Consider a long, quiet country road with houses scattered 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 4 miles of one of the base stations. Required:
a. Give a greedy efficient algorithm that achieves this goal, using as few base stations as possible.
b. Prove that the greedy choice that your algorithm makes is the optimal choice.