Homework 17

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 6.1 #2 (page 205) (10 points) Keep in mind that the goal for part b is to be as efficient as possible. Make sure your algorithm description is clear and unambiguous. Don't forget to analyze your algorithms!
2. IDAA 6.2 #2 (page 216) (5 points) Read carefully and notice which technique it is asking you to use. Also, the solutions are integers, so you if don't get integers you have made a mistake somewhere.
3. IDAA 6.4 #6 (page 233) (15 points) In case it isn't clear, the three operations are insert, deleteMax, and getMax. Give your solution in a nicely formatted table.
4. This problem: Compute

   11¹³²⁹ mod 100

   by hand (That is, you are not allowed to use a calculator, computer, abacus, or any other computational device besides your brain) using one of the binary exponentiation algorithms. Show all of your work. You are permitted to verify that your answer is correct with the use of a computer or calculator. (10 points)