Comp 251: Assignment 3
• You are provided some starter code that you should fill in as requested. Add your code only
where you are instructed to do so. You can add some helper methods, but this is at your own
risk; helper methods could cause your methods to crash when called from other programs if
not added responsibly. Do not modify the code in any other way and in particular, do not
change the methods or constructors that are already given to you, do not import extra code
and do not touch the method headers. The format that you see on the provided code is the
only format accepted for programming questions. Any failure to comply with these rules
will give you an automatic 0.
• The starter code includes a tester class. If your code fails those tests, it means that there is
a mistake somewhere. Even if your code passes those tests, it may still contain some errors.
We will grade your code with a more challenging set of examples. We therefore highly
encourage you to modify that tester class, expand it and share it with other students on the
myCourses discussion board. Do not include it in your submission.
• Your code should be properly commented and indented.
• Do not change or alter the name of one of the files you must submit. Files with the wrong
name will not be graded. Make sure you are not changing file names by duplicating them.
For example, main (2).java will not be graded. Make sure to double-check your zip file.
• Do not submit individual files. Include all your files into a .zip file and, when appropriate,
answer the complementary quiz online on MyCourses.
• You will automatically get 0 if the files you submitted on MyCourses do not compile.
• You should compile all your files directly from command line without using a package, by
using the command javac *.java
1. (40 points) We will implement the Ford-Fulkerson algorithm to calculate the Maximum Flow
of a directed weighted graph. Here, you will use the files WGraph.java and FordFulkerson.java, which are available on the course website. Your role will be to complete two methods
in the template FordFulkerson.java.
The file WGraph.java is the similar to the file that you used in your previous assignment to
build graphs. The only differences are the addition of setters and getters methods for the
Edges and the addition of the parameters “source” and “destination”. There is also an additional constructor that will allow the creation of a graph cloning a WGraph object. Graphs are
also encoded using a similar format than the one used in the previous assignment. The only
difference is that now the first line corresponds to two integers, separated by one space, that
represent the “source” and the “destination” nodes. An example of such file can be found on
the course website with the file ff2.txt. These files will be used as an input in the program
FordFulkerson.java to initialize the graphs. This graph corresponds to the same graph
depicted in [CLRS2009] page 727.
Your task will be to complete the two static methods fordfulkerson(Integer source,
Integer destination, WGraph graph, String filePath) and pathDFS(
Integer source, Integer destination, WGraph graph). The second method
pathDFS finds a path through a Depth First Search (DFS) between the nodes “source” and
“destination” in the “graph” through non-zero weight edges. You must return an ArrayList of
Integers with the list of unique nodes belonging to the path found by the DFS. If no path is
found, return an empty ArrayList. The first element in the list must correspond to the “source”
node, the second element in the list must be the second node in the path, and so on until the last
element (i.e., the “destination” node) is stored. The method fordfulkerson must compute
COMP 251 – HW3 Page 2 of 3 Fall 2018
an integer corresponding to the max flow of the “graph” and the graph itself. The method
fordfulkerson has a variable called myMcGillID, which must be initialized with your
McGill ID number.
Once completed, compile all the java files and run the command line java FordFulkerson
ff2.txt. Your program must use the function writeAnswer to save your output in a file. An
example of the expected output file is available in the file ff226000000.txt. This output
keeps the same format than the file used to build the graph; the only difference is that the a line
has been added; the first line now represents the maximum flow (instead of the “source” and
“destination” nodes). If the fordfulkerson method was unable to compute the maximum
flow, it should output a result of -1 (and not throw an exception). The other lines represent the
same graph with the weights updated with the values that represent the maximum flow. The
file ff226000000.txt represent the answer of the example showed in [CLRS2009] page
727. You are invited to run other examples of your own to verify that your program is correct.
2. (40 points) We want to implement the Bellman-Ford algorithm for finding the shortest path in
a graph where edge can have negative weights. This question extends the previous question on
the implementation of the Dijkstra’s algorithm done in the assignment 2. You will need to execute this program to use the same auxiliary class Wgraph used in question 1. Your task is to
fill the method BellmanFord(WGraph g, int source) and shortestPath(int
destination) in the file BellmanFord.java.
The method BellmanFord takes a object WGraph named g as an input (See Assignment 2)
and an integer that indicates the source of the paths. If the input graph g contains a negative cycle, then the method should throw an exception. Otherwise, it will return an object BellmanFord that contains the shortest path estimates (the private array of integers
distances), and for each node its predecessor in the shortest path from the source (the private array of integers predecessors).
The method shortestPath will return the list of nodes as an array of integers along the
shortest path from the source to the node destination. If this path does not exists, the method
should throw an exception.
Please take a look at the code, we defined some exceptions that you should use when appropriate if one of your methods fails to terminate.
Input graphs are available on the course webpage to test your program. Nonetheless, we invite
you to also make your own graphs to test your program.
3. (20 points) You will complete this section through MyCourses. Note that you MUST use your
own results to answer those questions. Answers to this quiz that would not conceptually match
the output of your program will be considered plagiarism (refer to course outline).
You will submit FordFulkerson.java and BellmanFord.java in a single zip file.