Final Asssessment - Final Exam Period
COMP-251, Fall 2020
Due: December 22th, 2020 (23:59 EST)
Please read the entire PDF before starting. You must do this longer form assessment individually.
It is very important that you follow the directions as closely as possible. They are designed to
help you construct your solution optimally, which will help maximize your grade when your
code is evaluated through automated tests.
To be eligible for full marks, you must:
• Follow all the directions below.
• Code your solution using the template provided with this handout. Do not modify the template
outside of the regions you are asked to modify.. • Make sure that your code compiles and is correct.
– Non-compiling code (code with syntax error) will receive a very low grade.
• Submit your code on codePost
– Make sure that your code passes ALL the given open test cases.
– Make sure your code is correct and efficient to pass ALL the blind test cases.
– We cannot make any exceptions for submissions because the final deadline is established by McGill.
Make sure you have a working codePost account and a first version submitted at least 24 hours
before the deadline. If you try to upload last minute for the first time and it does not work, you
will receive a grade of 0 for the project.
• Make sure you adhere to the code of conduct and integrity, and do not engage in any act of academic
dishonesty, including but not limited to, using unauthorized aid and assistance, and committing plagiarism. In submitting this exam, you confirm that your conduct during this final assessment adheres to the
Code of conduct and academic integrity (https://www.mcgill.ca/students/srr/academicrights) – This assessment is individual. You cannot share any code, test cases, strategies or other information about the assessment with other students or on the internet.
– You may use all resources shared in the context of the course (textbooks, slides, recordings, old
Piazza posts, etc), as well as Java Documentation, but nothing else.
– You will not share or disseminate this final assessment on any platform or through personal
communication.
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The problem
It was November 2nd, 2020, and I was sitting in front of my computer thinking of an exercise to give to
COMP251 students as a long term assessment. I had been procrastinating for almost 3 hours and I wasn’t
even close to having a decent idea for an exercise. While surfing the internet every page was talking about
the United States Presidential elections. This year they were scheduled for Tuesday, November 3, 2020 (i.e.,
the day after writing this assessment outline). I did not know that US elections usually take place on the first
Tuesday in November. This information is not useful at all for COMP251, but I thought it would be cool to
share anyway. Thanks to the internet, I also discovered that the US electoral system is quite complicated!
Particularly, I found the following interesting information:
1. The American electorate were to decide between incumbent President Donald Trump and his Democratic challenger, former Vice President Joe Biden.
2. The American people indirectly elect the president because even if each voter selects between Mr.
Trump and Mr. Biden, they are actually voting for a representative of that candidate’s party known
as an elector. The totals are not calculated nationwide, but the president is elected by an Electoral
College selected state-by-state. The electoral college meets a few weeks after election day, to carry
out the task of choosing the president (to vote for the candidate who got the majority of the votes in
their own state). This system is usually known as a ‘winner-takes-all’ because the candidate with the
highest number of votes in a state claims all the electoral votes of that state.
3. For the 2020 elections, it was guaranteed that every state had at least one delegate (the number of
electoral votes of a state) and at least one registered voter.
4. For the 2020 elections, there are 538 delegates, but for our test cases we can have at most 2016 delegates.
5. In 2016, Mr. Trump beat Mrs. Clinton in Florida by a margin of just 2.2%, but that meant he claimed
all 29 of Florida’s crucial electoral votes.
6. National polls were giving Mr. Biden an average lead of over 10%. However, is that enough, given the
indirect way the United States elects its president?
7. There were over 100 million cast ballots in historic early voting, with millions more heading to the
polls on Tuesday. Then, the electoral threshold (maximum number of allowed voters) was this year set
to be 1 billion (109
) cast ballots.
8. If there were a tie (either at the State or National level) between Mr. Trump and Mr. Biden, the US
House of Representatives determines the president. As of November 2nd, 2020, Republicans were in
the majority, with control of 26 state delegations, and as a consequence, Mr. Trump would be elected
as the new president.
9. Based on the State Polls, Joe Biden was leading key states (the so-called battleground states including
Michigan, Wisconsin, and Pennsylvania) that gave Mr. Trump his victory back in 2016.
10. Most State Polls were wrong about the 2016 presidential election. For example, the CBC’s Presidential
Poll Tracker gave Mrs. Clinton a 3.4-point lead in the national polls over Mr. Trump on the election
day. She was projected to win North Carolina, Florida, Michigan, Pennsylvania, and Wisconsin;
however, Mr. Trump won all of these states and secured more than the 270 electoral college votes
needed to win the White House.
At this point in my procrastination, I got interested in the polls that compiled information about the voting
preferences per state. Particularly, for each State, I compiled the information regarding i) The expected
number of people who are projected to vote for Mr. Biden, ii) The expected number of people who are
projected to vote for Mr. Trump and iii) The number of people who have not made a voting decision yet.
The technical description of the polls makes it clear that the numbers of the first two categories are not likely
to change because they are votes from people with long-time roots in a particular political party. On the
other hand, people in the third category are the ones who expressed no preference and did not lean towards
either of the major parties. At this point (also of my procrastination), I realized that it would be great to
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have a very efficient algorithm to know the minimum number of people that Mr. Biden needs to convince
in order to secure the presidency of the United States of America. I was about to start coding my solution
when I realized that this could be a nice and fun exercise for COMP251 students. The idea is that I would
provide you the files (some of them will be open cases and others will be blind cases) containing the following
information:
• The first line of my file contains a single integer (i.e., num states) that represents the number of states
taken into account by a poll.
• Following num states lines each contain four integers (separated by spaces) with the following information.
1. The number of delegates for a specific state.
2. The number of people who will vote for Mr. Biden in that state.
3. The number of people who will vote for Mr. Trump in that state.
4. The number of people who have not made a voting decision in that state yet.
For each provided file you must calculate the minimum number of people that Mr. Biden would have to
convince to earn the US presidency. If it is not possible for Mr. Biden to win the election, you must output
the integer r 1.
Let see some examples of my files with the expected answers:
Sample Input 1:
3
7 2401 3299 0
6 2401 2399 0
2 750 750 99
Sample Output 1: 50
Sample Input 2:
3
7 100 200 200
8 100 300 200
9 100 400 200
Sample Output 2: -1
Sample Input 3:
3
32 0 0 20
32 0 0 20
64 0 0 41
Sample Output 3: 32
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Given the different electoral fraud claims and legal challenges launched after election day and the long process
to give a verdict, it would be fundamental that you algorithm would be correct and efficient. In other
words, your algorithm must take all possible instances of the described problem to the right result (you
do not want your algorithm to be used as a proof of electoral fraud and get a very low mark) and your
algorithm must do that in a reasonable amount of time as a function of the size of the input (you do not
want your algorithm to take days to produce results and get a very low mark). In order to guarantee that, we
recommend you to: i) review the algorithms covered in class looking for the optimal technique to be applied
to the problem and, ii) generate a good number of quality test cases (or develop a proof of correctness) to
be sure that your algorithm is correct.
Your task: completing the solution method
For this part of the assessment, you will create a function called solution which gets the following parameters:
• An int variable called num states that represents the number of states considered by the Poll.
• An int[] array of integers called delegates with the number of delegated for the num states states.
• An int[] array of integers called votes Biden with the number of votes for Mr Biden for the
num states states.
• An int[] array of integers called votes Trump with the number of votes for Mr Trump for the
num states states.
• An int[] array of integers called votes Undecided with the number of Undecided votes for the
num states states.
The function solution must return and int representing the minimum number of people that Mr Biden
needs to convince in order to secure the presidency of the United States of America, or r 1 if it is impossible
and Mr Trump has already secured the re-election.
The signature of the function solution in the java file US elections is as follows.
public static int solution(int num_states, int[] delegates, int[] votes_Biden, int[]
votes_Trump, int[] votes_Undecided){
}
Please complete the body of the function solution and please do not change the methods or constructors
that are already given to you, do not import extra code and do not touch the method headers.
Note: main function
We have already implemented a main function to read the data from the files, to create the variables and
arrays that are passed as arguments to the function solution and finally to call the function solution.
Please note that this function will not be graded, and it is there only to make sure that all of the Comp251
students understand the input of the function solution and to test your own code.
The main function is defined in the java file US elections. Please do not change or alter the function main
in any way.
What To Submit?
Attached to this assignment is a file called US elections.java. PLEASE note that you only need to
complete the body of the function solution. Then, please do not change or alter the name of the file (
US elections) you must submit, or the method headers in this file. Files with the wrong name will not be
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graded. Make sure you are not changing file names by duplicating them. You are allowed to create helper
functions, but those functions must be located inside the ( US elections) file. Do not modify the code in
any other way and in particular, do not change the methods or constructors that are already given to you,
do not import extra code and do not touch the method headers.
You have to submit only the US elections.java. file. Please DO NOT zip (or rar) your files, and do not
submit any other files.
Where To Submit?
You need to submit your assignment on CodePost. Please note that you do not need to submit anything to
myCourses.
When To Submit?
Please do not wait until the last minute to submit your final assessment. You never know what could go
wrong during the last moment. Please also remember that you are allowed to have multiple submission. So,
submit your partial work early and you will be able to upload updated versions later (as long as they are
submitted before the deadline).
How will this assessment be graded?
Each student will receive an overall score for this assessment. This score evaluates the correctness and
efficiency of your solution.
• Correctness and time score: This score is between 0% and 100% depending on the number of test
cases your code has passed. We have hundreds of test cases (3 open cases and several blind cases). The
open cases will be run within your submissions and you will receive automated test results (i.e., the
autograder output) for them. You MUST guarantee that your code passes these cases. The blind test
cases are inputs that you have not seen and they will test the correctness and speed of your algorithm
on those inputs once the deadline of the assignment is over.
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