Homework 19

General Comments

• Most problems are found in one of the following:
  1. IDAA: Introduction to the Design and Analysis of Algorithms
  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. IDAA 9.1 #9(b) (page 324). Assume the adjacency lists are stored in alphabetical order and start from vertex a. Give the value in the priority queue at every step of the algorithm. Draw the graph and darken the edges of the minimum spanning tree. (you may photocopy that page from the book if you wish). Finally, give the weight of the minimum spanning tree. (10 points)
2. IDAA 9.2 #1(b) (page 331-332). Show the sets of vertices for every step of the algorithm. Draw the graph and darken the edges of the minimum spanning tree (you may photocopy that page from the book if you wish). Finally, give the weight of the minimum spanning tree. (10 points)
3. IDAA 9.4 #1 (page 342). Be careful to keep the nodes in your tree in the proper order. In other words, follow the algorithm in the book very carefully. Show every step of the algorithm, not just the final tree. (10 points)