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4
A Maze can be thought of a series of rooms that has four walls that are either opened exposing the next room or are blocking the view of the next room. In short a room(Vertex) has four walls(edges) that are either there or not(boolean). The openings are determined by sets.
LET'S BEGIN
First we will create a room class. The variables that will be needed initially are four walls, a thought of a matrix(x and y), an adjacency list, a room name consisting of a number(ie. 0, 1, 2, 3,...,n), and a pointer to the previous room.
Room Class
import java.util.*;
public class Room{
// represent four walls
public Wall north, east, south, west; // the wall class will be created next
public int x, y; // represent the row and column of the maze
public List<Room> adj; // adjacency list using linked list
public int roomName; // for this the room will be a number
public Room prev; // last room pointer
// now we code the constructer
public Room(int x, int y){
this.x = x;// row
this.y = y;// column
adj = new LinkedList<Room>();
prev = null;// we have not progressed, so prev is nothing
roomName = 0;// we will use the concept of arrays start 0
}// end of constructor
// we have to increment the room name so lets do it
public int getRoomName(){
return roomName++;
}// end of getRoomName()
}// end of
Wall Class
public class Wall{
public Room currentRoom, nextRoom;// room in now, next room
public boolean isGone = false;// is the wall there
// Two constructors will be created
// which will account for walls with or
// without neighbors
// with a neighbor
public Wall(Room a, Room b){
currentRoom = a;
nextRoom = b;
}
// without a neighbor
public Wall(Room r){
currentRoom = r;
nextRoom = null;
}
}// end of Wall class
I will explain how disjoint sets work in a future tut, but a quick explanation:Disjoint sets are sets whose intersect is the null set. We will use this notion to join the sets or room names and create the maze by unionizing the rooms.
JoinRoom class
public class JoinRoom{
private int[] set; // this is an array to store a set of rooms
public JoinRoom(int elem){
set = new int[e];
// initialize every element in the set
for(int i = 0; i < set.length; i++){
set[i] = -1;
}
}// end of constructor
// find using compression
public int find(int r){
if(set[r] < 0){
return r;
} else {
return set[r] = find(set[r]);
}
}// end of find
public void unionRooms(int roomA, int roomB){
if(set[roomB] < set[roomA]){
set[roomA] = roomB;
} else {
if(set[roomA] == set[roomB]){
set[roomA]--;
}
set[roomB] = roomA;
}
}// end of union rooms
}// end of joinRoom class
NOW WE CREATE OUR MAIN CLASS TO GENERATE THE MAZEWe will create the class and have it extend JPanel for our artwork. We have to think of private variables that will be needed.
public class Maze extends JPanel{
// the maze can be seen as a matrix of squares so well use a multidimensional array of the room
// class
private Room[][] rooms;// the maze can be seen as a matrix of squares so well use
private ArrayList<Wall> walls; // List of walls
private Random rand;// We are going to have to randomize the rooms chosen to unionize
private int height;// users desired height of matrix
private int width;// users desired width of matrix
private int num;// we will have to increment a few times so lets just use num as an incrementor
private JoinRooms ds;// we are going to join rooms so well label the variable ds for disjoint set
// we are going to need variables for our panel
private int x_cord; // x-axis rep
private int y_cord;// y-axis rep
private int roomSize;
private int randomWall;
}// end of class
Now we need the constructor. We want the constructor to take height and width of the matrix. We also want the constructor to initialize our multidimensional room array and our arraylist of walls(the bottom right will always be the exit). We will also call the generate the random maze which will initialize the maze to be a matrix of squares. Finally we will set the size of our panel.
public Maze(int height, int width) {
this.height = height;
this.width = width;
rooms = new Room[height][width];
walls = new ArrayList<Wall>((height - 1) * (width - 1));
generateRandomMaze();
setPreferredSize(new Dimension(800, 700));
}
To generate the random maze we will first have to create a initial multidimensional array of rooms with the walls intact except for the top left and bottom right room. We will now initialize our JoinRooms class to be essentialy a array of rooms. We also have to initialize our random room generator and use our incrementer(num) to decrement.
private void generateRandomMaze() {
generateInitialRooms();// see next method
ds = new JoinRoom(width * height);
rand = new Random(); // here is the random room generator
num = width * height;
while (num > 1) {
// when we pick a random wall we want to avoid the borders getting eliminated
randomWall = rand.nextInt(walls.size());
Wall temp = walls.get(randomWall);
// we will pick two rooms randomly
int roomA = temp.currentRoom.y + temp.currentRoom.x * width;
int roomB = temp.nextRoom.y + temp.nextRoom.x * width;
// check roomA and roomB to see if they are already members
if (ds.find(roomA) != ds.find(roomB)) {
walls.remove(randomWall);
ds.unionRooms(ds.find(roomA), ds.find(roomB));
temp.isGone = true;
temp.currentRoom.adj.add(temp.nextRoom);
temp.nextRoom.adj.add(temp.currentRoom);
num--;
}// end of if
}// end of while
}
// name the room to display
private int roomNumber = 0;
/**
* Sets the grid of rooms to be initially boxes
* This is self explanitory, we are only creating an reverse L for all
* The rooms and there is an L for the border
*/
private void generateInitialRooms() {
for (int i = 0; i < height; i++) {
for (int j = 0; j < width; j++) {
// create north walls
rooms[i][j] = new Room(i, j);
if (i == 0) {
rooms[i][j].north = new Wall(rooms[i][j]);
} else {
rooms[i][j].north = new Wall(rooms[i - 1][j], rooms[i][j]);
walls.add(rooms[i][j].north);
}
if (i == height - 1) {
rooms[i][j].south = new Wall(rooms[i][j]);
}
if (j == 0) {
rooms[i][j].west = new Wall(rooms[i][j]);
} else {
rooms[i][j].west = new Wall(rooms[i][j - 1], rooms[i][j]);
walls.add(rooms[i][j].west);
}
if (j == width - 1) {
rooms[i][j].east = new Wall(rooms[i][j]);
}
rooms[i][j].roomName = roomNumber++;// we will name the rooms
}
}
// initalize entrance and exit
rooms[0][0].west.isGone = true;// you can replace .west.isGone with .north.isGone
// this is just saying the roomName for top left is 0
rooms[0][0].roomName = 0;
// we will remove the south wall of the last room
rooms[height - 1][width - 1].south.isGone = true;
// this is just saying the roomName for bottom right is the last element in the mxn room matrix
rooms[height - 1][width - 1].roomName = (height * width);
}
Voila, the initialization and the maze is joined with only one path from start to finish lets display it on our panel(I like to call this my art canvas).
// The code will display the maze
// I urge you to play with the variable
// values to see how this portion of the
// code works and changes
public void paintComponent(Graphics g) {
x_cord = 40;
y_cord = 40;
// could have taken height as well as width
// just need something to base the roomsize
roomSize = (width - x_cord) / width + 7;
// temp variables used for painting
int x = x_cord;
int y = y_cord;
for (int i = 0; i <= height - 1; i++) {
for (int j = 0; j <= width - 1; j++) {
if (!(rooms[i][j].north.isGone)) {
g.drawLine(x, y, x + roomSize, y);
}//end of north if
// west wall not there draw the line
if (rooms[i][j].west.isGone == false) {
g.drawLine(x, y, x, y + roomSize);
}// end of west if
if ((i == height - 1) && rooms[i][j].south.isGone == false) {
g.drawLine(x, y + roomSize, x + roomSize,
y + roomSize);
}// end of south if
if ((j == width - 1) && rooms[i][j].east.isGone == false) {
g.drawLine(x + roomSize, y, x + roomSize,
y + roomSize);
}// end of east if
x += roomSize;// change the horizontal
}// end of inner for loop
x = x_cord;
y += roomSize;
}// end of outer for loop
}
Finally, we can create the main method for our code. This should be very clear and doesnt need detail(If not ask in comments).
public static void main(String[] args) {
// we will use the scanner for userInput
Scanner userInput = new Scanner(System.in);
int m, n;// these are variables for the size of maze (m x n)
System.out.print("Enter the size of your maze: ");
// store the input
m = userInput.nextInt();
n = userInput.nextInt();
// use JFrame to put the created panel on
JFrame frame = new JFrame();
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.setSize(500, 800);
frame.getContentPane().add(new Maze(m, n));
frame.pack();
frame.setVisible(true);
}// end of main
Here is the complete code from our main class
import java.awt.Dimension;
import java.awt.Graphics;
import java.util.ArrayList;
import java.util.Random;
import java.util.Scanner;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class Maze extends JPanel {
private Room[][] rooms;// m x n matrix of rooms
private ArrayList<Wall> walls; // List of walls
private Random rand;// for random wall
private int height;// height of matrix
private int width;// width of matrix
private int num;// incrementor
private JoinRoom ds;// union paths
// paint methods //
private int x_cord; // x-axis rep
private int y_cord;// y-axis rep
private int roomSize;
private int randomWall;
public Maze(int height, int width) {
this.height = height;
this.width = width;
rooms = new Room[height][width];
walls = new ArrayList<Wall>((height - 1) * (width - 1));
generateRandomMaze();
setPreferredSize(new Dimension(800, 700));
}
private void generateRandomMaze() {
generateInitialRooms();// see next method
ds = new JoinRoom(width * height);
rand = new Random(); // here is the random room generator
num = width * height;
while (num > 1) {
// when we pick a random wall we want to avoid the borders getting eliminated
randomWall = rand.nextInt(walls.size());
Wall temp = walls.get(randomWall);
// we will pick two rooms randomly
int roomA = temp.currentRoom.y + temp.currentRoom.x * width;
int roomB = temp.nextRoom.y + temp.nextRoom.x * width;
// check roomA and roomB to see if they are already members
if (ds.find(roomA) != ds.find(roomB)) {
walls.remove(randomWall);
ds.unionRooms(ds.find(roomA), ds.find(roomB));
temp.isGone = true;
temp.currentRoom.adj.add(temp.nextRoom);
temp.nextRoom.adj.add(temp.currentRoom);
num--;
}// end of if
}// end of while
}
// name the room to display
private int roomNumber = 0;
/**
* Sets the grid of rooms to be initially boxes
* This is self explanitory, we are only creating an reverse L for all
* The rooms and there is an L for the border
*/
private void generateInitialRooms() {
for (int i = 0; i < height; i++) {
for (int j = 0; j < width; j++) {
// create north walls
rooms[i][j] = new Room(i, j);
if (i == 0) {
rooms[i][j].north = new Wall(rooms[i][j]);
} else {
rooms[i][j].north = new Wall(rooms[i - 1][j], rooms[i][j]);
walls.add(rooms[i][j].north);
}
if (i == height - 1) {
rooms[i][j].south = new Wall(rooms[i][j]);
}
if (j == 0) {
rooms[i][j].west = new Wall(rooms[i][j]);
} else {
rooms[i][j].west = new Wall(rooms[i][j - 1], rooms[i][j]);
walls.add(rooms[i][j].west);
}
if (j == width - 1) {
rooms[i][j].east = new Wall(rooms[i][j]);
}
rooms[i][j].roomName = roomNumber++;// we will name the rooms
}
}
// initalize entrance and exit
rooms[0][0].west.isGone = true;// you can replace .west.isGone with .north.isGone
// this is just saying the roomName for top left is 0
rooms[0][0].roomName = 0;
// we will remove the south wall of the last room
rooms[height - 1][width - 1].south.isGone = true;
// this is just saying the roomName for bottom right is the last element in the mxn room matrix
rooms[height - 1][width - 1].roomName = (height * width);
}
public void paintComponent(Graphics g) {
x_cord = 40;
y_cord = 40;
// could have taken height as well as width
// just need something to base the roomsize
roomSize = (width - x_cord) / width + 7;
// temp variables used for painting
int x = x_cord;
int y = y_cord;
for (int i = 0; i <= height - 1; i++) {
for (int j = 0; j <= width - 1; j++) {
if (!(rooms[i][j].north.isGone)) {
g.drawLine(x, y, x + roomSize, y);
}//end of north if
// west wall not there draw the line
if (rooms[i][j].west.isGone == false) {
g.drawLine(x, y, x, y + roomSize);
}// end of west if
if ((i == height - 1) && rooms[i][j].south.isGone == false) {
g.drawLine(x, y + roomSize, x + roomSize,
y + roomSize);
}// end of south if
if ((j == width - 1) && rooms[i][j].east.isGone == false) {
g.drawLine(x + roomSize, y, x + roomSize,
y + roomSize);
}// end of east if
x += roomSize;// change the horizontal
}// end of inner for loop
x = x_cord;
y += roomSize;
}// end of outer for loop
}
public static void main(String[] args) {
// we will use the scanner for userInput
Scanner userInput = new Scanner(System.in);
int m, n;// these are variables for the size of maze (m x n)
System.out.print("Enter the size of your maze: ");
// store the input
m = userInput.nextInt();
n = userInput.nextInt();
// use JFrame to put the created panel on
JFrame frame = new JFrame();
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.setSize(500, 800);
frame.getContentPane().add(new Maze(m, n));
frame.pack();
frame.setVisible(true);
}// end of main
}// END OF CLASS
That concludes the tutorial on maze creation. Enjoy.
Optional things you should try with this maze program:
1. Print the maze to a txt file
2. Accept a text file to generate maze
3. Display the solution to the maze(hint: add dijkstra(), leftHand(), or anotherAlgorithm(search for path) and dont forget to modify paintComponent() method when solved
Edited by mr mike, 23 May 2011 - 05:30 PM.
leathalwire pointed out a typo
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