Escape the Maze
In this lab we begin our exploration of algorithms, the conceptual heart of computer science. You’ll develop a simple algorithm to escape a maze and implement it in Java.
If you need help with today’s lab, please join this Zoom meeting. It will be staffed during normal lab hours: 9AM–9PM CST.
1. Algorithm Design and Implementation (50 Minutes)
Let’s learn more about algorithms—systematic ways that we and computers use to solve problems.
1.1. Escape Plans
Open and make a copy of this maze spreadsheet. Click "Add Ons → Maze Creator → Redraw Maze” to generate a random maze. Note that you may have to wait a minute for the "Maze Creator" menu to appear. Click through any scary warnings and the script should run. Feel free to change the number of rows and columns to create a larger or smaller example.
Working online with a partner (or multiple), develop an algorithm to escape from mazes like the ones drawn on the spreadsheet above. You should limit yourself to the following actions:

canMove()
: returnstrue
if you can move forward,false
otherwise (if you are blocked by a wall) 
move()
: moves one square forward if possible; otherwise does nothing 
turnRight()
: turns right, does not change your position 
turnLeft()
: turns left, does not change your position 
isFinished()
: returnstrue
when you have reached the end position
1.2. Evaluating Algorithms
As you begin implementing your maze escape algorithm, think about the different ways that computer scientists evaluate algorithms. Here are some of the components of a good algorithm:

It works. It should definitely solve the problem you are trying to solve, or at least have a good probability of solving it in most cases.

It should perform well. It should not require a huge amount of resources to solve the problem—whether those resources are time, computational horsepower, computer memory, or disk space.

It should be understandable. Good algorithms are easy to understand and reason about. The best ones are simple, and sometimes we even call them elegant. Complex algorithms are hard to understand, making it difficult to think about what they will do in certain cases.

The implementation should be clear and understandable. Many times we encounter algorithms while reading computer code. So just as the algorithm must be clear, the implementation in computer code must also be clear. We will have a lot more to say about code quality throughout the semester—particularly on the MPs.
These are not noncontradictory goals. Frequently the desire for simplicity clashes with attempts to improve performance, or handle all inputs correctly. But particularly when you are starting off as a computer science, err on the side of simplicity. Remember: computation is (increasingly) cheap, humans are expensive. If it takes me 10 times longer to understand or modify your algorithm, it is not worth a only minor improvement in performance. Let your algorithms waste a bit of computer time, but never human time.
1.3. Analyzing Your Algorithm
Once you have developed your algorithm, consider the following questions before proceeding:

What are the limitations of your algorithm? Will it always find its way out of any maze, or just mazes with certain properties?

How could you improve your algorithm? Would it help to keep track of other state, or have other operations (like
moveRight()
) available to you?
1.4. Implementing Your Algorithm
Now let’s implement the maze solving algorithm that you designed in the first half in Java.
Move over to the lab homework problem at this point. Today’s homework uses the CS 125 mazemaker Java library, which uses a wellknown algorithm to automatically generate mazes. You can find the mazemaker source code and documentation on GitHub 1 Note that the version used on the homework problem is bit different than what is posted online, but largely the same.
1.4.1. Your algorithm’s performance
Once you have a working algorithm, spend some time understanding its performance. Answer the following questions 2:

How many steps—each consisting of moving one square—does it take to finish the maze? Because the maze generation is random, you might want to run multiple trials and average the results.

For a maze with dimensions N by M, what is the minimum number of steps required to complete the maze, assuming you start at the bottom left and exit at the top right?

How much worse does your algorithm do? Why?

Can you come up with ways to improve your algorithm?
1.4.2. Your algorithm’s limitations
Now spend some time thinking about the limitations of your algorithm. In particular, the mazes that are generated by our maze creator all have something in common: They have no loops! This is due to the operation of the maze generation algorithm, which uses a simple depthfirst search over the twodimensional space. To make things more interesting, we could have inserted some holes at the end—but we didn’t.
But suppose you ran your algorithm on a maze with loops. Think up one way it could get stuck. So it’s possible that your algorithm may not work! But, assuming that the start and end point are always on the exterior wall of the maze, try to convince your partner that your algorithm will still work.
1.5. A Randomized Algorithm
The mazesolving algorithm you implemented above is deterministic. Provided the same maze, it will always navigate through it in the same way. You may want to rerun your algorithm on the same maze a few times to convince yourself of this.
Deterministic algorithms are great—easy to understand and reason about. But there is a different class of algorithms called randomized algorithms. As their name implies, these algorithms use randomness as part of their logic. In some cases, this allows them to dramatically outperform the best known deterministic algorithm.
One randomized algorithm that you may have seen in action is a spacefilling algorithm called a random walk. If you’ve ever watched a Roomba 3, you’ve seen a random walk in action. It turns out that mapping is a hard problem for robots to solve. So, rather than trying to map an area, early robotic vacuums 4 just implemented a random walk:

Go straight until you hit something

Turn a random amount but sufficient to not continue into the obstacle

Repeat
To a human observer this looks crazy—how is it ever going to get every spot? But it turns out that there is some fairly sophisticated mathematics that shows that, given a certain number of passes, your random robot maid will get every spot with very high probability. Or at least chase a duck:
1.5.1. Implement a random walk
Inspired by your vacuum, try reimplementing your mazesolving algorithm using a random walk. More or less, here’s how that works:

Go forward until you are facing a wall

Randomly turn right or left

Repeat
Once you are done, compare the running time of your randomized algorithm with the deterministic algorithm you implemented above. Are you surprised? With your partner, try to develop an explanation for the difference in performance.
2. Before You Leave
Don’t leave lab until:

You’ve escape the maze!

And so has everyone else in your lab!
If you need more help completing the tasks above please come to online office hours or post on the {forum}.