Lab 6: Mazes - Breadth First Search

Overview

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

Materials

  • IntelliJ
  • Lab partner

Setup

  1. Download the skeleton for this project.
  2. Unpack the code into a new IntelliJ Java project.

Description

In Lab 4, we explored creating a maze using a stack to organize our potential spots to open. The stack allowed us to search in a depth-first search manner for possible next Cells to open. In other words, we would explore as far as possible, and backttrack if we reached a dead end in our journey, because we were search the youngest potential Cell next.

But there are other ways to search. We now want to investigate a breadth-first search approach, where the oldest potential Cell is expanded next, and do so within the context of searching rather than creating.

In this lab, you will create the necessary data structures to search a maze with breadth-first search, and compare this to a depth-first search technique.

Step 1 - ListQueue<E>

To implement the generic version of a Queue with nodes, you should use the generic ListNode<E> class we implemented last lab.

Step 1.1 - Implementation

Write a class called ListQueue<E>. This will need to implement the Queue<E> interface, and have at least a ListNode<E> called front and another called back as fields.

Step 1.2 - public void add(E value)

Create a new ListNode<E> that stores the value.

If the queue isEmpty, then set front to this new ListNode<E>.

Otherwise, the current back should refer to this new ListNode<E> as its next.

Finally, redirect back to reference this new ListNode<E>.

Step 1.3 - public E remove()

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

Save the value stored in front, and redirect front to point to the next ListNode<E>.

Return the value you stored.

Step 1.4 - public E element()

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

Return the value stored in the front ListNode<E>.

Step 1.5 - public int size()

If front is null, return 0.

Otherwise, return the number of ListNode<E> that are chained from the front node.

Step 1.6 - Testing

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

Step 2 - ArrayQueue<E>

Write a class called ArrayQueue<E>. This will need to implement the Queue<E> interface. The E[] stuff field is provided for you, you will need to add the necessary ints to track the data. I recommend starting with front and size both equal to 0.

Step 2.1 - public void add(E value)

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, taking care to reorder the elements so that the front is at index 0.
  • Redirect the stuff reference to the new array.
  • Reset front to be 0.

Now, you can always add the value to the back spot in the stuff array, and increment the size.

Step 2.2 - public E remove()

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

Save the value in the front index of the array.

Increment the value of front.

Decrement the value of size.

Return the item you stored.

Step 2.3 - public E element()

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

Return the item in the front spot of the stuff array.

Step 2.4 - public int size()

Return the size field.

Step 2.5 - Testing

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

Step 3 - Solving Mazes

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 either a Stack or a Queue. This is because the behavior of both is abstracted into a Searcher class. The Searcher class has method names like the Queue.

Step 3.1 - public Trail solve(Searcher<Trail> solver)

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

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

While the solver still has potential Trails:

  • Remove the next Trail from the solver.
  • 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 solver.

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

Step 3.2 - Testing

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

Step 4 - Evaluation

Create 10 mazes of size 30x30 and for each maze, record the number of visited nodes as a percentage of the total number of open spaces in the initial maze.

Use this data to compare the Stack (from your previous lab) versus Queue search strategies. Does either strategy have any clear strengths or weaknesses?

Grading

  • To Complete this lab, complete all the steps.