Computational metrology deals with algorithms for measuring things, such as manufactured parts, and one of the standard algorithms is to determine the flatness of an edge of a manufactured part based on a set of points that are sampled along that edge (say, by a laser range-finder or a scanning electron microscope). Since it is extremely rare for such a set of points to be perfectly collinear, we need a rigorous way of defining flatness in this context. One such way is to define the flatness of a set, S, of n two-dimensional points as the smallest distance between two parallel lines, L1 and L2, such that all the points of S are either on one of these lines or between them. This distance is known as the width of S. Describe an O(n log n)-time algorithm for determining the width of such a set, S, of n points in the plane.