CSCI 2600 — Principles of Software
Homework 6: Generics and Least-Cost Paths
Due: Tuesday, Aug. 6, 2024, 11:59:59 pm
Submission Instructions
• This assignment uses the same repository as Homework assignments 4 and 5, so when you
are ready to start working on Homework 6, pull Homework 6 ffles from the repository by
right-clicking on your Homework 4 project in Eclipse and selecting Team → Pull... Make
sure that When pulling is set to Merge, then click Finish.
• Be sure to commit and push the ffles to Submitty. Follow the directions in the version control
handout for adding and committing ffles.
• Be sure to include any additional ffles in your repo using Team → Add to Index.
• Important: You must press the Grade My Repository button, or your answers will not
be graded.
IMPORTANT NOTES:
You should have package hw6 with the usual directory structure. Write your code under src/main/java/hw6
and your tests under src/test/java/hw6 (shows as hw6 under src/test/java in Package Explorer).
 If your directory structure is incorrect, autograding will fail resulting in a grade of 0!
Introduction
This assignment lays the groundwork for an application you’ll build in a later homework assignment.
This assignment has two main parts. In the ffrst part, you will make your graph class(es) generic.
In the second part, you will implement a different path-ffnding algorithm for graphs known as
Dijkstra’s algorithm.Augmenting Your Graph and LEGO Paths
Problem 1: Making Your Graph Generic
In a subsequent homework assignment, your mission will be to ffnd the shortest route to visit a
certain set of buildings. A graph is an excellent representation of a map, and luckily you have already
speciffed and implemented a graph. Unfortunately, your graph only stores Strings, whereas the
route-ffnding application needs to store non-String data types in nodes and edges. More generally,
your graph would be much more widely useful if the client could choose the data types to be stored
in nodes and edges.
Your task is to convert your graph ADT to a generic class. Rather than always storing the data
in nodes and edge labels as Strings, it should have two type parameters representing the data
types to be stored in nodes and edges. Directly modify your existing classes under hw4 package
— there is no need to copy or duplicate code. Also remember that you need to keep your Graph
ADT implementation as general and universal as possible. In particular, it means that you are not
allowed to have any bounds on type parameters because it would restrict the client from using your
Graph ADT implementation in a certain way. For example, if some client wanted to create a graph
with node data as Object and edge labels as Object, it should be possible.
When you are done, your previously-written Homework 4 and Homework 5 tests, as well as ProfessorPaths
 will no longer compile. Modify these classes to construct and use graph objects parameterized
 with Strings. All code must compile, and all tests must pass when you submit your homework.
Depending on your changes, some of your tests may no longer be valid. Try to adapt your tests
to the new implementation or discard them and write the new ones as they should help you build
conffdence in your implementation. On the other hand, don’t overdo it: as with any testing, stop
when you feel that the additional effort is not being repaid in terms of increased conffdence in your
implementation.
Build tools and generic code
We want you to conffgure Eclipse to show generics problems as errors. By default, Eclipse shows
generics problems as warnings (indicated by yellow lines and markers). You can conffgure Eclipse
to instead issue errors (indicated by red lines and markers) for these problems. Doing so will help
you remember to write acceptable generics code. Autograding on Submitty will also be conffgured
to treat any generics warnings as compilation errors.
In order to properly conffgure Eclipse, go to Window → Preferences and select Java → Compiler
→ Errors/Warnings. Under Generic types, change the value of Unchecked generic
type operation to Error.
Note that there is another setting named Usage of a raw type that is set to Ignore by default.
We recommend that this option be set to Warning because it is speciffc to the Eclipse compiler
and checks for more stringent requirements than required by the Java Language Speciffcation.Hint: Sometimes you may ffnd that classes which previously compiled are now reporting “[some
class] cannot be resolved” errors in Eclipse. You can ffx these errors by doing a clean build: go to
Project → Clean..., select your csci2600 project, and hit OK.
Problem 2: Weighted Graphs and Least-Cost Paths
In a weighted graph, the label on each edge is a length, cost, or weight representing the cost of
traversing that edge. Depending on the application, the cost may be measured in time, money,
physical distance, etc. The total cost of a path is the sum of the costs of all edges in that path,
and the minimum-cost path between two nodes is the path with the lowest total cost between those
nodes.
Dijkstra’s algorithm
You will implement Dijkstra’s algorithm, which ffnds a minimum-cost path between two given nodes
in a graph with nonnegative edge weights. Below is a pseudocode algorithm that you may use in
your implementation. You are free to modify it as long as you are essentially still implementing
Dijkstra’s algorithm. Your implementation of the algorithm may assume a graph with Double edge
weights.
The algorithm uses a priority queue. The standard Java library includes an implementation
of a PriorityQueue.Dijkstra’s algorithm assumes a graph with all nonnegative edge weights.
start = starting node
dest = destination node
active = priority queue. Each element is a path from start to a given node.
A path’s "priority" in the queue is the total cost of that path.
Nodes for which no path is known yet are not in the queue.
finished = set of nodes for which we know the minimum-cost path from start.
// Initially we only know of the path from start to itself, which has a cost
// of zero because it contains no edges.
Add a path from start to itself to active
while active is non-empty:
// minPath is the lowest-cost path in active and is the minimum-cost
// path for some node
minPath = active.removeMin()
minDest = destination node in minPath
if minDest is dest:
return minPath
if minDest is in finished:
continue
for each edge e = 〈minDest, child〉:
// If we don’t know the minimum-cost path from start to child,
// examine the path we’ve just found
if child is not in finished:
newPath = minPath + e
add newPath to active
add minDest to finished
If the loop terminates, then no path exists from start to dest.
The implementation should indicate this to the client.
Getting the LEGO Data
You will write a modiffed version of your ProfessorPaths application in which your application ffnds
paths between LEGO parts instead of professors and uses Dijkstra’s algorithm instead of BFS.Before you get started, obtain LEGO datasets. We have not added these ffles to your Git repositories
because some of them are very large. Instead, download the ffles from the Course Web site:
• LEGO dataset up to year 1960 (inclusive)
• LEGO dataset up to year 1970 (inclusive)
• LEGO dataset up to year 1980 (inclusive)
• LEGO dataset up to year 1990 (inclusive)
• LEGO dataset up to year 2000 (inclusive)
• LEGO dataset up to year 2010 (inclusive)
• LEGO dataset up to year 2020 (inclusive)
• LEGO dataset up to 04/07/2024 (inclusive)
Store the ffles in data/ directory. You might have to add the data/ directory under the project
root. As you can see, the size of the ffle grows rapidly with the year number because more and
more LEGO parts and sets are introduced every month. We provide you with a variety of datasets
to help you test the performance of your application. With the largest lego2024.csv dataset your
code may take up to several minutes to construct the graph and up to a minute to ffnd paths.
You might also need to increase the maximum amount of heap memory allocated by JVM to your
application. Please read Oracle Documentation for the java command for more details. If your code
is taking substantially longer to run or if it fails with the out of memory error, consider revising
your code to make it faster and/or reduce its memory footprint.
IMPORTANT: Do not commit LEGO CSV ffles that we provided into your repository! There is
a limit on each repository and committing such a large ffle may break this limit. This is easily
taken care of in Eclipse Team Provider for Git, as you can simply exclude lego*.csv. For those
not using Eclipse, make sure to add lego*.csv to your .gitignore ffle. Note that CSV ffles that
you create yourselves must be added to the repository. When naming your ffles, make sure they do
not fall under the exclusion rule that you set up as described above.
Take a moment to inspect the ffles. The format is very similar to the format of the RPI Courses
dataset from Homework 5. Each line in lego*.csv is of the form:
"part","set"
where part is the part number, color, and part name of a LEGO part all combined into a single
String. set is the set number, version, release year, and set name of a LEGO set all combined into
a single String. If a part and a set appear in the same line of a CSV ffle, it means that this part is
included in the set. As before, the CSV format used in this assignment assumes that every value
must be enclosed in double quotes (the " character). These double quotes only serve as delimiters,
i.e., they are not part of the actual part or set String. However, note that part and set Strings may
contain double quotes as a part of the String itself.Dijkstra’s Algorithm in LegoPaths
Dijkstra’s algorithm requires weighted edges. To simulate edge weights over the LEGO dataset,
the weight of the edge between two parts will be based on how well-connected those two parts
are. Specifically, the weight is the inverse of how many LEGO sets two parts are in together
(equivalently, the weight is the multiplicative inverse of the number of edges in the multigraph
between them). For example, if “6541 Black Technic Brick” and “65486 White Plate” appeared in
five sets together, the weight of the edge between them would be 1
5
. Thus, the more well-connected
two parts are, the lower the weight and the more likely that a path is taken through them. In
summary, the idea with the LEGO data is to treat the number of paths from one node to another
as a “distance”. If there are several edges from one node to another then that is a “shorter” distance
than another pair of nodes that are only connected by a single edge.
Things to note:
• A path from a part to itself is defined to have cost 0.0.
• Calculations for the weight of the edges in your graph should be done when the graph is loaded.
This assignment is different from the previous one in that when the graph is initialized there
is only one edge between nodes and that edge is the weighted edge. The one edge between
any two parts will have the label containing the multiplicative inverse of how many sets they
share.
• You should implement your Dijkstra’s algorithm in LegoPaths rather than directly in your
graph.
Place your new LEGO application in src/main/java/hw6/LegoPaths.java in package hw6.
In choosing how to organize your code, remember to avoid duplicating code as much as possible.
In particular, reuse existing code where possible, and keep in mind that you may need to use the
same implementation of Dijkstra’s algorithm in a different application.
For this assignment, your program must be able to construct the graph and find a path in less
than 300 seconds using the largest 2024 LEGO dataset. We will set the tests to have a 300,000 ms
(300-second) timeout for each test and run with assertions disabled.
As before, you are welcome to write a main() method for your application, but you are not
required to do so.
The interface of LegoPaths is similar to that of ProfessorPaths in Homework 5, but with a
few differences in arguments and output:
• public void createNewGraph(String filename) is the same. It creates a brand new
graph and populates the graph from filename, where filename is a data file of the format for
lego*.csv and is located in data/. As in Homework 5, relative paths to data files should
begin with data/. Consult section “Paths to files” in Homework 5 if you are having trouble
making Eclipse work with these relative paths.• public String findPath(String PART1, String PART2) finds the path with Dijkstra’s
algorithm instead of BFS and returns its output in the form:
path from PART1 to PARTN :
PART1 to PART2 with weight w1
PART2 to PART3 with weight w2
...
PARTN−1 to PARTN with weight wN−1
total cost: W
where W is the sum of w1, w2, ..., wN−1.
In other words, the only changes in output from Homework 5 are the way the edge labels are
printed and the addition of a “total cost” line at the bottom. The output should remain the same
as before when no path is found or the parts are not in the graph. In particular, do not print the
“total cost” line in those cases.
If there are two minimum-cost paths between PART1 and PARTN , it is undefined which one is
printed.
For readability, the output of findPath() should print numeric values with exactly 3 digits after
the decimal point, rounding to the nearest value if they have more digits. The easiest way to
specify the desired format of a value is using format strings. For example, you could create the
String “Weight of 1.760” by writing:
String.format("Weight of %.3f", 1.759555555555);
In findPath(), the total cost should be computed by summing the values of the individual weights
with full precision, not the rounded values.
As in Homework 5, a path from a part to itself should be treated as a trivially empty path. Because
this path contains no edges, it has a cost of zero. Think of the path as a list of edges. The sum of
an empty list is conventionally defined to be zero. So, your findPath() should produce the usual
output for a path but without any edges, i.e.:
path from PART to PART:
total cost: 0.000
This only applies to parts in the dataset. A request for a path from a part that is not in the dataset
to itself should print the usual “unknown part PART” output.
Also, as in Homework 5, if the user gives two valid node arguments PART1 and PART2 that have
no path in the specified graph, output:
path from PART1 to PARTN :
no path foundThe following example illustrates the required format of the output:
path from 31367 Green Duplo Egg Base to 98138pr0080 Pearl Gold Tile Round 1 x 1 with Blue, Yellow and Black Minecraft Print:
31367 Green Duplo Egg Base to 3437 Green Duplo Brick 2 x 2 with weight 1.000
3437 Green Duplo Brick 2 x 2 to 3437 Red Duplo Brick 2 x 2 with weight 0.003
3437 Red Duplo Brick 2 x 2 to 41250 Blue Ball, Hard Plastic, 51mm (approx. 6 studs diameter) with weight 0.053
41250 Blue Ball, Hard Plastic, 51mm (approx. 6 studs diameter) to 2780 Black Technic Pin with Friction Ridges Lengthwise and Center Slots with weight 0.100
2780 Black Technic Pin with Friction Ridges Lengthwise and Center Slots to 98138pr0080 Pearl Gold Tile Round 1 x 1 with Blue, Yellow and Black Minecraft Print with weight 1.000
total cost: 2.156
To help you with formatting your output correctly, we provide several sample files described below:
Description An example of the call to findPath() Sample file
A minimum-cost
path is found.
System.out.print(lp.findPath("31367 Green
Duplo Egg Base", "98138pr0080 Pearl Gold
Tile Round 1 x 1 with Blue, Yellow and Black
Minecraft Print"));
sample hw6 output 00.txt
No path exists.
System.out.print(lp.findPath("880006 Black
Stopwatch", "3007d White Brick 2 x 8 without
Bottom Tubes, 1 End Slot"));
sample hw6 output 01.txt
Character not
found.
System.out.print(lp.findPath("35480 Green
Plate Special 1 x 2 Rounded with 2 Open
Studs", "27ac01 Light Yellow Window 1 x 2
x 1 (old type) with Extended Lip and Solid
Studs, with Fixed Glass"));
sample hw6 output 02.txt
Both characters
not found.
System.out.print(lp.findPath("76371pr0201
White Duplo Brick 1 x 2 x 2 with Bottom
Tube, Target and Water Splash Print", "75266
White Duplo Car Body, Camper / Caravan
Roof"));
sample hw6 output 03.txt
A path to the
character themselves.
System.out.print(lp.findPath("3035
Dark Gray
Plate 4 x 8 to 3035 Dark Gray Plate 4 x 8",
"3035 Dark Gray Plate 4 x 8 to 3035 Dark
Gray Plate 4 x 8"));
sample hw6 output 04.txt
A path to the unknown
character
themselves.
System.out.print(lp.findPath("2412a White
Tile Special 1 x 2 Grille with Bottom
Groove", "2412a White Tile Special 1 x 2
Grille with Bottom Groove"));
sample hw6 output 05.txtProblem 3: Testing Your Solution
Just as with Homework 5, create smaller *.csv files to test your graph building and path finding.
Place them in the data/ directory. Write tests in JUnit classes and place those tests in hw6 package
(src/test/java/hw6/ directory). Just as in Homework 4 and 5, run EclEmma to measure your
code coverage. We will be measuring coverage too. You must achieve 85% or higher instruction
(statement) coverage for all classes except for *Test classes to receive full credit on this part. We
measure the coverage of your Java code as executed by your test suite.
Tests do not directly test the property that your graph is generic. However, Homework 4 and
Homework 5 tests use String edge labels, while Homework 6 uses numeric values. Supporting all
three test drivers implicitly tests the generic behavior of your graph.
Reflection [0.5 points]
Please answer the following questions in a file named hw6 reflection.pdf in your answers/ directory.
Answer briefly, but in enough detail to help you improve your own practice via introspection
and to enable the course staff to improve Principles of Software in the future.
(1) In retrospect, what could you have done better to reduce the time you spent solving this
assignment?
(2) What could the Principles of Software staff have done better to improve your learning experience
in this assignment?
(3) What do you know now that you wish you had known before beginning the assignment?
We will be awarding up to 1 extra credit point (at the discretion of the grader) for particularly
insightful, constructive, and helpful reflection statements.
Collaboration[0.5 points]
Please answer the following questions in a file named hw6 collaboration.pdf in your answers/
directory.
The standard integrity policy applies to this assignment.
State whether you collaborated with other students. If you did collaborate with other students,
state their names and a brief description of how you collaborated.
Grade Breakdown
• Instructor hw4 tests: 5 pts. (auto-graded)
• Instructor hw5 tests: 5 pts. (auto-graded)
• Quality of hw6 test suite, percent of your tests passed: 5 pts. (auto-graded)
• Quality of hw6 test suite, percent coverage: 5 pts. (auto-graded)
• Instructor LegoPaths tests: 16 pts. (auto-graded)• Code quality (Code organization, Genericity, Rep invariants, Abstraction functions, Specifications,
comments): 11 pts.
• Quality of small CSV datasets (number of datasets, their variety, covering edge cases, following
testing heuristics reviewed in class, etc.): 2 pts.
• Collaboration and reflection: 1 pt., up to 1 extra credit point (at the discretion of the grader)
for particularly insightful, constructive, and helpful reflection statements.
Extra Credit Code Performance Competition
We will run all submissions through a benchmark and award extra credit points to top 20 students
whose code took the least amount of time to run the benchmark. Points will be awarded according
to the following table:
Position Extra credit points
1 15
2 12
3 10
4 8
5 7
6 6
7 5
8 4
9 3
10 2
11-20 1
The benchmark will consist of:
• Loading the lego1970.csv dataset
• Loading the lego2024.csv dataset
• Finding a path of length one
• Finding a path of length two
• Finding a path of length four
• Finding a path of length more than four
• Finding a path when no path exists
All submissions will be tested in the exact same environment on the same machine. Time will
be measured in milliseconds using Java.lang.System.currentTimeMillis() method. Code that
returns incorrect results or causes an out of memory error will be disqualified from the competition.Hints
Documentation
When you add generic type parameters to a class, make sure to describe these type parameters
in the class’ Javadoc comments so that the client understands what they are for.
As usual, include an abstraction function, representation invariant, and checkRep() in all
classes that represent an ADT. If a class does not represent an ADT, place a comment that
explicitly says so where the Abstraction function and Rep invariant would normally go. For
example, classes that contain only static methods and are never constructed usually do not
represent an ADT. Please come to office hours if you feel unsure about what counts as an
ADT and what doesn’t. You may comment out checkRep() when running on Submitty, but
leave the commented code in your files.
Code Organization
In deciding how to organize your code, remember that you may need to reuse Dijkstra’s
algorithm in future homework assignments. These assignments have nothing to do with
LEGO and, depending on your implementation, might use a different generic type for nodes.
Structure your code so that your implementation of Dijkstra’s algorithm is convenient to use
for other applications.
What to Turn In
You should add and commit the following files to your hw04 Git repository:
• src/main/java/hw6/LegoPaths.java
• src/main/java/hw6/*.java [Other classes you create, if any]
• data/*.csv [Your .csv test files. Do not commit lego*.csv that were provided to you]
• src/test/java/hw6/*Test.java [JUnit test classes you create]
• answers/hw6 reflection.pdf
• answers/hw6 collaboration.pdf
Additionally, be sure to commit any updates you make to the following files:
• src/main/java/hw4/*.java [Your graph ADT]
• src/test/java/hw4/*Test.java [Your graph ADT test classes]
• src/main/java/hw5/*.java [Your ProfessorPaths]
• src/test/java/hw5/*Test.java [Your ProfessorPaths test classes]Errata
None yet.
Check the Submitty Discussion forum regularly. As usual, we will announce errors there.
Parts of this homework were copied from the University of Washington Software Design and
Implementation class by Michael Ernst.

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