Cell Tower Placement: There is a long straight country road with expensive houses scattered along it. The houses are owned by affluent stock traders who require cell phone service. You consult for the company that needs to provide the cell service to every house without exception. The towers only have a range of four miles. You want to place the cell phone towers at locations along the road so that no house is more than four miles from the nearest cell phone tower. You know exact mileage along the road where each house is located. Design a greedy algorithm that will determine the set of locations for the cell towers that requires the fewest cell towers. Denote the location of the ith house as Mi and the location of the jth cell tower by Tj. A. Specify using pseudo code an efficient greedy algorithm to achieve this goal with the fewest cell towers. B. Prove your algorithm always finds the optimal solution. C. Analyze your algorithms complexity.

You must use the following notation: Si: ith contestants swim time; Bi: ith contestants bike time; Ri: ith contestants run time; If your argument involves different orderings make sure your notation clearly differentiates the two orderings. Follow the structure of the proof in class used to prove correctness of the algorithm that solves Minimizing the Total Weighted Time to Completion. There will be slight differences since the function to be minimized here does not involve weights.