In the art gallery guarding problem we are given a line L that represents a long hallway in an art gallery. We are also given a set X = {x₀,x₁, . . . ,x_n−1} of real numbers that specify the positions of paintings in this hallway. Suppose that a single guard can protect all the paintings within distance at most 1 of his or her position (on both sides). Design an algorithm for finding a placement of guards that uses the minimum number of guards to guard all the paintings with positions in X.