CSCI 255 Fall 2019
Introduction to Algorithms and Discrete Structures		Archived Class
Charles Cusack
Computer Science
Hope College
Main
Schedule
Grading
Gradebook
Homework
Policies
Advice
College
    Policies
Notes
Programs
Tutorials
Others
Admin

Homework 15

General Comments

  • Most problems are found in one of the following:
    1. Algorithms: Algorithms, Dasgupta, Papadimitriou, Vazirani
    2. AIDMA: An Active Introduction to Discrete Mathematics and Algorithms
  • For full credit, provide context for each problem, show all calculations, and justify all answers by providing enough comments to explain your reasoning.
  • You will lose a significant amount of credit if you do not provide context, calculations, and justifications for a problem.
  • Numbers and/or algebra by themselves are not enough. A correct answer with no justification will be worth no more than half credit, and sometimes much less than that.
  • Precision is very important. You cannot skip steps, make guesses, or use flawed logic. Any of these things can lead to incorrect answers.
  • Homework assignments must be very neatly written or typeset (e.g. using Word or OpenOffice).
  • Remember that you can get up to 50% credit on a problem if you get significant outside assistance. Thus, if you are totally stuck on a problem it might be worth getting help. However, you must indicate any assistance/collaboration (See the Homework Assistance section on the Policies page). Failure to do so could result in a failing grade for the course! Note that getting help from the Help Center or me does not count as significant outside assistance, but talking with your classmates or searching on the Internet does!
  • If a problem asks for an algorithm, you should give the most efficient algorithm you can find to ensure full credit. You should also specify the complexity of the algorithm with justification, whether or not the problem asks for it.

Details

  1. (10 points) Algorithms 3.2 b
  2. (10 points) Algorithms 3.3
  3. (10 points) Algorithms 3.11. This one is not too difficult if you use one or more of the algorithms described in this chapter. Make sure you justify the fact that it has the desired complexity.
  4. (12+4 bonus) Algorithms 3.28.
    • Be very careful with part (c) since it is really easy to interpret it wrong and/or make a mistake while constructing the graph.
    • (d) and (e) are a bit more difficult and will require some thinking, so they are bonus problems.
    • (f) can be done if you assume the results of (d) and (e) are correct even if you can't complete those parts.
    • (f) is asking you to describe the algorithm and justify that the complexity is linear.