**Required for Undergraduates:** 6 of the following 9 problems

**Required for Graduate Students:** 7 of the following 9 problems

**Points:** 10 pts per problem

- Please review the
homework and grading policy
outlined in the course information page.
- 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 followingProblem 01 02 03 04 05 06 07 08 09 ... Credit RC RC RC EC RC RC NA RC RC ... 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.

- 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.
- Start early, be concise but rigorous, and enjoy!

- Be sure to review the appendix on probability if you need extra background in that area.
- All logs are base 2 unless otherwise specified.
- Unless otherwise specified, all problems and exercises are from CLRS, Introduction to Algorithms, 2nd edition.

- Problem 7-1. Hoare Partition.
- Problem 7-5. Median-of-3 partition.
- Problem 9.2-4. Worst case performance of randomized select.
- Problem 13.4. Treaps. (editorial comment: This is a really cool data structure.)
- Problem 14-1. Point of maximum overlap.
- Exercise 14.1-7. More on inversions.
- Exercise 14.3-6. Min Gap.
- 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.)
- Exercise 15.1-4, 15.1-5. Assembly line scheduling.

cliff@ieor.columbia.edu