Homework 9

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).
• You must indicate any assistance/collaboration you had on an assignment as specified on the Policies page.
• 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

Read the section and problem numbers carefully!

1. IDAA 2.2 #12. Give a clear description of your algorithm and prove that it requires at most O(n) steps. (10 points)
2. IDAA 2.3 #6 (10 points)
3. IDAA 2.3 #11. Hint: For part b, it is possible to improve the algorithm by decreasing the constant factors involved in the computation, but you won't be able to change the complexity class. (6 points)