CS 201: Data Structures

Homework 6

This assignment is due by 10pm on Monday October 2 and is worth 20 points.

1 Goals

The goal of this assignment is to learn about and get some practice with a Linked List data

structure. You will also get lots of practice at following sequences of pointers from one object to

another.

2 Your Assignment

This is a partner assignment. Unless I tell you otherwise, you will work with the same partner you

had for HW4. This will be the last assignment with that partner.

In this assignment we’ll be exploring some approximate solutions to a well known problem in

computer science called 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 x-coordinate 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 travelled 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. Start with a one-point tour (from

the first point back to itself), and iterate the following process until there are no points left.

• Nearest Neighbor Heuristic: For each point you add to the tour, add it 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.)

• Smallest Increase Heuristic: For each point you add to the tour, add it to the position

where it results in the least possible increase in total tour length. (If there is more

than one place to insert the point, add it to the first such place you discover.)

CS 201: Data Structures

Homework 6

Layla Oesper

Fall 2017

Your Task

I have provided you with several auxilary classes that will make your job much easier. Download the

HW6.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.

∗ Recall, the Euclidean distance between two points (x1, y1) and (x2, y2) is defined as follows:

p

(x1 − x2)

2 + (y1 − y2)

2

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.

CS 201: Data Structures

Homework 6

Layla Oesper

Fall 2017

You will implement these functions using a single linked list as the underlying data structure. 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

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. 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 linked list ad 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() drawTo() methods in 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) : 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. Start with some local variable smallestDist = Double.MAX VALUE that keeps track of

the minimum total distance of a path through all nodes. Loop through all nodes of the linked

list and determine what the new total distance of a tour would be if you inserted Point p

after each Point currently in the tour. You do not need to loop through the entire linked

list to compute the new distance for each insertion point, nor would that be a very efficient

approach. Instead, you need to use the following equation:

newDistance = currentTotalDistance – currentPoint.distanceTo(nextPoint) +

currentPoint.distanceTo(p) + p.distanceTo(nextPoint)

CS 201: Data Structures

Homework 6

Layla Oesper

Fall 2017

If newDistance is less than smallestDist, update smallestDist with this value and save

a reference to the current node. After the loop finishes, insert a new node for Point p after

the saved node associated with smallestDist.

• 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

Note that the “< tsp3.txt” part of the line is just telling Java to get its input from the file

tsp3.txt instead of waiting for the user to type it at the keyboard. If the program just hangs

without doing anything, you probably forgot the “<” or the “< tsp3.txt”. Lastly, 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 real-valued 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 HW6.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)

CS 201: Data Structures

Homework 6

Layla Oesper

Fall 2017

(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 1 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 2 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.

CS 201: Data Structures

Homework 6

Layla Oesper

Fall 2017

Figure 1: Insert Nearest Solution to usa13509.txt

Figure 2: Insert Smallest Solution to usa13509.txt

3 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]HW6, zip this directory, upload it to Moodle. For

example, if my partner was Schiller my directory would be named OesperSchillerHW6 and the

resulting file would be OesperSchillerHW6.zip.

3.1 Grading

This assignment is worth 20 points. Below is a partial list of the things that we’ll look for when

evaluating your work.

CS 201: Data Structures

Homework 6

Layla Oesper

Fall 2017

• 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? Don’t forget to follow the Style

Guidelines on Moodle.