The element distinctness (ED) problem is given a set S of n numbers, report yes if every element of S is unique and no if there are duplicates. Any comparison-based algorithm for this problem requires (n logn) time.

Consider the closest-pair (CP) problem: Given a set R of n real numbers, which two numbers in R have the smallest difference? Show that any comparison-based algorithm for the closest-pair problem requires (n logn) time using the reduction method with the element distinctness lower bound.

Pseudocode with complexity explanation is fine.