Eecs 281 Homework 13-1

EECS 281: Data Structures and Algorithms

Winter 2018

Faculty Instructors

Mr. Kevin Angstadt,

Mr. Marcus Darden, 2644 Beyster,

Dr. David Paoletti, 2645 Beyster,

Office Hours

Office hours will be posted to the Google Calendar on Canvas

Other resources

Course web page (all sections): Canvas:

Course forum/chat (all sections):  Piazza, please sign up here:

Course administrative email (used for special circumstances such as illness):

EECS 281 is an introductory course in data structures and algorithms at the undergraduate level.  The objective of the course is to present a number of fundamental techniques to solve common programming problems.  For each of these problems, we will determine an abstract specification for a solution and examine one or more potential representations to implement the abstract specification, focusing on those with significant advantages in time/space required to solve large problem instances.  When appropriate, we will consider special cases of a general problem that admit particularly elegant solutions.

Students must have obtained a grade of C or better in each of EECS 203 and EECS 280, or have equivalent knowledge of discrete mathematics and C++ programming.  MATH 465 or MATH 565 are accepted in lieu of EECS 203.  Due to the overwhelming number of students interested in this course, we will strictly enforce the prerequisites.  If you failed to complete, or if you received a grade of C- or below in any of the prerequisites, then you must drop EECS 281 this term, and re-enroll at a later term, after you have completed all prerequisites with a grade of C or better.

Students will be expected to use the "make" utility to automate C++ compilation.  Also, students should be able to generate plots using MS-Excel, OpenOffice, Gnuplot, or similar tools.  Students with questions about whether they have sufficient preparation for this course should speak with the instructor(s) as soon as possible.

Per departmental policy, each student may attempt EECS 281 twice at most.  One attempt in EECS 281 is defined as one instance where EECS 281 appears on your UM transcript - including but not limited to a letter grade (A-E), withdrawal (W), pass/fail (P/F), incomplete (I).  At most one attempt from Summer 2014 or earlier will count towards this limit.  If you drop EECS 281 prior to the date which a W would appear on your transcript, then that would not count as an attempt for the purposes of this policy.  Exceptions to this policy can be granted by the appropriate Chief Program Advisor under extraordinary circumstances only.

Readings come from (both are available electronically to UM students at no extra cost):

  • Introduction to Algorithms, 3rd Edition, by Cormen, Leiserson, Rivest, and Stein.  MIT Press, 2009 (click on Available Online below the Holdings tab)
  • The C++ Standard Library: A Tutorial and Reference, 2nd ed., by N Josuttis.  Addison Wesley Publishing, 2012

There may also be some handouts that the faculty will provide.  You are required to read the contents of the course website and regularly visit Piazza, where we will post important course-related information.

Your work in this course is composed of: attending lecture and lab sections, reading assigned material, completing lab assignments, completing projects, taking a midterm exam, and taking a final exam.  Final grades will be based on the total points earned on the labs, projects, and exams.  Factors such as improvement and course participation may be used to adjust your final grade, especially if it falls on a borderline.  The weight assigned to each category is as follows:

Lab Assignments20% (each lab assignment weighted equally)

Projects40% (each project weighted equally)

Midterm Exam20%

Final Exam20%

We make every effort to grade correctly, however we do sometimes make mistakes.  Arithmetic errors can be corrected in person by your IA or GSI.  If you believe something was graded incorrectly, you may submit it for a regrade.  All exam regrade requests must be made on Gradescope.  Regrade requests for other assignments must be made via email explaining the technical reason(s) that would make a regrade necessary.  The email must be sent to with “EECS 281 Regrade Request” in the subject line.  All regrade requests must be submitted no later than five working days after the graded work is returned to the student - after that, your score on the assignment in question stands.  This includes requesting that errors in recording a score in Canvas be fixed.  Regrade requests must be an objective argument about which specific rubric items were inconsistently or improperly applied, not a subjective argument about what things should be worth.  The work in question will be regraded carefully from scratch in its entirety, with consideration given to the written request.  As a result, your grade might go up, stay the same, or go down.

For the midterm exam, we will begin accepting regrade requests two calendar days after your exam is released to you on Gradescope.  This is to force you to wait until you have carefully reviewed your exam responses and the rubric before submitting a regrade request.  Regrade requests for the midterm exam will still close five working days after the scores are released, not after we begin accepting regrade requests.  For the final exam, your exam will not be released to you, and you will need to see an instructor in office hours to view your exam.  In that case, the instructor will regrade your final exam with you side-by-side.

Incompletes will generally not be given except in extreme circumstances. In accordance with university policy, doing poorly in a course is not a valid reason for an incomplete. If you are having problems in the course, please talk to the instructor(s) as soon as you are able.

To pass this course, you MUST achieve at least 55% on the Programming Projects AND 50% (curved score) on the exams AND 60% overall in the course (after exam cuving).  You must achieve ALL of these thresholds separately - very high exam scores will not compensate for very low project scores, and vice versa.  If you receive at least 220 project points AND at least 100 exam points total for the term AND at least 60% overall in the course, you are guaranteed at least a grade of C in the course.  Rounding is not guaranteed, so 219.999999 project points OR 99.999999 exam points OR 59.999999% overall in the course does not guarantee passing.

The Midterm and Final Exams will be curved if needed, and any curve applied can only be in your favor.  When this is done, your score may go up but it will never go down.  After curving, the table below gives you a lower bound as to what your grade would be.  That is, we may perform a final curving, which again may improve someone’s grade, but never reduce it.  Rounding is not guaranteed, thus 90% overall guarantees at least a grade of A-, 89.999999% does not - the cutoff must go somewhere and no matter where it goes, there will always be somebody barely on either side of it.

Grades shown here are superseded by the “Minimum Competency” rules shown above.  If you achieve ALL thresholds, then the guarantee that you will receive at least a C in the course trumps the scale shown in the table below.  However, if you fail to meet at least one of the thresholds, then you may still receive a C- or below even if the scale shown in the table below says that you should be getting a higher grade.  For example, if you have 60% overall, and achieve at least the minimum 55% on projects and 50% on exams, you will receive a C, even though the table below says that you should receive a D.  On the other hand, if you only achieve 50% on projects, but 100% on everything else, then despite that being 80% overall, your grade will be a C-, even though the table below says that you should receive a B-.








































Your grade is based solely on your performance for the work assigned in the course.  We must be consistent in how we evaluate students in order to be fair to all students, hence we must uniformly enforce all deadlines and course policies, and we cannot give extra credit or makeup assignments on an individual basis.  If you need a certain grade in the course in order to make satisfactory progress towards your major or minor, keep a scholarship, avoid having a contingent job offer rescinded, avoid problems with your academic standing, etc., then you must earn the grade yourself by paying attention to the work assigned for the course throughout the term.  The course grade is not open to student negotiation.  While factors such as improvement can be used to move you across a grade boundary in a very borderline case, this decision rests solely with the instructors and is not negotiable.

We do caution you that from our experience, those who aim for only the minimum often finish the term with a result that they are disappointed with.  Even if your goal is only to receive a passing grade, it is still in your best interest to put forth your best effort throughout the term.  You are likely taking EECS 281 to help you get a job, and we want you to succeed in getting a job.  However, note that many employers want to see a good understanding of data structures and algorithms (and not just a grade for EECS 281) - if you take EECS 281 with the intent of just barely scraping by the course, then you may encounter difficulty in the job search process.

We will assign approximately 10 lab assignments over the course of the semester (each equally weighted).  Lab submissions must not include external materials (e.g., web downloads) unless specifically requested in the assignment.  Any external sources used must be clearly cited in the lab solution set.  Lab work is typically due as some combination of: (1) a sheet of paper turned in at the end of the lab period; (2) a quiz submission to the EECS 281 Canvas site; (3) a submission to the EECS 281 autograder. There are no drops - experience shows that students would often just entirely skip "the hardest lab" or the last lab of the term, and those choices will harm your understanding of important concepts discussed in those labs.  In the event of an extreme medical or personal situation, we may prorate a lab written score (based on your scores on other portions of the lab) or extend a lab quiz deadline as appropriate.  In order to request this accommodation, you must email before the deadline and provide documentation.

Four projects will be assigned during the term.  Project submissions must not include external materials (e.g., web downloads) unless specifically requested in the assignment.  These projects will require substantial time commitment on every student’s part - you cannot start a project a few days before it is due and expect to receive a good grade on it, even if this might have worked for you in EECS 280.  However, we expect that effort spent on programming projects will help the student to gain a conceptual understanding of the material.We strongly recommend that students begin working on projects early, both to lower stress and have more time to ask questions.

The projects together total 40% of the course grade (10% each).  The breakdown of points for each project grade will be specified in the project assignment.  Categories include:

  • functional correctness;
  • execution speed to obtain correct solution;
  • principles and practices (readable code, efficient algorithms and implementation, comments, use of topics from class); and
  • documentation of your solution.

For each project, we will do a final grading run after the deadline, where every student’s project is run one-by-one on the autograder with hidden test cases.  The purpose of running every student’s project one-by-one is to even out the playing field by giving everybody the same computing resources when determining project grades, so your score should not be penalized because your runtime or memory usage was affected by other students’ projects being run in parallel.  The purpose of the hidden test cases (they will be randomly generated cases, not the trickiest corner cases) is to ensure that your project works in general, and not just for the autograder.  We will use your best submission for final grading, unless you complete a form requesting that we use your last submission within 48 hours after the project deadline.  “Best submission” is defined as the submission with the highest displayed score prior to the deadline.  If multiple submissions are tied as being your best submission, then we will use the most recent of those submissions for final grading.  The score resulting from final grading is the score that will go in the gradebook.  This means that your overall highest displayed score on the autograder may not necessarily be the score that goes in the gradebook.  It is possible that your score may go up, stay the same, or go down as a result of the final grading.  Most of the time, scores do not change by more than a few tenths of a point, but a change between one to two points is still nothing we will be alarmed about.  If a student’s score decreases by more than two points, the autograder will prompt us to manually review the situation.

You will have roughly 2-3 weeks (roughly half the time in a spring term) to work on each project.  Projects will be submitted online to an autograder, and will only be accepted via the autograder.  Specific details of the project submission process will be described on the course website.

Sometimes unexpected events or other academic commitments make it difficult to get a project in on time. Everybody is given two (2) late days for the semester to use on whatever project(s) and for whatever reason, no questions asked.  You can use them for illness, family emergency, computer or equipment failure, loss or erasure of files, internet access problems, work for other courses, and other outside commitments.  Use them wisely!  You must use one late per calendar day after the deadline in order to submit a project late. If you want to submit a project one day after the deadline, it will simply cost you one late day.  If you want to submit a project two days after the deadline, and you have already used one late day on that project for the day after the deadline, then it will simply cost you a second late day.  However, if you want to submit a project two days after the deadline, but you did not use a late day on that project for the day after the deadline, then it will still cost you two (not one) late days.

Aside from the late days, projects will not be accepted once the autograder closes, except in extreme documented medical and personal emergencies.  We advise you to use your late days for when the unexpected occurs, and not for starting a project late.  Often, it will be better to submit a partially working assignment on time rather than spend an uncertain amount of additional time in getting it to work completely.  Because of auto-grading, it is important to carry out the project tasks in such a way that you have at least a partially working project early on, which you enhance every day until the project becomes due.

All projects are to be written in C++.  The student is free to use any environment to develop a program, but any submitted program must compile and run in the CAEN Linux computing environment ( the GCC version 6.2.0 compiler.  You are responsible for making sure that your projects run correctly in this environment.  “My code runs fine locally, but just not on CAEN” will not be considered justified for receiving special consideration.  Using CAEN Linux computing as your development environment will reduce the chance of encountering nasty surprises when your project is graded.

There will be one midterm exam and one final examination.  The midterm examination is scheduled for Wednesday, February 21th, 6:30pm - 8:00pm.  The final examination is scheduled for Thursday, April 19th, 8:00am - 10:00am, with a conflict exam time of Thursday, April 19th, 10:30am - 12:30pm.

If you miss an exam without a documented medical or personal emergency, you will receive a score of zero for that exam.  If you have an exam conflict, or need SSD accommodations, you must fill out the Alternate Exam Request form on Canvas, and submit any requested documentation prior to the specified deadline, when given.  Alternate exam requests are not accepted via email or Piazza.  The exam dates are given at the beginning of the term so that you can avoid scheduling job interviews or other personal commitments on exam days.  Per university policy, when alternate exam times are available, they are not elective.  You must have a documented and valid conflict in order to take an alternate exam.

The following reasons may justify an alternate exam request:

  • Disabilities - must be documented with an official SSD form.
  • Varsity athletic competitions and travel - must be verified by a university official from the Athletics Department.
  • Conflicting exams and classes - if it is scheduled to end at least 30 minutes before or begin at least 30 minutes after the EECS 281 exam, then it is not a conflict, even if it takes place on central campus.
  • Religious holidays.
  • Family emergencies.
  • Illness or injury - the physician’s note must specifically require that we excuse you from the exam and provide an approximate date of recovery, “patient was seen in UHS” note is insufficient.

The following reasons do not justify an alternate exam request:

  • Job interviews - unless the company verifies that you do not have a choice with regards to interview date.
  • Conferences - unless a university faculty member verifies that you absolutely cannot opt out of attendance.
  • Employment.
  • Athletic practice.
  • Club meetings.
  • Vacation, weddings, travel home - cheaper flights or accommodation will not be accepted as justification.

These are not exhaustive lists, but you can notice that most of the reasons that do not justify an alternate exam request are personal outside commitments, for which participation is voluntary.  If you have a personal outside commitment that conflicts with either exam, and you are unwilling to budge on that outside commitment, please drop EECS 281 this term and re-enroll in another term which you can make the exam dates.  For circumstances not listed above that may be in the grey area, you may email to ask if it will be considered justified.  If you wish to have an answer in time to drop the course without a W if needed, you should ask no later than one week prior to that deadline.  Note that the times for the final exam are set by the registrar’s office, and are not a subject of negotiation.

Your first and best option is to ask your question during the office hours of a member of course staff.  The next best option is to post your question to Piazza, which will be monitored regularly.  Students are allowed/encouraged to post answers to Piazza questions; however, posted questions and answers must not reveal solutions to the projects or lab questions.  You should not rely on private email to ask course-related questions.  Members of the course staff may or may not answer questions sent by private email.

We do understand that students sometimes have questions of a personal or sensitive nature.  For such matters, we ask that you see your instructor during office hours.  If you have a conflict with all posted hours, you should send an email to to schedule another time.  

  • Policy on Collaboration and Cheating

Acts of academic misconduct will be reported to the Engineering or LS&A Honor Councils, as appropriate.  We will not even consult with you first if we have sufficient evidence and/or testimony.  If found guilty, we will comply with the grade sanctions recommended by the appropriate administrators.  In addition to the impact on your grade, you will be required to disclose the conviction to employers or graduate/professional schools that inquire about history of academic misconduct and/or disciplinary action, even if any indication of the misconduct never goes on or eventually gets expunged from your university records.  Cheating includes but is not limited to any attempt to copy somebody else's work (with or without modification) that is not meant to be publicly accessible, gain access to solutions that you should not have access to, game the autograder, turn in an assignment on behalf of somebody or have somebody do so for you (both students will be equally responsible), use unauthorized resources on an exam, and work on your exam before being told to start or after being told to stop - note that “attempt” means that you do not necessarily need to be successful in order for us to pursue charges.  Unacceptable collaboration includes but is not limited to the knowing exposure of your own exam answers, project solutions, or lab solutions; or the use of someone else's answers or solutions made public.  This includes solution sets and student solutions from past incarnations of EECS 281.  This means that students are not permitted to use previous solution sets.  Any misrepresentation of another person’s work as your own is unacceptable in EECS 281, and is a violation of the honor code.  Other acts of academic misconduct include providing forged or falsified documentation in an attempt to get an extension on a project, get excused from a lab written part, get extended time on an exam, delay taking an exam, etc.

If you are repeating EECS 281, you may reuse code from projects that you completed during your previous term of enrollment, provided that the code you are reusing is your own.

At the same time, we encourage students to help each other learn the course material.  As in most courses, there is a boundary separating these two situations.  You may give or receive help on any of the concepts covered in lecture or discussion and on the specifics of C++ syntax.  You are allowed to consult with other students about the conceptualization of a project, or the general approach for lab solutions.  However, all written work, whether in scrap or final form, must be done by you (or within your partnership, where applicable).

You are not allowed to work out the programming details of the projects or specific details of the lab problems with anyone (except within your partnership, where applicable) or to collaborate to the extent that your programs/lab solutions are identifiably similar.  You are not allowed to look at or in any way derive advantage from the existence of solutions prepared in prior terms, whether these solutions are copies of former students' work or solution sets handed out by course staff.  For the projects, we will be using a sophisticated automated program to correlate projects against each other and past solution sets - it is capable of flagging projects that differ by only variable names.  For the labs, the exams will enforce this policy better than we can - if this is how you choose to do your lab assignments, then your exam scores will likely suffer.

Under no circumstances should you show any code that you will turn in for a grade (for a programming project or a lab assignment) to any persons other than the EECS 281 instructional staff.  Similarly, under no circumstances should you look at code written by another EECS 281 student (current or past) when preparing your own solutions.

If you have any questions as to what constitutes unacceptable collaboration or exploitation of prior work, please talk to the instructor(s) right away.  You are expected to exercise reasonable precautions in protecting your own work.  Don't let other students borrow your account or computer, don't leave your work in a publicly accessible directory, and take care when discarding printouts.  In addition, if you use an online repository such as GitHub, make sure that your work does not go inside a public repository.

  • Student Mental Health and Wellbeing

University of Michigan is committed to advancing the mental health and wellbeing of its students.  If you or someone you know is feeling overwhelmed, depressed, and/or in need of support, services are available.  For help, contact Counseling and Psychological Services (CAPS) at (734) 764-8312 and during and after hours, on weekends and holidays, or through its counselors physically located in schools on both North and Central Campus.  You may also consult University Health Service (UHS) at (734) 764-8320 and, or for alcohol or drug concerns, see

For a listing of other mental health resources available on and off campus, visit

The course staff reserves the right to make fair and reasonable revisions to the syllabus at any time as they see fit. When a revision occurs, it will be announced, and it is your responsibility to be informed of such.

The syllabus page shows a table-oriented view of the course schedule, and the basics of course grading. You can add any other comments, notes, or thoughts you have about the course structure, course policies or anything else.

To add some comments, click the "Edit" link at the top.

Course Summary:

First Half Course Grade Composition:
  • 1 Midterm Exam: 13%
  • 2 Programming Assignments: 26%
  • 2 Homeworks: 10%
  • Class Participation: 1%

Homeworks will be due before lecture and must be turned in as hard copy in class. Programming assignments must be turned in online. Do not email any of your assignment to the teaching staff.

If your individual effort is lacking, a failing grade is a distinct possibility. Roughly, you'll get the lower grade if you failed the exams and do not show sufficient efforts. Insanely great work gets an A+, excellent work an A, good work a B, and acceptable work a C.

Regrade and Late Days

You have five working days from when a piece of graded work is returned to ask for a regrade. To ask for regrade, you must submit a written request explaining the technical reasons that would make a regrade necessary. A regrade means regrading your whole work and may result in overall lower grade.

You have two free late days, including weekends, to use on any of your programming assignments. It is your responsibility to keep track of your own remaining free late days. Once the free late days are used up, late programming assignments will be assessed a penalty that is a fraction of the total assignment grade according to the following schedule:

  • the first 24 hours or fraction thereof: 4%,
  • the second 24 hours or fraction thereof: 8%, on top of the 4% above,
  • the third 24 hours or fraction thereof: 12%, plus 12% above,
  • the fourth 24 hours or fraction thereof: 16%, plus 24% above,
  • the fifth 24 hours or fraction thereof: 20%, plus 40% above,
  • no late work will be accepted beyond 120 hours (5 days) after the deadline.
For example, suppose the assignment is worth 100 points and you turn in your work late by 24 hours and 10 minutes. If you have no free late days left, your late penalty will be 12 points. If you still have one free late day left, your late penalty will be 8 points. Free late days will be consumed first before the late penalty schedule is applied. Homeworks are not provided free late days. Instead, the above penalty schedule will apply immediately on all late homeworks. Since we have the free late days and late penalty schedule, no extension will be granted.

Start your assignments early, and plan to have them finished a few days ahead of the due date. Many unexpected problems arise during programming. In addition, the computer labs and submission/autograder machine can become crowded and computers crash and networks fail. Extensions will not be granted even if these things happen. Plan for them to happen.

General Policy on Collaboration

All works must be completed individually.

You are encouraged to discuss ideas and techniques broadly with other members of your class, but not the specifics of assigned problems. Sharing of code or intermediate designs is expressly prohibited. If you receive substantial help from others, you must acknowledge them in your work. If you use any published materials (books, papers, or materials found on the Web) in your solution, you must give full citation that help facilitate the locating of the original materials (for example, the URL of the Web site).

You must not discuss exam questions with others nor lookup solutions to homework and exam questions online. You are forbidden to solicit help or copy of old homeworks, assignments, exams, or solutions from other students, including those who have taken this course prior to the current term. You are also forbidden to give help or copy of homeworks, assignments, exams, or solutions to others. To do either will be considered a violation of the CoE Honor Code.

Acts of cheating and plagiarizing are Honor Code violation and will be reported to the Engineering Honor Council. Cheating is when you copy, with or without modification, someone else's work that is not meant to be publicly accessible. Plagiarizing is when you copy, with or without modification, someone else's work that is publicly available without acknowledging the original author. To incorporate publicly available code in your solution is considered cheating in this course. To pass off the implementation of an algorithm as that of another or to use libraries not expressedly allowed is considered cheating and violation of the Honor Code. For example, if the assignment asks you to implement sort using heap sort and you turn in a working program that uses insertion sort in place of the heap sort or if you use STL's heapsort, it will be considered cheating. If you can not implement a required algorithm, you must inform the teaching staff when turning in your assignment.

You are required to read the CoE Honor Code. To break/hack into a computer is not only a violation of the Honor Code, but also a criminal offense. It will be reported to the criminal justice system and will be charged and prosecuted to the full extent of the law.
  1. Specific Policy Applicable to Homeworks You are allowed to consult both online and offline sources, including humans, to help solve homework problems. If you do consult outside sources, i.e., other than yourself and the teaching staff, you MUST cite them. You do not need to cite the teaching staff nor the textbooks nor the lecture slides. These are the only exceptions. What you turn in must be your individual work. Your classmates can give you an idea on how to approach a problem, but they cannot give you any solution to these problems. If you find an online solution to any of these problems, you are allowed to consult them, but not to use them verbatim. You must phrase your solution in such a way that shows you have understood the problem and solution. Violation of any part of the above policy will be a violation of the Honor Code. If you turn in a handwritten solution, please write legibly. Illegible scribble will earn zero points.
  2. Specific Policy Applicable to Exams You will be asked to attest that you have read, understand, and will abide by the following policy prior to the start of an exam. You may therefore want to review it now and ask for any clarifications necessary prior to taking any exam in this course.
In case of conflicts, the specific policies override the general policy, and the general policy overrides the JI Honor Code. The parts that are not in conflict still apply.

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