Homework 8

General Comments

• For full credit, provide context for each problem, show all calculations, and justify all answers by providing enough comments to explain your reasoning.
• Homework assignments must be very neatly written or typeset (e.g. using Word or OpenOffice).
• 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. (8) Complete the Kevin Bacon Assignment. You may work in pairs on this problem, but not on the rest of the assignment.
2. (6) Find a valid topological sorting of the following DAG using the DFS-based algorithm. Show all of your work, including the timestamps! (Print/copy/redraw the graph and write the timestamps on the nodes.) Do not forget to give the final topological ordering!

3. (6) Design a decrease-by-half algorithm that computes ⌊log₂ n⌋. Do not forget to give the work case complexity!
   Note: Do not look up an algorithm. Come up with your own!