Students' grades in the class will be based on the class final, one midterm, the initial prerequisites quiz, and homwork. The final will count for 50%, the midterm for 25%, the homework for 20%, and the quiz for 5%. Among the homeworks, the worst one will be dropped. There is also an important additional constraint: if the homework score is below 45% of the attainable total, then the final grade cannot be better than a C.
The grading will not be done to a curve. Instead, the grading scale will be as follows. If HWP denotes your percentage of points on all homeworks (except your worst one), MTP1 and MTP2 denote your percentages on the first and second midterm, FEP your percentage on the final, and QZP your percentage on the quiz, then we calculate p = 5%QZP+20%HWP+25%MTP+50%FEP. Then, if HWP is at least 45%, you get the grade from the table below. If HWP% is less than 45%, you get the worse of C and the grade dictated by the table.
| p | Grade |
| 75% | A |
| 67% | A- |
| 60% | B+ |
| 55% | B |
| 50% | B- |
| 43% | C+ |
| 36% | C |
| 25% | D |
The homeworks will also contain specifically marked extra credit problems. These will be significantly more difficult than the other problems. In order to obtain a grade of A+, you will need to satisfy all requirements for an A, and also obtain at least 40% of the points on extra credit problems. Extra credit problems do not help you improve your grade if you are not already in the A range.
Homework is assigned roughly every 1-2 weeks from the textbook. Usually, homework either asks you to "give an algorithm", or to give a proof for some fact. When you are asked to give an algorithm, it also means proving your algorithm's correctness, and giving a (brief) analysis of its running time. The latter two are at least as important as the algorithm itself, and failing to include these parts will give you only partial credit.
Solutions to the homeworks will be handed out on paper in class about one week after the submission deadline. We will not make any solutions available in electronic formats. When returning homework, we also post some cumulative statistics about the class performance.
If you think that we deducted points from your solution unfairly, you have two weeks after we return your homework to ask the TA for a regrade. After those two weeks, we will not consider regrade requests. (If you know that you want a regrade and cannot make the TA's office hours for two weeks, you can notify the TA early, and schedule a later meeting.) If during the regrading process, we discover that your score was in fact too high, your score may also get lowered. If the TA's answer is not satisfying, you can contact the instructor. On the other hand, if your complaint is about grading policy rather than any particular decision of a grader, you should contact the instructor directly.
Homework should normally be submitted in class, on paper. If you cannot submit your homework in class, or are submitting late, you have three options: (1) submit it to the instructor in person, (2) submit it to the TA in person, (3) slide it under the instructor's door. No other means of submission are acceptable (unless you have explicit permission from the instructor) - in particular, please do not leave homework in the instructor's mailbox. (In exceptional cases, such as travel, you can contact the instructor to obtain permission to submit electronically.)
Every student in the class has a total of 5 late days of homework (business days) that can be arbitrarily spread out among homework assignments without the need to provide a reason. These are meant as an unbureaucratic way of dealing with legitimate reasons for late submission. You may use them for other reasons if you choose, but this does not mean you are entitled to 5 late days in addition to any legitimate ones.
No solution will ever be accepted more than 5 business days (one week) late. Occasionally, we will set a tighter homework submission deadline, usually so we can return sample solutions in time before an exam. If a submission is late, and the 5 total late days are exceeded, then 20% of the original score on the homework are deducted for each excessive late day.
For counting late days, a solution counts as submitted on a certain day if it was submitted in one of the above three ways by 5pm on that day. Homework submissions after 5pm count as the next day. If a solution is submitted in multiple parts on different days, then the official submission date is that of the last part that was submitted.
Warning: The numbering of exercises in an old preliminary version of the textbook used in the past is different from the printed version in the bookstore. The numbers given here refer to the bound, printed version. Make sure you are solving the right problems.
The seventh homework assignment has been posted. It is due in class on Thursday, 04/30/2009. It cannot be submitted late. Sample solutions will be provided in class.
The sixth homework assignment has been posted. It is due in class on Thursday, 04/23/2009.
The fifth homework assignment has been posted. (It does not contain an extra-credit problem.) It is due in class on Tuesday, 04/14/2009.
The fourth homework assignment consists of problems 7.45, 7.46, 8.9, and 8.18 from the textbook. The extra-credit problem is 8.42. Please read Section 8.6 and 8.7 in addition to the material covered in class. The fourth homework is due in class on Tuesday, 03/31/2009.
The third homework assignment consists of problems 7.9, 7.13, 7.27, and 7.33. The extra credit problem is given below. Please also read Sections 7.7-7.9 in the textbook, in addition to the material covered in class. The third homework is due in class on Thursday, 03/05/2009.
Extra-Credit Problem: Suppose you play the following two-player game: you have to defend n space stations, which the other player tries to attack. Each space station has c units of energy. The game is round-based. In each round t, the following happens:
Prove that if you know all of the a(t,i) in advance (that is, you know where your opponent will attack in the future, and how much), then you can always survive arbitrarily long so long as the energy level c is at least 2. (Bonus: I don't know if this is also true for c=1, or some other c < 2. If you can prove it or give a counter-example, I would be very interested in seeing it.)
The second homework assignment consists of problems 6.14, 6.16, 6.20, 6.26, and the Fibonacci Heap problem below. The extra credit problem is the Traveling Salesman problem given below. In solving these problems, it might be helpful to read at least Section 6.3 in addition to the material covered in class. The second homework is due in class on Thursday, 02/19/2009.
Fibonacci Heap Problem: In class, we had the rule that once a node lost its second child, it itself was removed from the tree. Several of you asked why after the second child. So here we consider what happens if we change the rule to "once a node loses its kth child, it is removed from the tree" (where k is a constant, and does not change with n or the degree of the node). Prove that for all operations (insert, delete-min, decrease), the amortized time per operation stays the same. Make sure you carefully analyze which parts of the proof from class stay the same, and which need to be revisited.
Extra-Credit Problem: The Traveling Salesman problem is the following: you are given n cities, and distances d(i,j) for each pair of cities. All distances are non-negative, symmetric (d(i,j) = d(j,i)) and satisfy the triangle inequality d(i,k) ≤ d(i,j) + d(j,k) for all i,j,k. Your goal is to find a tour that visits each city (at least) once, and minimizes the total distance traveled. This is an NP-hard problem. The obvious algorithm takes time Θ(n!). Describe (and prove correct) an algorithm solving Traveling Salesman in time O(2n poly(n)).