# CSE 373, Winter 2018: Project 4: Generating and solving mazes

## Overview

In this project, you will implement Kruskal's algorithm and Dijkstra's algorithm to help you both generate and solve mazes.

This is a team assignment. This entire project is due on Sat, Mar 10 at 11:30pm.

When working on this assignment, we expect you meet these baseline expectations at all times:

### Expectations

Here are some baseline expectations we expect you to meet:

• Follow the course collaboration policies

• DO NOT use any classes from java.util.*. There are only two exceptions to this rule:

1. You may import and use java.util.Iterator and java.util.NoSuchElementException.

2. You may import and use anything from java.util.* within your testing code.

• DO NOT modify instructor-provided code (unless told otherwise)

## Part 0: Initial Setup

1. Download the project from this link and open it in your IDE. See the instructions from project 1 if you need a reminder on how to do this.

2. Copy all of your data structures, algorithms, and tests from the previous project to this new one.

Your ArrayHeap will not immediately compile. This is ok. We will explain what changes you need to make in the next section.

3. Finally, make sure everything works.

Try running TestGraph.java and make sure the tests run.

Try running SanityCheck.java, and try running checkstyle. Checkstyle should still report the same 5 errors with SanityCheck.java as it did with the previous projects.

## Part 1: Make ArrayHeap compile

Take a look at IPriorityQueue. You may notice that the interface now allows all subclasses to implement an optional method: remove(...).

You may optionally implement this method while implementing Dijkstra's algorithm later in the project.

For now, add the method to your ArrayHeap class and throw an UnsupportedOperation exception so that your code will compile.

## Part 2: Try running the maze generator

Task: make sure you can run MainWindow

Navigate to the mazes.gui package and run MainWindow.java. This will launch a program that will (eventually) generate and solve mazes.

The GUI consists of two main regions. The large region at the top, which will initially contain your maze, and a few options and buttons at the bottom.

Here is a brief explanation of the user interface:

• The "Base maze shape" combobox controls what underlying "shape" your maze will have. The default is "Grid", which creates a maze where each room is a rectangle.

Try switching the option to "Voronoi" and click the "Generate new maze" button to the left. This will generate a maze where the rooms are more irregular.

• The "Maze generator" combobox controls the actual maze generation process – it takes the initial set of room and removes edges to generate a plausible maze.

The default option is "Do not delete any edges", which, as you may have guessed, does not delete any edges.

Now, try picking one of the "Delete random edges" options and generate a new maze. You should now see some of the edges removed and see something that more closely resembles a maze.

Unfortunately, the "randomly remove edges" strategy is not that great. If we remove 30% of the edges, the maze is too easy. If we remove 50% of the edges, we often end up with an unsolvable maze. (The red dots in the upper-left and lower-right corners are our starting and ending points).

The final option labeled "Run (randomized) Kruskal" is what you will eventually need to implement. It turns out we can use the properties of minimum spanning trees to generate a much more interesting (and yet always solvable) maze!

• The "Find shortest path" button will, once implemented, draw the shortest path between the two red dots.

Clicking this button should currently cause the program to crash – we haven't implemented it yet.

• If you want to customize the different options (e.g. change the number of rows and columns in the grid maze, change the percentage of edges removed), look at the MainWindow.launch method. Feel free to change any of the constants there -- we will not be looking at this file when grading, so we don't care what changes you make.

## Part 3: Implement ArrayDisjointSet

Notes:

• Be sure to use implement your disjoint set using the array-based representation we discussed in lecture.

• We have provided you a few tests for this class (TestArrayDisjointSet), but they're deliberately minimal. We strongly encourage you to add more tests to make sure your ArrayDisjointSet is working correctly.

## Part 4: Implement Graph's constructor

Task: implement the Graph constructor and numVertices and numEdges methods.

Notes:

• You can find this class inside the misc.graphs package.

• Your constructor is currently designed to accept a list of vertices and a list of edges.

However, you may find this somewhat inconvenient to work with, especially once you start implementing the findShortestPathBetween(...) method.

So, you will probably want to add extra fields so that you can store the graph in a more useful representation (e.g. as an adjacency list or adjacency matrix).

• This class uses generics in a slightly more complicated way then you've seen in previous projects. We've tried to insulate you from this as much as possible, but it's possible you may run into unexpected issues or have difficulty getting your code to compile depending on what exactly you're doing.

If this happens to you, please ask for help either on Piazza or during office hours ASAP and we'll help you get unstuck as best as we can.

This is a class about data structures and algorithms, not a class about Java, so we don't want you to waste your time struggling with Java-related issues.

• You should make sure to look over the misc.graphs.Edge class. Any objects of type E implement the Edge methods.

However, be sure not modify this class.

• You can find (again fairly minimal) tests for this class in TestGraph.

## Part 4: Implement Graph.findMinimumSpanningTree(...)

Notes:

• You should implement findMinimumSpanningTree(...) using Kruskal's algorithm.

• You can use top topKSort(...) to sort your edges. This will mean your algorithm will not run in $$\mathcal{O}((|E| + |V|)\alpha(|V|))$$ time, but that's ok.

• If you do want to implement Kruskal's algorithm as efficiently as possible, feel free to implement a linear sort such as Bucket sort and use that instead.

The only caveat is that your sorting algorithm needs to be a private helper method within your Graph class. It doesn't really make sense for the sorting algorithm to live in a class about graphs, but we need to do this due to limitations in our grading scripts. (They copy specific files from your projects, so if you add extra code in unexpected places, they may not be copied over.)

## Part 5: Implement KruskalMazeCarver

If you remember when we were running the maze program from before, the "remove random walls" algorithms ended up generating pretty poor mazes. They either removed too many walls and created trivial mazes, or removed too few and created impossible ones.

What we really want is an algorithm that (a) generates a random-looking maze, (b) makes sure the maze is actually solvable, and (c) removes as few walls as possible.

It turns out that we can use algorithms such as Prim and Kruskal to do exactly that!

Here's the trick: we take the maze, treat each room as a vertex and each wall as an edge, assign each wall a random weight, and run any MST-finding algorithm. We then remove any wall that was a part of that MST.

This will end up satisfying all three criteria! By randomizing the wall weights, we remove random walls which satisfies criteria (a). A MST-finding algorithm, by definition, will ensure there exists a path from every vertex (every room) to every other one, satisfying criteria (b). And finally, because MST-finding algorithms try and avoid cycles, we avoid removing unnecesary edges and end up with a maze where there really is only one solution, satisfying criteria (c).

Your task here is to implement this algorithm within the KruskalMazeCarver class.

Other notes:

• You can find this class inside the mazes.generators.maze package.

• Make sure you understand how to use the Maze and Wall objects. The Wall object is a subclass of Edge, which means you should be able to pass a list or set of Walls into your Graph constructor (along with the corresponding list of Rooms).

• You may import and use java.util.Random while implementing this class.

• If you're stuck, try taking a look at RandomMazeCarver, which is located within the same package. Your algorithm will be a little more complicated, but it may serve as a good source of inspiration.

• To test your method, try running the program and generate a few mazes after selecting the "Run (randomized) Kruskal" option.

## Part 6: Implement Graph.findShortestPathBetween(...)

Finally, you will implement the code to actually solve the mazes.

Notes:

• You should implement findShortestPathBetween(...) using Dijkstra's algorithm.

• To represent infinity, use the Double.POSITIVE_INFINITY constant.

• While we definitely do encourage you to look at the pseudocode we provided in lecture, please be sure to take them with a grain of salt.

While we tried to write the pseudocode in a way that stuck a good balance between giving you a high-level overview vs making details clear, it's possible that we accidentally omitted a few details or included a minor bug somewhere.

In addition, you may find it convenient to arrange your code in a slightly different way then what the pseudocode suggests, especially since you're trying to solve a slightly different problem then what the lecture slides are solving: The version of Dijkstra's algorithm we provided in lecture is trying to find the shortest paths from the start to every other node; you're trying to find the shortest path from the start to a specific node.

• One challenge you may run into is figuring out how exactly to update the costs of the vertices.

Feel free to solve this problem however you want – however, if you're stuck, we recommend using one of two approaches:

1. Modify your ArrayHeap class and implement the remove method. Then, to update a vertex, you can remove and insert back in vertices.
• Rather then inserting your vertices directly into your heap, you may want to create and insert a custom inner class instead. (Why do you suppose that is?)

• Once you're done and all your tests are passing, try re-running the program and click the "Find shortest path" button. If everything went well, the program should now draw a red line connecting the start and the end!

(Or, if there is no valid path, display an alert box stating so.)

## Part 7: Complete individual writeup

Each group member should answer and submit these questions independently at this canvas page.

2. How was the project? Did you enjoy it?
3. Do you have any suggestions for improving the project?
1. Which parts of the project did you work on, and which parts did your partner program?
2. How was your partnership? Do you feel you and your partner contributed equally to this project?

## Ideas for extensions

To make sure we have enough time to grade everything, we do not plan on offering extra credit on this assignment.

However, if you're bored and have some free time, something you could try exploring is implementing other algorithms for generating mazes.

In particular, Kruskal's algorithm tends to generate mazes that have lots of short "cul-de-sacs", which lowers the difficulty of the overall maze.

A better algorithm might instead try and generate longer, more "windy" paths.

This website has a good overview of a few different maze generation algorithms if you want to investigate more.

## Deliverables

The following deliverables are due on Sat, Mar 10 at 11:30pm.

A single person from your partnership should submit a zip file conaining the entire contents of your src folder on Canvas.

Before submitting, be sure to double-check and make sure that...

• You added the remove(...) method to ArrayHeap. We do not plan on testing this method, so it's fine if all it does is throw an UnsupportedOperation exception.
• Your ArrayDisjointSet class is fully implemented and passes all tests.
• Your Graph class is fully implemented and passes all tests.
• Your KruskalMazeCarver class is fully implemented.
• You ran the checkstyle plugin within Eclipse and fixed all style errors.

Both partners should turn in a .txt or .pdf file containing their answers to part 7 on Canvas if you haven't already. This is due at the same time as the rest of your project.