Como posso encontrar outras soluções do labirinto em java?

Question

Eu preciso escrever um programa que pegue o labirinto no arquivo txt fornecido e imprima os caminhos da solução para o console. Escrevi este programa como você pode ver abaixo, mas só consigo encontrar 1 solução. Se houver mais de uma solução no labirinto, preciso encontrar todas elas. Não tenho ideia de qual abordagem devo tomar para isso. Você pode dar uma ideia, por favor?

Aqui está meu trabalho:

maze.txt (enviado como argumento)

11111111111111111
10110011000111111
11001110111001111
10110001011100111
11101111011011001
11101001011011111
11011011011001011
10111100111110111
11011011011111101
11100111011000011
10011110100111101
10100110111111101
11111111111111111

Classe do motorista:

import java.io.*;
import java.util.Arrays;

public class Driver {
    public static void main(String[] args) {

        //Reading source file
        int rowNum = 0, colNum = 0;
        File mazeFile = new File(args[0]);

        try (BufferedReader br = new BufferedReader(new FileReader(mazeFile))) {
            System.out.println("Input of Readed File:\n");
            String line;
            while ((line = br.readLine()) != null) {
                colNum = line.length();
                rowNum++;
                System.out.println(line);
            }
        } catch (IOException e) {
            e.printStackTrace();
        }

        //creating new maze array
        char[][] maze = new char[rowNum][colNum];
        System.out.println();
        System.out.print("ROW: "+rowNum+" COL: "+colNum);

        //Setting maze's elements
        try (BufferedReader br = new BufferedReader(new FileReader(mazeFile))) {
            int readed,rNum=0,cNum=0;
            while ((readed = br.read()) != -1) {
                if(readed == 10){

                }
                else if(rNum<rowNum && cNum < colNum){
                    maze[rNum][cNum] = (char)readed;
                    cNum++;
                }
                else if(cNum >= colNum){
                    rNum++;
                    cNum=0;
                }
            }
        } catch (IOException e) {
            e.printStackTrace();
        }

        //Printing created maze...
        System.out.println("\nCreated Maze: \n");

        for (int i = 0; i<rowNum ; i++) {
            for (int j = 0; j < colNum; j++) {
                System.out.print(maze[i][j]);
            }
            System.out.println();
        }

        System.out.println("\nSolution: \n");
        //Creating myStack object for making stack operations
        Stack myStack = new Stack(1000);

        //Creating mazeSolver object for solving maze
        MazeSolver mazeSolver = new MazeSolver(myStack,maze,1,1,colNum-2,rowNum-2,rowNum,colNum);
        mazeSolver.solve();

        //Printing inside of our stack.
        //myStack.showElements();

        //Creating answer array
        char[][] answer = maze;

        //Our path is drawn by re-reading the stored data in our stack structure.
        for (int i = rowNum-1; i >=0; i--) {
            for (int j = colNum-1; j >=0; j--) {
                int x[] = myStack.peek();
                if(i == x[0] && j == x[1]){
                    answer[i][j] = '#';
                }
            }
        }

        //Minor visual improvements ...
        for (int i = 0; i<rowNum ; i++) {
            for (int j = 0; j < colNum; j++) {
                if(answer[i][j] == '1' || answer[i][j] == '0')
                    answer[i][j] = '.';
            }
        }

        //Printing our answer
        for (int i = 0; i<rowNum ; i++) {
            for (int j = 0; j < colNum; j++) {
                System.out.print(maze[i][j]);
            }
            System.out.println();
        }
    }
}

Classe de pilha:

public class Stack {
    int topOfStack;
    int capacity;
    int[][] Stack;

    public Stack(int capacity) {
        this.capacity = capacity;
        Stack = new int[capacity][2];
        topOfStack = -1;
    }

    void push(int y, int x)
    {
        if(topOfStack == capacity){
            System.out.println("Stack Overflow...");
        }
        else{
            Stack[++topOfStack] = new int[] { y, x };
        }
        //System.out.println("###Pushed Element: "+Stack[topOfStack][0]+" "+Stack[topOfStack][1]);
    }

    int[] pop() {
        if (topOfStack < 0) {
            System.out.println("Stack is empty...");
            return null;
        }
        //System.out.println("Pulled Element: "+Stack[topOfStack][0]+" "+Stack[topOfStack][1]);
        topOfStack--;
        return Stack[topOfStack];
    }

    int[] pop2() {
        if (topOfStack < 0) {
            System.out.println("Stack Underflow");
            return null;
        }
        else {
            int x[] = Stack[topOfStack--];
            //System.out.println("Pulled Element: "+x[0]+" "+x[1]);
            return x;
        }
    }

    int[] peek()
    {
        if (topOfStack < 0) {
            System.out.println("Stack Underflow");
            return null;
        }
        else {
            int x[] = Stack[topOfStack];
            return x;
        }
    }

    void showElements()
    {
        System.out.println("\n\n");
        for (int i = topOfStack; i >=0; i--) {
            System.out.println("Stack Elements "+i+":"+" "+Stack[i][0] +" "+Stack[i][1]);
        }
    }

    int size(){
        int i;
        for (i = 0; i <= topOfStack; i++) {
        }
        return i;
    }
}

Classe MazeSolver:

public class MazeSolver {
    Stack workStack;
    char[][] maze;
    int startPointX;
    int startPointY;
    int endPointX;
    int endPointY;
    int numberOfRows;
    int numberOfCols;
    static final char Wall = '1';
    static final char Free = '0';
    static final char Success = '#';

    public MazeSolver(Stack workStack, char[][] maze,int startingPointX, int startingPointY, int endPointX, int endPointY, int RowNum, int ColNum) {
        this.workStack = workStack;
        this.maze = maze;
        this.startPointX = startingPointX;
        this.startPointY = startingPointY;
        this.endPointX = endPointX;
        this.endPointY = endPointY;
        this.numberOfRows = RowNum;
        this.numberOfCols = ColNum;
        workStack.push(startPointY,startingPointX);
    }

    boolean canMoveEast(){
        if((maze[startPointY][startPointX + 1] == Free) && (startPointX + 1 <= numberOfCols))
        {
            return true;
        }
        else
            return false;
    }

    boolean canMoveWest(){
        if((maze[startPointY][startPointX - 1] == Free) && (startPointX - 1 <= numberOfCols)){
            return true;
        }
        else
            return false;
    }

    boolean canMoveNorth(){
        if((maze[startPointY-1][startPointX] == Free) && (startPointY - 1 <= numberOfRows)){
            return true;
        }
        else
            return false;
    }

    boolean canMoveSouth(){
        if((maze[startPointY+1][startPointX] == Free) && (startPointY + 1 <= numberOfRows)){
            return true;
        }
        else
            return false;
    }

    boolean canMoveNorthEast(){
        if((maze[startPointY-1][startPointX+1] == Free) && (startPointY - 1 <= numberOfRows) && (startPointX + 1 <= numberOfCols)){
            return true;
        }
        else
            return false;
    }

    boolean canMoveNorthWest(){
        if((maze[startPointY-1][startPointX-1] == Free) && (startPointY - 1 <= numberOfRows) && (startPointX - 1 <= numberOfCols)){
            return true;
        }
        else
            return false;
    }
    boolean canMoveSouthEast(){
        if((maze[startPointY+1][startPointX+1] == Free) && (startPointY + 1 <= numberOfRows) && (startPointX + 1 <= numberOfCols)){
            return true;
        }
        else
            return false;
    }
    boolean canMoveSouthWest(){
        if((maze[startPointY+1][startPointX-1] == Free) && (startPointY + 1 <= numberOfRows) && (startPointX - 1 <= numberOfCols)){
            return true;
        }
        else
            return false;
    }

    boolean solve()
    {
        maze[startPointY][startPointX] = Success;

        //Checked if we reached our goal
        if((startPointY == endPointY) && (startPointX == endPointX)){
            return true;
        }

        if(canMoveEast()){
            workStack.push(startPointY,startPointX+1);
            startPointX++;
            solve();
        }
        else if(canMoveWest()){
            workStack.push(startPointY,startPointX-1);
            startPointX--;
            solve();
        }
        else if(canMoveNorth()){
            workStack.push(startPointY-1,startPointX);
            startPointY--;
            solve();
        }
        else if(canMoveSouth()){
            workStack.push(startPointY+1,startPointX);
            startPointY++;
            solve();
        }
        else if(canMoveNorthEast()){
            workStack.push(startPointY-1,startPointX+1);
            startPointY--;
            startPointX++;
            solve();
        }
        else if(canMoveNorthWest()){
            workStack.push(startPointY-1,startPointX-1);
            startPointY--;
            startPointX--;
            solve();
        }
        else if(canMoveSouthEast()){
            workStack.push(startPointY+1,startPointX+1);
            startPointY++;
            startPointX++;
            solve();
        }
        else if(canMoveSouthWest()){
            workStack.push(startPointY+1,startPointX-1);
            startPointY++;
            startPointX--;
            solve();
        }
        else if(true){
            try {
                maze[startPointY][startPointX] = Wall;
                int[] back = workStack.pop();
                startPointY = back[0];
                startPointX = back[1];
                solve();
            } catch (Exception e) {
                System.out.println("There is no solution!");
                System.exit(0);
            }
        }

        return false;
    }
}

Resultado que obtive:

Input of Readed File:

11111111111111111
10110011000111111
11001110111001111
10110001011100111
11101111011011001
11101001011011111
11011011011001011
10111100111110111
11011011011111101
11100111011000011
10011110100111101
10100110111111101
11111111111111111

ROW: 13 COL: 17
Created Maze: 

11111111111111111
10110011000111111
11001110111001111
10110001011100111
11101111011011001
11101001011011111
11011011011001011
10111100111110111
11011011011111101
11100111011000011
10011110100111101
10100110111111101
11111111111111111

Solution: 

.................
.#...............
..##...#.........
....###.#........
........#........
........#........
........#........
.......#.........
........#........
........#..####..
.........##....#.
...............#.
.................

Process finished with exit code 0

Resultado que preciso:

Input of Readed File:

11111111111111111
10110011000111111
11001110111001111
10110001011100111
11101111011011001
11101001011011111
11011011011001011
10111100111110111
11011011011111101
11100111011000011
10011110100111101
10100110111111101
11111111111111111

ROW: 13 COL: 17
Created Maze: 

11111111111111111
10110011000111111
11001110111001111
10110001011100111
11101111011011001
11101001011011111
11011011011001011
10111100111110111
11011011011111101
11100111011000011
10011110100111101
10100110111111101
11111111111111111

Solution 1: 

.................
.#...............
..##...#.........
....###.#........
........#........
........#........
........#........
.......#.........
........#........
........#..####..
.........##....#.
...............#.
.................

Solution 2:

.................
.#...............
..##.............
....#............
...#.............
...#.............
..#..............
.#....##.........
..#..#..#........
...##...#..####..
.........##....#.
...............#.
.................

Process finished with exit code 0

Answer 1

O resultado que você deseja é 'Uma variedade de soluções que podem ir de (Nordeste, Noroeste) a (Sudeste, Sudoeste)', e você precisa resolver usando pilha? Se assim for, sugiro que você use duas pilhas, uma para salvar todas as possibilidades (que armazenam todos toEast, toWest etc onde você pode ir), uma para salvar os atuais acontecimentos (cada solução possível, como um buffer)

Basta adicionar a lógica que salva o processo atual no buffer e imprimir o caminho quando for uma solução em seu código original. Se não for uma solução e não puder alcançar (Sudeste, Sudoeste), rastreie e restaure sua pilha de buffer. Para essa lógica, você precisará de outro local de salvamento de pilha, onde escolheu pela última vez uma variedade de direções.

Em resumo,

Stack1 => to save all possibilities
Stack2 => current paths. If not a solution, delete and restore
Stack3 => where you chose one direction from many. Need to traceback the path.

Stack2 copies Stack1 whenever you progress,
when reach the goal you print your Stack2 as a solution,
if not, pop until your latest decision informed by popping Stack3.