Homework 12

Comments

• Most problems are found in one of the following:
  1. ADM: The Algorithm Design Manual
  2. IDMA: An 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.
• NEW! 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

The following problems are from pages 195-197 of IDMA.

Problem	Notes
516	Questions 1 and 4 are pretty straightforward. Question 3 includes the possibility of taking however many courses you want, as long as the requirement is met.
517.1-3	The setup for the problem is on page 195. See page 196 for questions 1-3. Question 1 can be done by generalizing the idea in the setup.
526	Don't use induction. It's actually easier than that. But be careful. If you think about it correctly, at some point in your proof you will consider multiple cases/possibilities.