Texts: For the Activity Selector Problem, suppose that instead of always selecting the first activity to finish, we instead select the last activity to start that is compatible with all previously selected activities. Describe how this approach is a greedy algorithm, and prove that it yields an optimal solution.
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5. (7 points) We consider the problem of placing towers along a straight road, so that every building on the road receives cellular service. Assume that a building receives cellular service if it is within one mile of a tower. Buildings can be at any location along the road, cellular towers can be at any location along the road and neither are restricted to be at whole number locations.
5a) Devise an algorithm that uses the minimum number of towers possible to provide cell service to d buildings located at positions 1, 2, . . ., d from the start of the road.
5b) Use mathematical induction to prove that the algorithm you devised produces an optimal solution, that is, that it uses the fewest towers possible to provide cellular service to all buildings.