Algorithms H2 Leaf Raking


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Sources: List in comments at the top of your file
Figure 1: My Front Yard
problem 1 Robot Leaf Mulcher
Figure 1 shows my new front yard. It was absolutely beautiful last spring when we bought the
house, and that continued into the summer, but then fall happened. The beautiful, mature trees
started dropping leaves! They dropped at such a rate that with a rake and leaf blower, we could
not keep up. After an entire afternoon of raking, the yard was again covered in leaves within 24
With the multiple passive-aggressive fliers left on our door by lawn companies, we’ve decided
to create a high-tech solution to our problem. Robot vacuums have been available for years, and
thankfully robot lawnmowers have recently started appearing in stores. To solve our leaf problem
and cash in on this trend, I would like to create a robot leaf mulcher. However, as good product
designers, we must first decide the best width of robot mulcher based on yard dimensions and
the layout of trees and bushes. I would prefer to create the widest mulcher possible for my yard,
allowing us to maximize battery life and minimize the amount of time the mulcher must traverse
the lawn.
Since the trees and bushes in my yard appear to have been planted haphazardly many years
ago, we must take their unmovable positions into account. A mockup of the lawn can be seen
in Figure 2. Before we build our first prototype robot mulcher, we need to know the maximum
width such that it will fit between any two trees in the yard, i.e. we need to determine distance
between the closest pair of tree or bush trunks (for simplicity, disregard the leaves and branches
around the base of the bushes).
Implement an algorithm which takes as input the locations of our trees and bushes as Cartesian
coordinates, and returns the maximum width of the robot mulcher we can use in the yard (i.e. the
closest pair of trees). Your program should have the following properties:
• Your algorithm must be written in Python (2 or 3) or Java (10).
Homework 2 – page 2
• You must download the appropriate wrapper code from Collab based on the language you
choose: and for Python, and for
• Implement the body of the closest_pair_distance() or closestPairDistance() function,
which receives as input the body of the input file as a list of lines. You must return the distance between the closest trees or bushes. An example input file is shown in Figure 3, which
has answer ≈ 4.12311. Note: the coordinates may be integers or floating point numbers.
• Two additional test files are provided, test1.txt and test2.txt, both with answer ≈
1.4142135623. You should produce additional tests, including edge cases.
• You may modify the or files to test your algorithm, but they will not be
used during grading.
• You must submit your or files on Collab. Do not zip
them. Do not submit,, or any test files.
• A few other notes:
– Your code will be run as:
python or python3 for Python,
or javac *.java && java Main for Java.
– You may upload multiple Java files if you need addional classes, but do not assign
packages to the files
In the case that I discover my robot mulcher becomes the envy of the neighborhood and super
popular, and this whole “professor thing” doesn’t work out for me, I may mass produce them and
become a robot mulcher salesman. Therefore, I would like this algorithm to be very efficient, so
that I can quickly determine the appropriate size of mulcher for any size lawn, even tree farms
with thousands of trees! If I put in the locations of thousands of trees and bushes, the algorithm
should still run in a reasonable amount of time. For this reason, an Ω(n
) algorithm is too slow;
to be efficient enough, your algorithm must run in O(n log n) time.
Homework 2 – page 3
Figure 2: A 2-D grid of locations of trees and bushes. I would like to create the widest robot
mulcher that will fit between any two trees or bushes, as pictured.
4 13
12 10
8 9
1 1
42 108
Figure 3: Example input, for which your algorithm should return ≈ 4.12311

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