关于算法:EECS-2011-数学结构模型

EECS 2011: Assignment 4
Due: as set in eClass.
May be done in groups of up to three students
TL;DR: implement one static method in one class. Submit that class. Cheating not
allowed but some external code use is officially permitted.
Motivation
The purpose of this assignment is to implement a commonly used graph algorithm and
use it to solve a related problem.
Introduction
Graph theory is the study of graphs, which are mathematical structures used to model
pairwise relations between objects. A graph in this context is made up of vertices (also
called nodes or points) which are connected by edges (also called links or lines).
The included skeleton implementation provides several methods to build a graph data
structure from a file, etc. It also provides an iterator that visits the elements. Note that not
all of the functionality is implemented.
You are encouraged to review the textbook chapters on graphs. You may also use the
Java examples from the Algorithms textbook1
(please cite them if you do). A starter code
is also supplied.
Description
In this assignment, you will have to write two implementations of graph algorithms. For
your convenience, some starting code is provided. Note that the starter code may either
not implement some of the required features, or might implement them improperly – e.g.,
via stubs. Note that the speed of your algorithms may strongly depend on the
implementation of the missing methods and on the choice of auxiliary data structures you
choose to utilize for your algorithms. You are permitted to use any java.util classes:
ArrayList, PriorityQueue, HashMap, etc.
The graph is implemented a class called Graph, implementing loading of the graph
content from a file. Take a look at the associated classed to confirm you understand the
overall structure of the classes.
Part 1
Finish the implementation of the following method in the Graphs class (note the -s
ending of the class name):
public static Set<String> nearby(Graph graph, String origin, int hops)
1 https://algs4.cs.princeton.edu/40graphs/
2
The method allows one to determine which cities are nearby a specified city, within a
specified number of edges, and returns a set of such cities as Strings, with the
corresponding distances (edge counts) appended to them after a comma. E.g., calling the
method with Oshawa as origin, and 2 as the number of edges should produce a set with
the following items:
“Port Perry, 1”, “Ajax, 1”, “Bowmanville, 1”, “Uxbridge, 2”, and “Ajax, 2”.
You will notice that the graph files contain the actual distances and possible travel times.
For your algorithm, these will merely indicate that there is an edge present between a pair
of vertices.
As usual, you are free to implement any private or protected methods and classes as you
see fit. However, you should not modify the signatures of the existing methods in the
classes supplied if you choose to modify the method bodies. The main method in the
A4demo class should be able to print the mock results of your algorithm, to illustrate the
API.
Part 2
Nothing needs to be submitted for this part.
Explore your implementation, by redesigning some methods or by modifying the input, to
see if the graphs based on distances and those based on times can produce different
outputs. Three csv files are supplied with this assignment, one based on an Ontario map,
and two more resembling graph examples in the SW textbook.
NOTES:

1. Do not use package-s in your project. Using packages will cost you a 10 %
   deduction from the assignment mark.
2. Some aspects of your code will be marked automatically (e.g., how it handles
   boundary cases and error conditions), using a custom tester class and/or custom
   unit tests. It is also imperative you test your classes. If any of the java files that
   you submit do not compile, the whole submission will be given a grade of zero,
   regardless of how trivial the compiler error is. The code you submit should
   compile using
   javac *.java
   command in either Windows, Linux, or macOS.

3. Your code should include Javadoc comments.
   Submission
   Find all the java files in your project and submit them electronically via eClass (do not
   zip, tar, rar, or 7z them). Submit only the file(s) you modified; you are expected to
   change only the Graphs class. You may create other classes if you deem them necessary.
   If working in a group, make only one submission per group and include a group.txt
   file containing the names and the student numbers of the group members. The deadline is
   3
   firm. Contact your instructor in advance if you cannot meet the deadline explaining your
   circumstances. The extension may or may not be granted, at instructor’s discretion.
   Grading
   The assignment will be graded using the Common Grading Scheme for Undergraduate
   Faculties2
   . We look at whether the code passes the unit tests, satisfies the requirements of
   this document, and whether it conforms to the code style rules.
   Academic Honesty
   Academic honesty will be strictly enforced in this course. Specifically, direct
   collaboration (e.g., sharing code or answers) is not permitted, and plagiarism detection
   software will be employed. You are, however, allowed to discuss the questions, ideas, or
   approaches you take.
   Cite all sources you use (online sources – including web sites, old solutions, books, etc.)
   in your code comments; using textbook examples is allowed, but these must be cited as
   well.
   E.g.,
   1) /**

   • Constructs an empty list with the specified initial capacity.
     *
   • @param initialCapacity the initial capacity of the list
   • @exception IllegalArgumentException if the specified initial

   capacity

   • is negative
   • uses code from www.xxx.yyy.edu/123.html for initialization
     *
     */

   2) //formula based on Jane Smart’s thesis, page XX, available at
   https://…
   a = b + c;
   Although using outside sources is allowed – with proper citing, if the amount of nonoriginal
   work is excessive, your grade may be reduced. You might find the following
   article useful to have an idea what kind of collaboration is appropriate:
   https://en.wikipedia.org/wiki/Clean_room_design

4. https://secretariat-policies.info.yorku.ca/policies/common-gr…