Homework 3: Building Mazes, part 1

Maze Creation

For the purposes of this assignment, we will define a maze to have the following characteristics:

It is a rectangular grid of cells.
Each cell can either be filled or empty.
One cell, on an edge of the grid, is designated the entrance. It must be empty. Another cell on the edge is the exit, and it too must be empty.

Your task is as follows:

Design a class to represent a maze as described above.
- Implement a method to generate a randomized, perfect maze.
- A perfect maze cannot contain any loops. Furthermore, it should have as many open squares as possible given this constraint.
- The randomization should ensure that each call creates a distinct maze.
Ensure that maze objects can be loaded and saved to disk.
Design a GUI (using Swing) to create mazes. Ensure a facility for loading and saving mazes. You may otherwise design the GUI however you deem appropriate.

Maze Navigation

Add the following features to your user interface:

Create a way for the user to navigate an explorer through the maze. The explorer should not be any larger than a grid cell. A simple square of a different color than the grid cell will suffice.
The explorer can move from its current square to any adjacent square that does not contain a wall. For the purposes of this program, "adjacent" squares cannot be diagonal.
The explorer should start at the maze entrance.
Allow the user to select whether the explorer leaves a visible trail as it moves.
Give the user a "reset" option to erase the path and return the explorer to the entrance.
Display an appropriate congratulatory message when the explorer reaches the exit.

As part of implementing the above features, create the Path class. Objects of the Path class are nodes in a singly-linked list. Each Path object should contain:

A cell location in the maze
A reference to the Path that represents the path from the entrance up to the current Path object. At the entrance, this reference should be null.
The total number of steps from the entrance to the end of the Path
Any methods as you see fit. Do not add any other data members. In particular, you must implement this as a singly-linked list, not as a doubly-linked list.