IC312: Data Structures (FA16)

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Project 1: A-Maze-ing Stacks and Queues

Overview

In this project you will implement the Stack and Queue interface using a LinkedList, ArrayList, and a CircularArrayList to both solve and generate mazes. Amazing! You will do so without using the java.util library, which means, you'll have to do ALL the implementation work yourself.

Due Date

This project is due Sunday, October 2nd at 2359

Grading

There are many different parts to the project. Based on how much you complete, the maximum grade is described below:

  • Grade: 25%
    • Complete the LinkedList implementation of a O(n) Queue
  • Grade: 45%
    • Complete the LinkedList implementation of a O(n) Queue
    • Use LinkedList implementation of a Queue to solve the provided mazes
  • Grade: 60%
    • Complete the LinkedList implementation of a O(n) Queue and O(1) Stack
    • Used LinkedList implementation of a Queue to solve the provided mazes
  • Grade: 75%
    • Complete the LinkedList implementation of a O(n) Queue and O(1) Stack
    • Used LinkedList implementation of a Queue to solve the provided mazes
    • Used LinkedList implementation of a Stack to generate new mazes
  • Grade: 80%
    • Complete the LinkedList implementation of a O(1) Queue and O(1) Stack
    • Used LinkedList implementation of a Queue to solve the provided mazes
    • Used LinkedList implementation of a Stack to generate new mazes
  • Grade: 85%
    • Complete the LinkedList implementation of a O(1) Queue and O(1) Stack
    • Complete the ArrayList implementation of a O(1) amortized Stack
    • Used LinkedList implementation of a Queue to solve the provided mazes
    • Used ArrayList implementation of a Stack to generate new mazes
  • Grade: 95%
    • Complete the LinkedList implementation of a O(1) Queue and O(1) Stack
    • Complete the ArrayList implementation of a O(1) amortized Stack
    • Complete the CircularArrayList implementation of a O(1) amortized Queue
    • Used CircularArrayList implementation of a Queue to solve the provided mazes
    • Used ArrayList implementation of a Stack to generate new mazes
  • Grade: 100%
    • Complete the LinkedList implementation of a O(1) Queue and O(1) Stack
    • Complete the ArrayList implementation of a O(1) amortized Stack
    • Complete the CircularArrayList implementation of a O(1) amortized Queue and O(1) amortized Stack
    • Used CircularArrayList implementation of a Queue to solve the provided mazes
    • Used CircularArrayList implementation of a Stack to generate new mazes

Partial credit and deductions will be provided based on quality of work. For example, we will heavily test your data structures at the extremes, so performance matters! Plus, if you have any \(O(n)\) operations in your stack and queue, that will impact the performance of your maze algorithms and be exposed in our testing.

You must full complete each of the List implementation for full credit. This includes the entire List interface in addition to the appropriate Queue/Stack interface.

Submission and Starter Code

All starter code for this project can be obtained via the ~aviv/bin/ic312-up and submission will occur via ~aviv/bin/ic312-submit.

You must submit the following edited file(s):

  • ic312/LinkedList.java
  • ic312/ArrayList.java
  • ic312/CircularArrayList.java
  • SolveMaze.java
  • DrawMaze.java
  • README : containing any attribution or notes for grading.
  • Any testing files you'd like us to look at and consider during grading.

Description

Solving and Generating Mazes

You will be asked to solve and generate mazes using a queue and a stack, respectively. These processes are independent of the implementation choices for the queue and stack.

Let's consider a maze as a 2-D array of spaces, where between each space there is a wall or not. The start point of the maze will be the upper left and the finish point is the lower right. For example, we will use the following maze maze0.ser in this example.

maze_labeled.png

Notice that the maze has a width and height, and we index spaces in the maze with (w,h). The top left index is (0,0), and the bottom right index is (width-1,height-1). The maze will always start in the upper left and finish in the bottom right. We will describe two spaces as "reachable" if they are adjacent and do not have a wall between them.

Solving a Maze with a Queue

The process of solving a maze with queue is a lot like "hunting" out the end point from the start point. To do that, we must ensure that we test all possible paths. The queue will allow us to track which spaces we should visit next.

The basic routine works as follows:

  • Initialize a queue with the start index (0,0)
  • Loop Until: queue is empty
    • Dequeue current index and mark it as visited
    • If current index is the finish point
      • Break! We've found the end
    • Enqueue all indexes for reachable and unvisited neighbors of the current index
    • Continue the loop.

Looking over this routine, imagine the queue, full of spaces. Each time you dequeue space you are searching around for more spaces to search out next. If you find any, you add them to the queue to eventually be analyzed later.

Because of the FIFO nature of a queue, the resulting search pattern is a lot like a water rushing out from the start space, through all possible path in the maze until the end is reached. This search pattern is also referred to as Breadth First Search (or BFS).

Here's a gif of what the solving routine will look like. The * shows a space being visited.

maze_solve.gif

For consistency, you should always enqueue the indexes into the queue in the order that they are provided via the getReachableUnvisited() neighbors method (see below). That is enqueue index 0 of the returned list first, then the next index, and so on. In this way, your algorithm match mine and should work like the animation above. The final state of your maze should look like below:

maze_solved.png

Drawing a Maze with a Stack

The process of drawing a maze is very similar to solving a maze, but instead the goal is to explore all spaces, removing walls along the way, such that there exist a path between any two spaces through a series of reachable spaces. That also means that there will exist a path from the from the start to the end.

The algorithm to ensure all reachability will work as follows:

  • Initialize a stack with the start index (0,0)
  • Loop Until: stack is empty
    • pop current index off the stack and mark it as visited
    • If current index has any unvisited neighbors
      • Choose a random unvisited neighbor index
      • Remove the wall between the chosen neighbor index and the current index
      • push the current index on the stack
      • push the randomly choose neighbor index on the stack
    • Continue the loop.

Looking over this routine, you should be able to invision how this procedure will dive through the maze randomly, like a snake, until the snake reaches a dead end (a space without any unlisted neighbors). The exploration of the snake would then have to backtrack until there is a space with unvisited neighbors and explore from there. Eventually, the snake will have explored the entire maze, at which point, you're done. This search pattern is also referred to as Depth First Search (or DFS)

Here's a gif of what the maze drawing routine would look like. The * shows a space being visited.

maze_draw.gif

For consistency, you should make a random choice from the reachable neighbors like so: 

int r = rnd.nextInt(l.size());

Where l is the list of reachable neighbors, rnd is a Random object, and r is the index of the randomly selected neighbor. If you follow this procedure, you should be able to match the generation routine in the above animation.

Maze files

You are provided with three sample maze files, maze0.ser, maze1.ser, and maze2.ser. The *.ser extension stands for "serialized" because each file is just serialization of a Maze object.

The maze files will serve two purposes for you: (1) it will provide you sample mazes to solve while you are unable to test your maze drawer, and (2) it will provide something to test against for your maze drawer. Each of the files were generated with the following commands:

  • java DrawMaze maze0.ser 10 10 10
  • java DrawMaze maze1.ser 10 20 30
  • java DrawMaze maze2.ser 25 25 25

To print the mazes, you can use the provided PrintMaze.java program.

Maze.java and Space.java

To facilitate your programming, all the basic maze functionality is provided to you in two java files: Maze.java and Space.java. You may look over that code (there are comments) but do not edit those files.

Here are some relevant methods you will need to call in your code. 

/* Maze class  methods*/

//return a List of index pairs of all the unvisited neighbors of the index (h,w)
public List<Pair<Integer,Integer>>  getUnvistedNeighbors(int h, int w)

//return a List of index pairs of all the unvisited and reachable
//neighbors (no walls between) of the index (h,w)
public List<Pair<Integer,Integer>> getReachableUnvistedNeighbors(int h, int w)

//remove a wall from index (h,w) at the directions
//Space.LEFT, Space.RIGHT, Space.UP, Space.DOWN
public void removeWall(int h, int w, int direction)

//mark index (h,w) visited
public void visit(int h, int w)

//check if a index (h,w) is visited
public boolean isVisited(int h, int w)

The ic312 package

You are not allowed to use java.util for this project, and instead, you will be building up and using the ic312 package of data structures. This package is imported in all the provided Java files: import ic312.*.

In the package directory you will find the following classes definitions. Of those, you you should not edit (but feel free to use and read over):

  • List.java : Definition of the List interface
  • Queue.java : Definition of the Queue interface
  • Stack.java : Definition of the Stack interface
  • Pair.java : A pair class for storing pairs of genericly defined objects (potentially of different types)

You will be required to edit the following files

  • LinkedList.java : A recursive Linked List implementation that implements the List, Queue, and Stack interfaces. You will need to complete the interface implementations for Stack and Queue and make sure it is O(1) in Stack/Queue operations (this will require adding a tail pointer).
  • ArrayList.java : A array based List implementation that implements List and Stack. It is interface implementation is incomplete for all interfaces, and you should complete it.
  • CircularArrayList.java : A circular array based implementation of a List that can implements a Stack and Queue. It is interface implementation is incomplete for all interfaces, and you should complete it.

As all of these items are part of a package, you should compile and use them outside of the package directory. What this means, is that, for example, to compile the LinkedList.java file after you edit it, you do so outside the package directory, like so: 

aviv@potbelly:sol$ javac ic312/LinkedList.java

If you were to do so within the package directory, you'll get an error that it can't find the interfaces. 

aviv@potbelly:sol$ cd ic312/
aviv@potbelly:ic312$ javac LinkedList.java 
LinkedList.java:4: error: cannot find symbol
public class LinkedList<T> implements List<T>,Queue<T>,Stack<T>{
                                      ^
  symbol: class List
LinkedList.java:4: error: cannot find symbol
public class LinkedList<T> implements List<T>,Queue<T>,Stack<T>{
                                              ^
  symbol: class Queue
LinkedList.java:4: error: cannot find symbol
public class LinkedList<T> implements List<T>,Queue<T>,Stack<T>{
                                                       ^
  symbol: class Stack
3 errors

The reason for this is that the package lookup procedures is path dependent. I agree this is a bit awkward and non-ideal, but this is the way it is.