Homework 6

Goals

• Solved a recurrence relation
• Developed a greedy algorithm.

Formal Description

1. You have a friend who proposes the the following would be faster than merge sort.

   Split the array into three equal portions
   Sort each of these portions
   Merge the resulting lists
       

   1. Develop a recurrence relation representing the performance of this algorithm
   2. Find a closed form of this recurrence relationship. Show your work, but this can be an image of solving this by hand.
   3. Is your friend correct? Defend your answer.
2. This is problem 5 from page 232 of your book.

   Let's consider a long, quiet country with houses scattered very sparsely along it. (We can picture the road as a long line segment with an eastern endpoint and a western endpoint.) Further, let's suppose that despite the bucolic setting, the residents of all these houses are avid cell phone users. You want to place cell phone base stations at certain points along the road, so that every house is within four miles of one of the base stations.

   1. Give an algorithm that achieves this goal, using the fewest number of base stations.
   2. Argue that your algorithm is correct.
   3. Give the performance of your algorithm.

Required Files

Submission