CSCI 255 Fall 2013Introduction to Algorithms and Discrete Structures Archived Class

# Homework 11

• 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 162-163 of IDMA
Problem
422
424
Problem A (below)
Problem A:
Solve the following recurrence relations. If you can provide an exact formula, do so. Otherwise, give a tight bound (not just an upper bound). Make sure you show all of your work.

1. T(n) = 2 T(n/2) + n3, T(1)=1
2. T(n) = T(n - 1) + n, T(1)=1