CSOR 4231 07F: Homework 5

Required : 4 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!

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 17.2-3. Counter with reset. Be sure to give careful pseudocode and then give a potential function analysis.
  2. Exercise 17.3-3. Potential function for a heap.
  3. Problem 17-2. Making Binary Search Dynamic.
  4. Exercise 21.3-3. Lower bound on union-find.
  5. Exercise 22.2-5. Breadth-first search.
  6. Exercise 22.3-4. Depth-first search.

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cliff@ieor.columbia.edu