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HW4: Linked Lists [PAIR]
This assignment is due by 1 PM on Friday, January 26 and is worth 20 points. You should
work on this project with the same partner as HW3.
Goals
The goal of this assignment is to learn about and get some practice with the Linked List
data structure, and traversing sequences of nodes. You will also get to learn a bit about a
very famous problem in computer science!
Note: There is a lot of information below! Most of it is explaining the context of the
assignment, how to check your code, and files that you will be using but won’t need to
implement. All you will need to do for this assignment is implement
the Tour.java class. The other files are scaffolding to make the rest of the assignment
work.
Your Assignment
In this assignment we’ll be exploring some approximate solutions to a well known
problem in computer science called the traveling salesperson problem (TSP). The idea
behind this problem is as follows: you are given n points on a map (so each point has an xcoordinate and a y-coordinate) and you want to find a route to visit all of the points on the
map (and arrive back where you started) while keeping the total distance traveled as
small as possible.
There are many places in the real world where the TSP comes up: How does UPS decide
the routes that it’s trucks take? What is the most efficient way for a machine to drill a set a
holes in a circuit board? Some important problems in bioinformatics (genome assembly)
can be transformed into instances of the TSP. You’ll probably see the TSP in future CS
classes.
Greedy Heuristics
The traveling salesperson problem is a notoriously difficult combinatorial
optimization problem, In principle, one can enumerate all possible tours, but, in practice,
the number of tours is so staggeringly large (roughly N factorial where N is the number of
stops on the tour) that this approach is useless. For large N, no one knows an efficient
method that can find the shortest possible tour for any given set of points. However, many
methods have been studied that seem to work well in practice, even though they are not
guaranteed to produce the best possible tour. Such methods are called heuristics. Your
main task is to implement the “nearest neighbor” and “smallest increase insertion”
heuristics for building a tour incrementally.
Nearest Neighbor Heuristic:
• Start with a one-point tour (from the first point back to itself).
• For each remaining point, add it to the current tour immediately after the point to
which it is closest. (If there is more than one point to which it is closest, insert it
after the first such point you discover.)
This means that for each point you add, you will search through the points that are already
in the tour, looking for the closest one to the one you will be adding.
Smallest Increase Heuristic:
• Start with an empty tour.
• Add the first point (so that the tour now goes from the first point back to itself).
• For each remaining point, add it to the position where it results in the least
possible increase in total tour length. (If there is more than one such position,
add it to the first such place you discover.)
This means that for each point you add, you will search through each possible place it can
go, checking how much adding the point to that position increases the total length of the
tour.
Your task
I have provided you with several auxiliary classes that will make your job easier. Download
the HW4.zip file from Moodle. The only place that you will have to add code is in the
file Tour.java. Inside this file I have already defined the nested class Node for you to use.
Also take a look at the code in the main() method which you might find useful for testing
out your code. Feel free to take a look at the other files if you would like, but you don’t
need to understand them. You should not modify any of the files except for Tour.java.
Point Class
You will use the Point object extensively in the code you write. You may look at the code
in Point.java, but all you really need to know to be a USER of this class is
the Point ADT:
MethodName(Parameters) Return
type description
Point(double x, double
y) Point Creates a Point object with (x,y) coordinates.
toString() String Returns a string representation of a Point object.
draw() void Draws a point using standard draw
drawTo(Point b) void Draws a line segment from the Point calling the
method to Point b.
distanceTo(Point b) double Returns Euclidean distance between
the Point calling the method and Point b.
Tour Class
The Tour.java class that you will implement will have the following methods (think of this
at the Tour ADT). See a later section of this document for additional notes and comments
on all methods.
MethodName(Parameters) Return
type description
Tour() Tour Creates an empty tour (has no stops).
toString() String Returns a description of the tour as a nicely
formatted string.
draw() void Draws the tour
size() int Returns the number of points, or stops in the tour.
distance() double Returns the total distance in the tour.
insertNearest(Point p) void Inserts p into the tour using the “nearest neighbor”
heuristic.
insertSmallest(Point
p) void Inserts p into the tour using the “smallest
insertion” heuristic.
You will implement the Tour class as a single linked list underneath the hood. You will
start with the code that I have provided you in Tour.java. Just to be clear, you MUST
implement your own single linked list to receive credit for this assignment; you may not use
any similar class provided by Java.
Additional Method Details and Hints
Here is some additional information about the methods I am asking you to implement.
• Tour() : Initialize head node of a linked list and any other variables you think will
be useful. I’ve implemented a version of this method for you. Feel free to modify if
you decide to add additional instance variables.
• String toString(): Create an empty String, loop through all nodes of the linked
list and add a description of each underlying Point (as a String) to the overall
String. This will be useful for debugging, as well as outputting final solutions to the
tour. Note: You may want to make use of the toString() method from
the Point class.
• void draw(): Loop through all of the nodes in the tour’s linked list and draw
each Point object, followed by a line from that Point to the next Point. Do this
for all nodes except for the last node in the list, for that node draw a line from the
last Point to the first (or head) Point. Make sure to use
the draw() and drawTo() methods in the Point class. Note: You DO NOT need
to implement any graphics code! All you need to do is call
the draw() and drawTo methods that are already implemented for
the Point class.
• int size(): Return the size of the linked list (in terms of nodes). In order to be
more efficient, make sure to keep track of this value rather than re-computing this
value whenever this method is called.
• double distance(): Start with a distance of 0. Loop through all nodes of your
linked list and compute the distance from each Point to the next Point, add this
distance to your total distance. When you get to the last Node in your list, add the
distance from this Point to the first Point. Make sure to use
the distanceTo(Point b) method from the Point class.
• void insertNearest(Point p): [Note: It may be helpful, from a debugging
perspective, to create an initial version of this method that just adds p to the
end of the Tour, so you can test the above methods before starting to
implement this one.] Once you’re ready to implement the true heuristic, start with
some local variable minDist = Double.MAX_VALUE that keeps track of the
minimum distance found thus far between Point p and the nodes in the linked list.
Loop through all Nodes of the linked list and compute the distance from the
underlying Point object to p. If the distance is less than minDist make that
distance the new minDist and save a reference to the current node. After your
loop finishes, insert a new node for Point p after the saved node that had the
minimum distance to p.
• void insertSmallest(Point p): This is the most difficult of all the the
methods to implement. Make sure your implement and test all other methods
first, before starting on this one.
The idea with this method is that we will search through all the potential “slots” in
which we could insert Point p, looking for the slot in which inserting p would have
the smallest increase in the overall distance of the tour. Thankfully, we do not need
to loop through the entire list to check the effect of inserting into each slot. If, for
instance, we want to know the effect of adding Point p between two Points
called a and b, we just need to compute the difference
between a.distanceTo(b) (i.e., the distance without p inserted here)
and a.distanceTo(p) + p.distanceTo(b) (i.e., the distance with p inserted here).
After looping through the current tour to see which slot would have the smallest
increase in distance if p were inserted, put p into that slot.
• main(): I also include some code in this method to help you with debugging of
your code. In particular, I suggest you test each function as you write it and that you
implement toString() first as it will be useful for debugging other methods. You
may certainly add and modify code in this main() method as you see fit.
Running Code on Input Files
I include with this assignment two programs that will handle reading a bunch of data points
from a file (see below for a description of the file format) and calling the appropriate
functions from the Tour class. These programs
are NearestInsertion.java and SmallestInsertion.java. To run one of these
programs on an input file, for example tsp3.txt, you will first need to compile it
using javac, and then run it with the following command:
java NearestInsertion tsp3.txt
We will uses these two programs to test your code, so you should make sure that your
code works as expected with them.
Input File Format
The input file format will begin with two integers w and h, followed by pairs of realvalued x and y coordinates. All x coordinates will be real numbers between 0 and w;
all y coordinates will be real valued numbers between 0 and h. As an example, the
file tsp3.txt could contain the following data:
600 400
532.6531 247.7551
93.0612 393.6735
565.5102 290.0000
10.0000 10.0000
The zip file HW4.zip includes several example input files, or you can define your own.
Below you will find some information about the expected output for these input file to help
you with debugging your own code.
Insert Nearest Solution to tsp10.txt
$ java NearestInsertion tsp10.txt
Tour distance = 1566.1363051360363
Number of points = 10
(110.0, 225.0)
(161.0, 280.0)
(157.0, 443.0)
(283.0, 379.0)
(306.0, 360.0)
(325.0, 554.0)
(397.0, 566.0)
(490.0, 285.0)
(552.0, 199.0)
(343.0, 110.0)
Insert Smallest Solution to tsp10.txt
$ java SmallestInsertion tsp10.txt
Tour distance = 1655.7461857661865
Number of points = 10
(110.0, 225.0)
(283.0, 379.0)
(306.0, 360.0)
(343.0, 110.0)
(552.0, 199.0)
(490.0, 285.0)
(397.0, 566.0)
(325.0, 554.0)
(157.0, 443.0)
(161.0, 280.0)
Insert Nearest Solution to usa13509.txt
$ java NearestInsertion usa13509.txt
Tour distance = 77449.97941714071
Number of points = 13509

See figure below for a visual representation of the solution.
Insert Smallest Solution to usa13509.txt
$ java SmallestInsertion usa13509.txt
Tour distance = 45074.77692017051
Number of points = 13509

See figure below for a visual representation of the solution.
Note: It should take less than a minute (probably even faster than that) to run through the
example with 13,509 points (unless you are animating the results). If your code is taking
much longer, try to narrow down what part of the code is taking the longest. Turning in an
efficient solution will be part of what we consider when grading your code.
Submission and Grading
You’ll submit all your files to Moodle as a zipped file. One one partner from each pair
needs to submit the assignment. Specifically, put these files into a directory
named [your\_last\_name\_your\_partner’s\_last\_name]HW4, zip this
directory, upload it to Moodle.
This assignment is worth 20 points. Below is a partial list of the things that we’ll look for
when evaluating your work.
• Do you implement all of the requested methods as they are described? We’ll test
this out by running your various methods on different test cases. I suggest you
focus on insertNearest before attempting insertSmallest, which is
significantly more difficult. You can still get up to 17 out of 20 points on this
assignment if you do everything except for insertSmallest.
• How efficient is your code? Are you looping extra times through the list of Nodes?
• Do your classes exhibit good organization and commenting? Make sure to take a
look at the Style Guidelines on Moodle.
Start early, ask lots of questions, and have fun! Eric, the lab assistants, and the prefect are
all here to help you succeed – don’t hesitate to ask for help if you’re struggling!

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