COMS 4231 02F: Homework 3

Assigned: Thursday, October 3, 2002
Due: Wednesday, October 16, 2002

Required: 6 of the following 8 problems
Points: 10 pts per problem

General Instructions

  1. Please review the homework and grading policy outlined in the course information page.

  2. On the first page of your solution write-up, you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following

    Problem01020304 0506070809...
    CreditRCRCRCECRC RCNARCRC...

    where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not attempted" (not applicable). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.

  3. You must also write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
  4. Start early, be concise but rigorous, and enjoy!

Specific Instructions

  1. Be sure to review the appendix on probability if your background is weak.
  2. All logs are base 2 unless otherwise specified.
  3. Unless otherwise specified, all problems and exercises are from CLRS, Introduction to Algorithms, 2nd edition.

Problems

  1. Exercise 5.4-6. Balls in bins. Please comment on the relevance of these questions to hashing.
  2. Problem 13.4. Treaps. (editorial comment: This is a really cool data structure.)
  3. Exercise 14.1-7. The mandatory inversions problem.
  4. Exercise 14.3-6. Min Gap.
  5. Problem 14-1. Maximum Overlap.
  6. Augment Skip lists so that rank and select queries can be supported in O(log n) expected time. Be sure to show that your additional fields can be maintained efficiently during insertions. (You do not need to address deletions.)
  7. Problem 15.6. Moving on a checkerboard.
  8. Exercise 15.1-1, 15.1-2. Scheduling.


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