**Required for Undergraduates:** 5 of the following 6 problems

**Required for Graduate Students:** 5 of the following 6 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!

- Unless otherwise specified, all problems and exercises are from CLRS, Introduction to Algorithms, 2nd edition.
- Be sure to answer these questions carefully. For the dynamic programming problems, prove that there is optimal substructure, give the recurrence and the give the dynami programming code. For the greedy algorithms, be sure to prove that ther is optimal substructure and that the greedy choice property holds.

- Exercise 15.2-2. Implementing matrix multiplication.
- Problem 15-2. Printing neatly.
- Problem 15-6. Moving on a checkerboard.
- Exercise 16.2-4. Driving in a desert.
- Problem 16-1. Parts a and b. Coin changing.
- Problem 16-2. Scheduling. Be sure to give an explanation of how you implement your algorithm.

cliff@ieor.columbia.edu