Description
Abstract
In this assignment, you will determine whether an arbitrary directed graph has a
valid topological sort in which some vertex, x, comes before some other vertex, y.
More than anything, this program should serve as a relatively short critical
thinking exercise. You will gain experience reading graphs from an input file,
representing them computationally, and writing graph theory algorithms. You will
also solidify your understanding of topological sorts, sharpen your problem
solving skills, and get some practice at being clever, because your solution to this
problem must be O(|V|2
). In coming up with a solution, I recommend focusing
first on developing a working algorithm, and then analyzing its runtime.
(Focusing too much on the runtime restriction might cloud your thinking as you
cook up a solution to this problem.)
If you use any code that I have given you so far in class, you should probably
include a comment to give me credit. The intellectually curious student will, of
course, try to write the whole program from scratch.
Deliverables
ConstrainedTopoSort.java
Note! The capitalization and spelling of your filename matter!
Note! Code must be tested on Eustis, but submitted via Webcourses.
1. Problem Statement
Given a directed graph, G, and two integers, x and y, determine whether G has a valid topological sort in which
vertex x comes before vertex y. (Notice that the problem does not ask whether x comes directly before y.) For
example:
G1
In G1, there is a valid topological sort in which vertex 2 comes before vertex 1 (2, 1, 3, 4). There is also a valid
topological sort in which vertex 1 comes before vertex 2 (1, 2, 3, 4). Both of those are also valid topological
sorts in which vertex 2 comes before vertex 4. (Notice that vertex 2 does not have to come directly before vertex
4.) However, there is no valid topological sort in which vertex 4 comes before vertex 1.
2. Input File Format
Each input file contains a single digraph. The first line contains a single integer, n ≥ 2, indicating the number of
vertices in the graph. (Vertices in these graphs are numbered 1 through n.) The following n lines are the
adjacency lists for each successive vertex in the graph, with a small twist: each adjacency list begins with a
single non-negative integer, k, indicating the number of vertices that follow. The list of vertices that follows will
contain k distinct integers (i.e., no repeats) on the range 1 through n. For example, the following text file
corresponds to the graph G1 that is pictured above:
g1.txt
4
1 3
2 3 4
1 4
0
3. Special Restriction: Runtime Requirement
Please note that you must implement a solution that is O(|V|2
), where V is the set of vertices in the graph. Recall
from our formal definition of big-oh that a faster solution is still considered O(|V|2
).
1 2
3 4
4. Method and Class Requirements
Implement the following methods in a class named ConstrainedTopoSort.
public ConstrainedTopoSort(String filename)
This constructor opens the file named filename and reads the graph it contains into either an adjacency
matrix or adjacency list. We will process multiple xy queries for this graph, but we only want to load it
into memory once. This method should throw exceptions as necessary.
public boolean hasConstrainedTopoSort(int x, int y)
Given integers x and y such that 1 ≤ x ≤ n and 1 ≤ y ≤ n, if this graph has a valid topological sort in
which vertex x precedes vertex y, return true. Otherwise, return false. Do this in O(|V|2
) time.
public static double difficultyRating()
Return a double indicating how difficult you found this assignment on a scale of 1.0 (ridiculously easy)
through 5.0 (insanely difficult).
public static double hoursSpent()
Return a realistic estimate (greater than zero) of the number of hours you spent on this assignment.
5. Style Restrictions (Same as in Program #1) (Super Important!)
Please conform as closely as possible to the style I use while coding in class. To encourage everyone to develop
a commitment to writing consistent and readable code, the following restrictions will be strictly enforced:
Capitalize the first letter of all class names. Use lowercase for the first letter of all method names.
Any time you open a curly brace, that curly brace should start on a new line.
Any time you open a new code block, indent all the code within that code block one level deeper than
you were already indenting.
Be consistent with the amount of indentation you’re using, and be consistent in using either spaces or
tabs for indentation throughout your source file. If you’re using spaces for indentation, please use at least
two spaces for each new level of indentation, because trying to read code that uses just a single space for
each level of indentation is downright painful.
Please avoid block-style comments: /* comment */
Instead, please use inline-style comments: // comment
Always include a space after the “//” in your comments: “// comment” instead of “//comment”
The header comments introducing your source file (including the comment(s) with your name, course
number, semester, NID, and so on), should always be placed above your import statements.
Use end-of-line comments sparingly. Comments longer than three words should always be placed above
the lines of code to which they refer. Furthermore, such comments should be indented to properly align
with the code to which they refer. For example, if line 16 of your code is indented with two tabs, and line
15 contains a comment referring to line 16, then line 15 should also be intended with two tabs.
Please do not write excessively long lines of code. Lines must be no longer than 100 characters wide.
Avoid excessive consecutive blank lines. In general, you should never have more than one or two
consecutive blank lines.
Please leave a space on both sides of any binary operators you use in your code (i.e., operators that take
two operands). For example, use (a + b) – c instead of (a+b)-c. (The only place you do not have to
follow this restriction is within the square brackets used to access an array index, as in: array[i+j].)
When defining or calling a method, do not leave a space before its opening parenthesis. For example:
use System.out.println(“Hi!”) instead of System.out.println (“Hi!”).
Do leave a space before the opening parenthesis in an if statement or a loop. For example, use
use for (i = 0; i < n; i++) instead of for(i = 0; i < n; i++), and use if (condition) instead of if(condition)
or if( condition ).
Use meaningful variable names that convey the purpose of your variables. (The exceptions here are
when using variables like i, j, and k for looping variables or m and n for the sizes of some inputs.)
Do not use var to declare variables.
6. Compiling and Testing on Eustis (and the test-all.sh Script!)
Recall that your code must compile, run, and produce precisely the correct output on Eustis in order to receive
full credit. Here’s how to make that happen:
1. To compile your program with one of my test cases:
javac ConstrainedTopoSort.java TestCase01.java
2. To run this test case and redirect your output to a text file:
java TestCase01 > myoutput01.txt
3. To compare your program’s output against the sample output file I’ve provided for this test case:
diff myoutput01.txt sample_output/TestCase01-output.txt
If the contents of myoutput01.txt and TestCase01-output.txt are exactly the same, diff won’t print anything to
the screen. It will just look like this:
seansz@eustis:~$ diff myoutput01.txt sample_output/TestCase01-output.txt
seansz@eustis:~$ _
Otherwise, if the files differ, diff will spit out some information about the lines that aren’t the same.
4. I’ve also included a script, test-all.sh, that will compile and run all test cases for you. You can run it on Eustis
by placing it in a directory with ConstrainedTopoSort.java and all the test case files and typing:
bash test-all.sh
Super Important: Using the test-all.sh script to test your code on Eustis is the safest, most sure-fire way to
make sure your code is working properly before submitting.
7. Grading Criteria and Miscellaneous Requirements
Important Note: When grading your programs, we will use different test cases from the ones we’ve released
with this assignment, to ensure that no one can game the system and earn credit by simply hard-coding the
expected output for the test cases we’ve released to you. You should create additional test cases of your own
in order to thoroughly test your code. In creating your own test cases, you should always ask yourself, “What
kinds of inputs could be passed to this program that don’t violate any of the input specifications, but which
haven’t already been covered in the test cases included with the assignment?”
The tentative scoring breakdown (not set in stone) for this programming assignment is:
100% Passes test cases. This portion of the grade includes tests of the difficultyRating() and
hoursSpent() methods.
Important Note! Additional point deductions may be imposed for poor commenting and whitespace. Significant
point deductions may be imposed for violating the style restrictions listed above. You should also still include
your name and NID in your source code.
Please be sure to submit your .java file, not a .class file (and certainly not a .doc or .pdf file). Your best bet is to
submit your program in advance of the deadline, then download the source code from Webcourses, re-compile,
and re-test your code in order to ensure that you uploaded the correct version of your source code.
Important! Programs that do not compile on Eustis will receive zero credit. When testing your code, you
should ensure that you place ConstrainedTopoSort.java alone in a directory with the test case files (source files,
the sample_output directory, and the test-all.sh script), and no other files. That will help ensure that your
ConstrainedTopoSort.java is not relying on external support classes that you’ve written in separate .java files but
won’t be including with your program submission.
Important! You might want to remove main() and then double check that your program compiles without
it before submitting. Including a main() method can cause compilation issues if it includes references to homebrewed classes that you are not submitting with the assignment. Please remove.
Important! Your program should not print anything to the screen. Extraneous output is disruptive to the
grading process and will result in severe point deductions. Please do not print to the screen.
Important! No file writing. Please do not write to any files from ConstrainedTopoSort.java.
Important! Please do not create a java package. Articulating a package in your source code could prevent it
from compiling with our test cases, resulting in severe point deductions.
Important! Name your source file, class(es), and method(s) correctly. Minor errors in spelling and/or
capitalization could be hugely disruptive to the grading process and may result in severe point deductions.
Similarly, failing to implement a required method, or failing to make certain methods public, private, static,
and/or non-static (as required), may cause test case failure. Please double check your work!
Input specifications are a contract. We promise that we will work within the confines of the problem statement
when creating the test cases that we’ll use for grading. Please reflect carefully on the kinds of edge cases that
might cause unusual behaviors for any of the methods you’re implementing.
Test your code thoroughly. Please be sure to create your own test cases and thoroughly test your code. You’re
welcome to share test cases with each other, as long as your test cases don’t include any solution code for the
assignment itself.
(New!) With this assignment, I’ve included fewer test cases than usual. I want to transfer more responsibility
for test case creation to you as you progress through this class and develop a stronger understanding of test
driven development.
Start early! Work hard! Ask questions! Good luck!
