(Generating Mazes Randomly) Write a method mazeGenerator that takes as an argument a two-d...

(Generating Mazes Randomly) Write a method mazeGenerator that takes as an argument a two-dimensional 12-by-12 character array and randomly produces a maze. The method should also provide the starting and ending locations of the maze. Test your method mazeTraversal from Exercise, using several randomly generated mazes.

Exercise

(Maze Traversal Using Recursive Backtracking) The grid of #s and dots (.) in Fig. is a two-dimensional array representation of a maze. The #s represent the walls of the maze, and the dots represent locations in the possible paths through the maze. Moves can be made only to a location in the array that contains a dot.

Fig. | Two-dimensional array representation of a maze.

Write a recursive method (mazeTraversal) to walk through mazes like the one in Fig.. The method should receive as arguments a 12-by-12 character array representing the maze and the current location in the maze (the first time this method is called, the current location should be the entry point of the maze). As mazeTraversal attempts to locate the exit, it should place the character x in each square in the path. There is a simple algorithm for walking through a maze that guarantees finding the exit (assuming there is an exit). If there is no exit, you’ll arrive at the starting location again. The algorithm is as follows: From the current location in the maze, try to move one space in any of the possible directions (down, right, up or left). If it’s possible to move in at least one direction, call mazeTraversal recursively, passing the new spot on the maze as the current spot. If it’s not possible to go in any direction, “back up” to a previous location in the maze and try a new direction for that location. Program the method to display the maze after each move so the user can watch as the maze is solved. The final output of the maze should display only the path needed to solve the maze—if going in a particular direction results in a dead end, the x’s going in that direction should not be displayed. [Hint: To display only the final path, it may be helpful to mark off spots that result in a dead end with another character (such as '0').]