Lab 4: Mazes - Depth First Search

Overview

In this lab, we will implement a generic version of the Stack data type within the context of searching a maze.

Materials

  • IntelliJ
  • Lab partner

Setup

  1. Download the skeleton for this project.
  2. Extract the code, then open the maze151dfs folder in IntelliJ to start a new project.

Description

In this lab, we will explore searching a maze for a goal using a stack to organize our potential Trails. The stack allows us to search in a depth-first search manner. In other words, we can explore down a trail as far as possible, and backtrack if we reached a dead end in our journey, because we search the youngest potential trail next.

In this lab, you will create the necessary data structures to search a maze in this depth-first search manner.

To start, run the code in MazeApp. You should see the GUI layout here.

There are a few new pieces to this GUI. First, you will see a choice for either ArrayStack or ListStack. You will find the starter code for these included in the maze.searchers directory.

Second, you will notice that there are statistics in the middle portion of the GUI, recording the number of OPEN, CLOSED, and VISITED squares.

Third, there is a box at the bottom, to report errors when things go wrong with the underlying implementations. It will also report the number of steps taken when a solution trail is found through searching.

Step 1 - ArrayStack<E>

Our first task is to implement a generic Stack class that can be used in many pieces of the code, for generating and then solving mazes.

Write a class called ArrayStack<E>. This will need to implement the Stack<E> interface. The fields and constructor are provided for you.

Step 1.1 - public void push(E item)

If there is no more room in the stuff array, you will need to resize.

  • Create a new array twice as big as stuff.
  • Copy over each item into the new array.
  • Redirect the stuff reference to the new array.

Now, you can always add the new item to top spot in the stuff array, and increment the top.

Step 1.2 - public E pop()

Call the emptyCheck method. This will throw an IllegalStateException if the stack is empty.

Decrement the value of top, and then return the item in the top spot of the stuff array.

Step 1.3 - public E peek()

Call the emptyCheck method. This will throw an IllegalStateException if the stack is empty.

Return the item in the top - 1 spot of the stuff array.

Step 1.4 - public int size()

Return the number of items in stuff.

Step 1.5 - public String toString()

Return a String representing the elements in the stack separated by spaces. For example, a stack of integers with 3 on top of 2 on top of 1 should return “1 2 3”. The oldest element in the stack should be the first in the string.

Step 1.6 - Testing

Run the ArrayStackTest suite, and ensure your above methods are passing these tests.

Step 2 - ListStack<E>

Next we will implement the generic version of a Stack with nodes, called ListStack<E>. This will need to implement the Stack<E> interface, and have at least a ListNode<E> called top as a field.,

Step 2.1 - ListNode

Look over the file called ListNode.java. This class implements the Node class we discussed. It should have an E value and a ListNode next reference as private components, along with public get and set methods for the value and next fields. There are two constructors. The first brings in and stores only an E value, and leaves the ListNode next as null. The second brings in both an E value, and a ListNode next, storing both.

Step 2.2 - public void push(E data)

Study the code provided. It will create a new ListNode that stores the data, has the current topas its next, and finally redirects top to reference this new ListNode.

Step 2.3 - public E pop()

Call the emptyCheck method. This will throw an IllegalStateException if the stack is empty.

Save the value stored in top, and redirect top to point to the next ListNode.

Return the value you stored.

Step 2.4 - public E peek()

Call the emptyCheck method. This will throw an IllegalStateException if the stack is empty.

Return the value stored in the top ListNode.

Step 2.5 - public int size()

If top is null, return 0. Otherwise, return the number of ListNode that are chained from the top node.

Step 2.6 - public String toString()

Return a String representing the elements in the stack separated by spaces. For example, a stack of integers with 3 on top of 2 on top of 1 should return “1 2 3”. The oldest element in the stack should be the first in the string.

Step 2.7 - Testing

Run the ListStackTest suite, and ensure your above methods are passing these tests.

Step 3 - Creating Random Mazes

Uncomment code labeled for this portion in

  • MazeController

First, you will be creating random mazes by implementing the tunnelRandomly function in the Puzzle class.

Step 3.1 - public void tunnelRandomly()

Create an ArrayStack of Positions, and push new Position(0,0) onto the stack.

While the stack still has Positions:

  • Pop the top Position from the stack.
  • Try to clear this Position.
  • If the clear was successful (returned true):
    • Add the CLOSED neighbors of this Position to the stack in a random order.

Step 3.2 - GUI

Run the GUI to interact with your code and make random mazes. You should see mazes similar to the image below.

Step 4 - Solving Mazes

Uncomment code labeled for this portion in

  • Trail
  • PuzzleTest
  • MazeController

A Trail is another recursive data structure, similar to a ListNode. The two fields of a Trail are a Position, denoting the end of the trail, and a link to another Trail called prev, which is a record of how you arrived at the current Trail. For the first step of a Trail, the prev is left as null.

In this step, you will use Trails to write an algorithm in the Puzzle class that solves a maze using depth-first search (DFS).

Step 4.1 - public Trail solve(Stack<Trail> solver)

If there is no Explorer in the maze or no goal in the maze, then return null.

Otherwise, push a new Trail starting at the Explorer’s position onto the solver stack.

While the stack still has potential Trails:

  • Pop the top Trail from the stack.
  • If the Trail end is the goal Position, return this Trail
  • If the Cell in the Maze at the Trail end is OPEN
    • Mark it as a VISITED Cell
    • Add new Trails based on this Trail for each of the neighbors to the stack.

If you empty the stack and have still not found the goal, then return null.

Step 4.2 - Testing

Run the PuzzleTest suite, and ensure your above methods are passing these tests.

Step 4.3 - GUI

Run the GUI to interact with your code. When you Randomize to create a random maze, add an Explorer and goal, and then click the Solve button, you should see something similar to the following image.

Step 5 - Evaluation

Create 10 mazes of size 30x30 and record the number of visited nodes as a percentage of the total number of open spaces in the initial maze. Also, record the number of steps used by your solver. You can choose either implementation for each data type.

Grading

  • To Complete this lab, complete all the steps.