {
        int[][] moves = getPosibleMoves(x, y, z);
        for (int i = 0; i < 9; i++) {
          if (moves[i] != null) {
            squares3DReference[moves[0]][moves[i][1]][moves[i][2]][0] = x;
squares3DReference[moves[i][0]][moves[i][1]][moves[i][2]][1] = y;
squares3DReference[moves[i][0]][moves[i][1]][moves[i][2]][2] = z;
queue3D.add(moves[i]);
if (moves[i][0] == gX && moves[i][1] == gY) {
break mainLoop;
visitedSquares[moves[i][0]][moves[i][1]][moves[i][2]] = true;
head++;
if (queue3D.size() == 0 || queue3D.size() == tail)
break mainLoop;
int[] nextInQueue = ((int[]) queue3D.get(tail));
x = nextInQueue[0];
y = nextInQueue[1];
z = nextInQueue[2];
tail++;
if (squares3DReference[gX][gY][0][0] == -1) {
clearPreviousSearchData();
return path2D;
fillpath2D(sX, sY, gX, gY);
Vector path = copyPath2D();
clearPreviousSearchData();
return path;
private int[][] getPosibleMoves(int x, int y, int z) {
int[][] moves = new int[9][3];
if (isMoveValid(x, y, z, x + 1, y, 0)) {
moves[0][0] = x + 1;
moves[0][1] = y;
moves[0][2] = 0;
else
moves[0] = null;
if (isMoveValid(x, y, z, x + 1, y - 1, 0)) {
moves[1][0] = x + 1;
moves[1][1] = y - 1;
moves[1][2] = 0;
else
moves[1] = null;
if (isMoveValid(x, y, z, x, y - 1, 0)) {
moves[2][0] = x;
moves[2][1] = y - 1;
moves[2][2] = 0;
else
moves[2] = null;
if (isMoveValid(x, y, z, x - 1, y - 1, 0)) {
moves[3][0] = x - 1;
moves[3][1] = y - 1;
moves[3][2] = 0;
else
moves[3] = null;
if (isMoveValid(x, y, z, x - 1, y, 0)) {
moves[4][0] = x - 1;
moves[4][1] = y;
moves[4][2] = 0;
else
moves[4] = null;
if (isMoveValid(x, y, z, x - 1, y + 1, 0)) {
moves[5][0] = x - 1;
moves[5][1] = y + 1;
moves[5][2] = 0;
else
moves[5] = null;
if (isMoveValid(x, y, z, x, y + 1, 0)) {
moves[6][0] = x;
moves[6][1] = y + 1;
moves[6][2] = 0;
else
moves[6] = null;
if (isMoveValid(x, y, z, x + 1, y + 1, 0)) {
moves[7][0] = x + 1;
moves[7][1] = y + 1;
moves[7][2] = 0;
else
moves[7] = null;
if (isMoveValid(x, y, z, x, y, z + 1)) {
moves[8][0] = x;
moves[8][1] = y;
moves[8][2] = z + 1;
else
moves[8] = null;
return moves;
private void fillpath2D(int sX, int sY, int gX, int gY) {
int[] gLoc = {gX, gY};
path2D.add(gLoc);
int x = gX;
int y = gY;
int z = 0;
while (x != sX || y != sY) {
int x2 = squares3DReference[x][y][z][0];
int y2 = squares3DReference[x][y][z][1];
int z2 = squares3DReference[x][y][z][2];
x = x2;
y = y2;
z = z2;
if (z == 0) {
int[] loc = {x, y};
path2D.insertElementAt(loc, 0);
PathFinderTest.java
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Vector;
public class PathFinderTest {
  static BufferedReader consoleReader = new BufferedReader(new InputStreamReader(System.in));
  static Map map;
  static int startX;
  static int startY;
  static int goalX;
  static int goalY;
  public static void main(String[] args) throws Exception {
    System.out.print("Enter map size.\nx = ");
    int width = Integer.parseInt(consoleReader.readLine());
    System.out.print("y = ");
    int height = Integer.parseInt(consoleReader.readLine());
    System.out.print("Enter strting location.\nx = ");
    startX = Integer.parseInt(consoleReader.readLine()) - 1;
    System.out.print("y = ");
    startY = Integer.parseInt(consoleReader.readLine()) - 1;
    System.out.print("Enter goal location.\nx = ");
    goalX = Integer.parseInt(consoleReader.readLine()) - 1;
    System.out.print("y = ");
    goalY = Integer.parseInt(consoleReader.readLine()) - 1;
    if (goalX < 0 || goalY < 0 || startX < 0 || startY < 0 || goalX >= width || goalY >= height || startX >= width || startY >= height) {
      System.out.println("Invalid parameters found. Program will exit");
      System.exit(0);
    map = new Map(width, height);
    map.clearGoalAndStartLocFromWater(startX, startY, goalX, goalY);
    printSolution(new Vector());
    PathFinder pathFinder = new PathFinder(map);
    long before = System.currentTimeMillis();
    Vector path = pathFinder.findPath(startX, startY, goalX, goalY);
    long after = System.currentTimeMillis();
    long time = after - before;
    printSolution(path);
    if (path.size() == 0)
      System.out.println("No path found.");
    else
      System.out.println("Path found.");
    System.out.println("Finding the path took " + time + " milliseconds");
  static void printSolution(Vector path) {
    boolean[][] pathOnMap = new boolean[map.getMapWidth()][map.getMapHeight()];
    for (int i = 0; path.size() > i; i++) {
      int[] move = (int[]) path.get(i);
      pathOnMap[move[0]][move[1]] = true;
    for (int y = 0; y < map.getMapHeight(); y++) {
      for (int x = 0; x < map.getMapWidth(); x++) {
        System.out.print(" ");
        if (pathOnMap[x][y] == false)
          System.out.print(" ");
        else
          System.out.print("0");
        if (x == startX && y == startY)
          System.out.print("S");
        else if (x == goalX && y == goalY)
          System.out.print("G");
        else
          System.out.print(map.terrainTypes.getNameFirstLetter(map.getSquareID(x, y)));
      System.out.println();
    System.out.println();
}TerrainType.java:
public class TerrainType {
  private int movementCost;
  private String name;
  TerrainType(int aMovementCost, String aName) {
    movementCost = aMovementCost;
    name = aName;
  public int getMovementCost() {
    return movementCost;
  public String getName() {
    return name;
  public String getNameFirstLetter() {
    return name.substring(0, 1).toUpperCase();
}TerrainTypes.java:
import java.util.Vector;
public class TerrainTypes {
  //Here are saved the terrain types with the map has. ElementAt 'i' in
  //setOfTypes is represented by the number in Map.terrain[x][y] witch is
  //equal to i, were x, y are random integer as soon as they do not
  //throw ArrayIndexOutOfBoundsException. Actually this is a coding to know
  //a specific square in the map to witch terrain type is refered in setOfTypes.
  private Vector setOfTypes;
  public TerrainTypes() {
    setOfTypes = new Vector();
    setOfTypes.add(new TerrainType(1, "Plains"));
    setOfTypes.add(new TerrainType(2, "Forst"));
    setOfTypes.add(new TerrainType(3, "Jungle"));
    setOfTypes.add(new TerrainType(4, "Mountain"));
    setOfTypes.add(new TerrainType(-1, "X"));
  public int getMovementCost(int i) {
    return ((TerrainType) setOfTypes.get(i)).getMovementCost();
  public String getName(int i) {
    return ((TerrainType) setOfTypes.get(i)).getName();
  public String getNameFirstLetter(int i) {
    return ((TerrainType) setOfTypes.get(i)).getNameFirstLetter();
  public int getHighestMovementCost() {
    int max = 1;
    for (int i = 0; setOfTypes.size() > i; i++) {
      int movementCost = ((TerrainType) setOfTypes.get(i)).getMovementCost();
      if ( movementCost > 0) {
        if (max < movementCost)
          max = movementCost;
    return max;
}I hope this program will be helpful.
Sogartar

Answer 1

Why is such a smart guy like you not using A*
It is a general known algorithm which will find the
optimal solution in a finite search-space (within a minimal time).
The calculation time for the A* algorithm is influenced by two parameters:
1 - cumulative cost
2 - minimal expected additional cost
The calculation of these two costs has a great influence on the
solution.
I think the actual problems most games experience with shortest path calculatoin are
1 - very little time to spent calculating the shortest path
The quickest solution might be the best for the game
If your solution takes 1 second for the calculation of a path for one element on the board (100x100)
What would it take for the game to calculate the path for all elements controlled by the computer ??
If the computer controls two players which each have 50 elements to control, it would take forever...
Don't even consider the usage of a larger board (200x200 would take 4 seconds/element when
algorithm has complexity O(n))
2 - low priority.
Users tend to forgive a bad shortest path-algorithm most of the time,
but not a bad display, bad pictures,...
This is why most shortest-path algorithms within games were
developed as a depth first search,
within some earlier games this was even developed as
a rule which went straight to the endlocation and
takes a right/left turn when blocked by water/wall/...
So the actual steps you should take are:
1 - develop a normal breath-first search (to get going)
2 - develop a normal depth-first search (to compare speed and solution with)
3 - develop a normal dijkstra algorithm (sometimes called A)
4 - develop a best first algorithm (called A*)
5 - develop other AI-algorithms building upon A* (tabu-search, limited memory A*,...)
6 - develop some other AI-algorithms (Genetic Algorithms, Simulated Annealing,...)
7 - compare and tweak/change all search-algorithms for
7 - a - size of maps (small versus huge)
7 - b - optimality of the solution
7 - c - actual usage for your game
8 - !!! very important !!!
Share the developed path algorithms along with remarks about speed, map-size,...
with the rest of us. I would be very interested in such library.
kind regards,