CSOR 4231 07F: Homework 4

Required : 5 of the following 6 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!
  5. Please turn in each problem on a separate piece of paper(s), with your name on it.

Specific Instructions

  1. Unless otherwise specified, all problems and exercises are from CLRS, Introduction to Algorithms, 2nd edition.
  2. 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.

Problems

  1. Exercise 15.4-2. Exercsie 15.4-4. Space efficient LCS.
  2. Problem 15-2. Printing neatly.
  3. Problem 15-3. Edit distance.
  4. Exercise 16.2-4. Driving in a real desert.
  5. Let S and T be two strings of characters. Give an efficient algorithm to determine whether S is a subsequence of T. Be sure to prove that your algorithm is correct.
  6. Problem 16-2. Scheduling. Be sure to give an explanation of how you implement your algorithm.


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cliff@ieor.columbia.edu