Algorithm:
Eller's algorithm creates 'perfect' mazes, having only a single path
between any two cells, one row at a time. The algorithm itself is
incredibly fast, and far more memory efficient than other popular
algorithms (such as Prim's and Kruskal's) requiring storage proportional
to only a single row. This makes it possible to create mazes of
indefinite length on systems with limited memory.
The algorithm is explained below:
- Create the first row. No cells will be members of any set
- Join any cells not members of a set to their own unique set
- Create right-walls, moving from left to right:
- Randomly decide to add a wall or not
- If the current cell and the cell to the right are members of the same set, always create a wall between them. (This prevents loops)
- If you decide not to add a wall, union the sets to which the current cell and the cell to the right are members.
- Create bottom-walls, moving from left to right:
- Randomly decide to add a wall or not. Make sure that each set has at least one cell without a bottom-wall (This prevents isolations)
- If a cell is the only member of its set, do not create a bottom-wall
- If a cell is the only member of its set without a bottom-wall, do not create a bottom-wall
- Decide to keep adding rows, or stop and complete the maze
- If you decide to add another row:
- Output the current row
- Remove all right walls
- Remove cells with a bottom-wall from their set
- Remove all bottom walls
- Continue from Step 2
- If you decide to complete the maze
- Add a bottom wall to every cell
- Moving from left to right:
- If the current cell and the cell to the right are members of a different set:
- Remove the right wall
- Union the sets to which the current cell and cell to the right are members.
- Output the final row
CODE:
// a utility class to represent single cell
import java.util.*;
public class Cel{
public boolean right,down;
public List<Cel> set;
public int x,y;
Cel(int a,int b){
x=a;
y=b;
right=false;
down=true;
set=null;
}
}
// class to implement the algorithm
import java.util.*;
public class maze{
static Random randomizer = new Random();
static int size;
static int[][] maze;
static Scanner in = new Scanner(System.in);
/* Step 2: Grouping ungrouped cells to form new sets */
static Cel[] makeSet(Cel[] row) {
for(int index = 0; index < row.length; ) {
Cel cell = row[index++];
if(cell.set == null) {
List<Cel> list = new ArrayList<Cel>();
list.add(cell);
cell.set=list;
}
}
return row;
}
/*********************************************************/
/* Step 3: Creating right walls */
static Cel[] makeRightWalls(Cel[] row) {
for(int i = 1; i < row.length; i++) {
if(isContainsInList(row[i-1].set,row[i])) {
row[i-1].right=true;
continue;
}
if(randomizer.nextBoolean())
row[i-1].right=true;
else
row=merge(row,i);
}
return row;
}
static Cel[] merge(Cel[] row,int i) { //utility function
List<Cel> currentList = row[i-1].set;
List<Cel> nextList = row[i].set;
for(Cel j : nextList) {
currentList.add(j);
j.set=currentList;
}
return row;
}
static boolean isContainsInList(List<Cel> set,Cel cell) { //utility function
for(Cel i : set) {
if(i==cell)
return true;
}
return false;
}
/*********************************************************/
/* Step 4: Creating down walls */
static boolean isNotDone(List<Cel> set){ //utility function
boolean rslt=true;
for(Cel x:set)
rslt=rslt&&x.down;
return rslt;
}
static Cel[] makeDown(Cel[] row){
for(int i=0;i<row.length;i++){
for(Cel x:row[i].set)x.down=true;
while(isNotDone(row[i].set)){
do{
row[i].set.get(randomizer.nextInt(row[i].set.size())).down=false;
}while(randomizer.nextBoolean() || );
}
}
return row;
}
/*********************************************************/
/* Driver function to execute the algorithm */
static public void driver(){
System.out.print("Enter size: ");
size=in.nextInt();
maze=new int[2*size+1][2*size+1];
Cel[] cur=new Cel[size];
for(int i=0;i<size;i++)
cur[i]=new Cel(0,i);
for(int i=2;i<=2*size;i++)
for(int j=2;j<=2*size;j++)
maze[i][j]=0;
for(int i=0;i<size;i++){
cur=makeSet(cur);
cur=makeRightWalls(cur);
cur=makeDown(cur);
if(i==size-1)
cur=end(cur);
printMaze(cur,i);
if(i!=size-1)
cur=genNextRow(cur);
}
//Creating upper and left boundary
for(int i=0;i<=2*size;i++)
maze[i][0]=maze[0][i]=maze[i][2*size]=maze[2*size][i]=1;
for(int i=2;i<=2*size;i+=2)
for(int j=2;j<=2*size;j+=2)
maze[i][j]=1;
for(int i=0;i<2*size+1;i++){
System.out.println();
for(int j=0;j<2*size+1;j++)
System.out.print(maze[i][j]+" ");
}
}
static Cel[] end(Cel[] row) {
for(int i = 1; i < row.length; i++) {
if(findPos(row[i-1].set,row[i]) == -1) {
row[i-1].right=false;
row=merge(row,i);
}
}
return row;
}
static int findPos(List<Cel> set,Cel x){
Cel[] tmpArray = new Cel[set.size()];
tmpArray = set.toArray(tmpArray);
for(int i=0;i<tmpArray.length;i++)
if(tmpArray[i]==x)
return i;
return -1;
}
static Cel[] genNextRow(Cel[] pre){
for(int i = 0; i < pre.length;i++ ) {
pre[i].right=false;
pre[i].x++;
if(pre[i].down) {
pre[i].set.remove(findPos(pre[i].set, pre[i]));
pre[i].set=null;
pre[i].down=false;
}
}
return pre;
}
static void printMaze(Cel[] row,int rowPos){
rowPos=2*rowPos+1;
for(int i=0;i<row.length;i++){
if(row[i].right)
maze[rowPos][2*i+2]=1;
if(row[i].down)
maze[rowPos+1][2*i+1]=1;
}
}
}
// driver class to execute the algorithm
public class runMe{
public static void main(String[] args) {
maze t =new maze();
maze.driver();
}
}
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