Maze.java

import java.util.ArrayList;

public class Maze {
    public static void main(String[] args) {
  //  System.out.println(count(5, 4));
//   path("", 5, 4);
//      System.out.println(pathRet("", 6, 3));

//        System.out.println(pathRetDiagonal("", 3, 3));

      boolean[][] board = {
            {true, true, true},
            {true, true, true},
            {true, false, true},
            {true,true,true},
            {true,false,false}
        };

        pathRestrictions("", board, 0, 0);
    }

    static int count(int r, int c) {
        if (r == 1 || c == 1) {
            return 1;
        }
        int left = count(r-1, c);
        int right = count(r, c-1);
        return left + right;
    }

    static void path(String p, int r, int c) {
        if (r == 1 && c == 1) {
            System.out.println(p);
            return;
        }

        if (r > 1) {
            path(p + "D", r-1, c);
        }

        if (c > 1) {
            path(p + "R", r, c-1);
        }
    }

    static ArrayList<String> pathRet(String p, int r, int c) {
        if (r == 1 && c == 1) {
            ArrayList<String> list = new ArrayList<>();
            list.add(p);
            return list;
        }

        ArrayList<String> list = new ArrayList<>();

        if (r > 1) {
            list.addAll(pathRet(p + 'D', r-1, c));
        }

        if (c > 1) {
            list.addAll(pathRet(p + 'R', r, c-1));
        }

        return list;
    }

    static ArrayList<String> pathRetDiagonal(String p, int r, int c) {
        if (r == 1 && c == 1) {
            ArrayList<String> list = new ArrayList<>();
            list.add(p);
            return list;
        }

        ArrayList<String> list = new ArrayList<>();

        if (r > 1 && c > 1) {
            list.addAll(pathRetDiagonal(p + 'D', r-1, c-1));
        }

        if (r > 1) {
            list.addAll(pathRetDiagonal(p + 'V', r-1, c));
        }

        if (c > 1) {
            list.addAll(pathRetDiagonal(p + 'H', r, c-1));
        }

        return list;
    }

    static void pathRestrictions(String p, boolean[][] maze, int r, int c) {
        if (r == maze.length - 1 && c == maze[0].length - 1) {
            System.out.println(p);
            return;
        }

        if (!maze[r][c]) {
            return;
        }

        if (r < maze.length - 1) {
            pathRestrictions(p + 'D', maze, r+1, c);
        }

        if (c < maze[0].length - 1) {
            pathRestrictions(p + 'R', maze, r, c+1);
        }
    }

}