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# Project 1 – Protect the Planes!

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CSE 3353

Project 1 – Protect the Planes!
In CSE 2341, you were tasked with determining if it was possible to fly between two cities given
a data representation of city connections. A hip new company called Algo Airlines has been
using your product with massive success, but they have come to you with another problem: they
have had to add so many new planes that they need to be sure they won’t crash into each other
during flight!
Algo Airlines wants to know how close their planes are flying to one another. In particular, they
want to know which pair of planes are flying the closest to one another so that they can alert the
planes via air traffic control to avoid one another. This is known as the Closest Pair Problem.
Consider the following graph of points, where each point is a plane in the air:

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## Description

CSE 3353

Project 1 – Protect the Planes!
In CSE 2341, you were tasked with determining if it was possible to fly between two cities given
a data representation of city connections. A hip new company called Algo Airlines has been
using your product with massive success, but they have come to you with another problem: they
have had to add so many new planes that they need to be sure they won’t crash into each other
during flight!
Algo Airlines wants to know how close their planes are flying to one another. In particular, they
want to know which pair of planes are flying the closest to one another so that they can alert the
planes via air traffic control to avoid one another. This is known as the Closest Pair Problem.
Consider the following graph of points, where each point is a plane in the air:
Note that we are only concerned with a 2D plane of x-y coordinates at the moment (assume that
all of Algo Airline’s planes fly on the same horizontal… plane). In data form, we can describe
each plane as having the following structure:
[
{
flightNumber: “BC1234”,
x: 2.0,
y: 3.2
},
{
flightNumber: “XY3456”,
x: 2.3,
y: 4.6
},
… and so on
];
As you can see on the graph, some planes are far apart while others are very close together.
The goal of this project is to come up with several algorithms of increasing efficiency to solve
the closest pair problem.
You can assume that the data will be well structured, because you will be generating the data
yourself as seen below.
You are tasked with the following:
a. Create a folder for this project. In terminal, navigate to this folder and run the
command npm init. npm stands for Node Package Manager, and is the tool
used to set up and run projects, as well as install third party libraries. You will be
guided through the process of creating what’s called a “package.json” file. At the
very least, provide a package name and description. For all other prompts simply
press Enter to let npm provide defaults.
b. Next, run the command npm install chance. You’ll notice that your directory
now has a new directory called node_modules. This is where third party libraries
get installed (if you list the contents of node_modules you will see a folder for
chance). Observe your package.json file: chance is now listed as a dependency.
c. Review the documentation for chance at the following site: http://chancejs.com.
You’ll note that it has lots of utility functions for creating random data. Note that
it’s not truly random, but for our purposes it’s random enough.
d. Write a program that will generate a dataset of 100 random airline points with the
structure given above (an array of objects). The x and y coordinates should be
floating point numbers bounded by [-10, 10], with 4 decimal points of precision.
The flightNumber should be two characters followed by four numbers. The results
should be output to a file called airline_map.json
2. Design and implement a brute force algorithm to solve the Closest Pairs problem. The
the two points that are closest to one another (x, y, and flightNumbers), and how far
apart they are.
a. Describe in plain english how your algorithm works. This can be in a separate
text file or as comments in the program.
b. What is the big-O runtime complexity of your algorithm? Explain by doing a T(n)
3. Duplicate your program from part 2. Channel your knowledge from Data Structures to
implement a sorting algorithm that runs in O(nlgn) time. Do not use the built in JS
Array.sort function. Sort the airline map in order of increasing y coordinates. Now that
the dataset is sorted, modify your brute-force algorithm to leverage that fact and
minimize the number of calculations.
b. What is the big-O runtime complexity of this algorithm, taking into account the
sorting algorithm as a part of the total runtime? Did it change from part 2?
c. Use the bash command time to do some real runtime analysis of your
programs. Which program runs faster on the same dataset, your program from
Part 2 or Part 3? Why do you think that is? (Note: you may need to re-run your
program from Part 1 and generate many more than 100 data-points to notice any
real difference). In your analysis, include the size of the dataset and how long
your program took to process that dataset. Provide multiple examples.
4. In a new file, describe and implement a recursive solution for the Closest Pairs problem.
The core idea is similar to the maximum subarray problem: if we divide the dataset in
half, we know that the closest pairs will either be on the left (or top) side, right (or bottom)
side, or crossing the boundary.
a. Tip: Your base case will not necessarily be a dataset of size n = 1, since you
cannot determine distance between a pair of points… with only 1 point.
b. Tip 2: Continue sorting the data as your first step before running your recursive
algorithm.
c. Describe in plain English how this algorithm works.
d. What is the big-O runtime complexity of this algorithm? Do a T(n) analysis of your
e. Using time again, how does the actual runtime of this algorithm compare to the
algorithms from part 2 and 3? Again, provide multiple examples on datasets of
different sizes. Is it exhibiting the expected behavior (according to your big-O
analysis)?
You should feed the same dataset for parts 2, 3, and 4 when running comparisons. As
expected, all three parts should give the exact same pairs of points as the closest pair. If they
give different results, then it is your job to find the source of error and correct it.
Suppose each plane also has a property called “heading” that describes the cardinal direction
that the plane is traveling. It is a floating point number in the range [0, 360] degrees, where 0
degrees is north, 90 is east, 180 is south, and 270 is west. Expand your data generation
function to include a randomly generated heading property to each data point.