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,−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.