Aformal description of the problems: the input is a set x of n points: x = {x1 < x2 < . . < xn}, where each xi (1 ≤ i ≤ n) represents a house. we need to select a subset y ⊆ x such that: (1) for every point xi ∈ x, there is a point xj ∈ y with |xi − xj | ≤ 5, and (2) the 2 size of y is minimum, subject to condition (1). describe a polynomial time greedy algorithm for solving this problem. you need to prove the correctness of the algorithm.