Problem 1. We are given a line L that represent a long hallway in an art gallery and a sorted set X={x1, x2, ., xn} of real numbers that specify the...

Problem 1. We are given a line L that represent a long hallway in an art gallery and a sorted set X={x1, x2, …, xn} of real numbers that specify the positions of paintings in this hallway. Suppose that a guard can protect all the paintings within distance at most 1 of his or her position (on both sides). Design an O(n)-time algorithm for finding a placement of guards that uses the minimum number of guards to protect all the paintings.