//************************************************** solve using
    //recursion. Note: this solution unmarks the path upon reaching
    //dead ends, so in the end only the path is left marked. It is
    //possible to write a solution that does not un-mark its traces,
    //but instead it clones and restores the maze.
    public void solveRec() {

	if (solve(new MazePos(START_I, START_J))) 
	    System.out.println("Got it: "); 
	else System.out.println("You're stuck in the maze."); 
	print(); 
	    
    }
    
    
    //find a path to exit the maze from this position. Works
    //recursively, by advancing to a neighbor and continuing from
    //there. If a path is found, return true. Otherwise return false. 
    public boolean solve(MazePos pos) {

	//base case
	if (!isInMaze(pos)) return false;
	if (isFinal(pos)) return true; 
	if (!isClear(pos)) return false; 

	//current position must be clear
	assert(isClear(pos)); 
	
	//recurse

	//first mark this  location 
	mark(pos, V); 

	//try to go south 
	if (solve(pos.south())) { 
	    //we found a solution going south: if we want to leave the
	    //maze clean, then unmark current cell and return; if we
	    //want to mark the path in the maze, then don't unmark
	    //mark(pos, C); 
	    return true;  }

	//else west 
	if (solve(pos.west())) {
	    //we found a solution going west: if we want to leave the
	    //maze clean, then unmark current cell and return; if we
	    //want to mark the path in the maze, then don't unmark  
	    //return
	    //mark(pos, C); 
	    return true; 
	}	   

	//else north 
	if (solve(pos.north())) {
	    //we found a solution going north: if we want to leave the
	    //maze clean, then unmark current cell and return; if we
	    //want to mark the path in the maze, then don't unmark  
	    //return
	    // mark(pos, C); 
	    return true; 
	}

	//else east 
	if (solve(pos.east())) {
	    //we found a solution going east: if we want to leave the
	    //maze clean, then unmark current cell and return; if we
	    //want to mark the path in the maze, then don't unmark  
	    //return
	    //mark(pos, C); 
	    return true; 
	}
	   
	//unmark all dead ends; since it was marked, the position must
	//have been clear
	mark(pos, C); 

	//if none of the above returned, then there is no solution
	return false;
    }
};