Describe an efficient greedy algorithm that, given a set {x1, x2, ..., xn, } of points on the real line, determines the smallest set of unit-length closed intervals that contains all of the given points. Prove that your algorithm is correct.

a. Briefly describe a greedy algorithm for the unit length interval problem.
b. State and prove a "swapping lemma" for your greedy algorithm.
c. Write a proof that uses your swapping lemma to show that your greedy algorithm does indeed produce a set of intervals that contain all of the points {x1, x2,...,xn} with the fewest number of intervals.