Simple DFS

 public void doSimpleDFS(Grid gridStates) {Random random = new Random();
        currentGrid = "000100020003000S";
        int counter = 0;
        while(!finished) {
            int rndChecker = random.nextInt(4);
            if (checkValidMove(currentGrid, rndChecker)) {
                currentGrid = move(currentGrid, rndChecker);
                if(currentGrid.equals(finalState)) {
                    finished = true;
                }
                counter++;
            }
        }
        System.out.println("I Found It!");
    }