Given an array of numbers X₁ = {x₁, x2, ..., n } an exchanged pair in X is a pair xi, xj such that i < j and xį > x¡ . Note that an element x; can be part of up to n - 1 exchanged pairs, and that the maximal possible number of exchanged pairs in X is n(n − 1)/2, which is achieved if the array is sorted in descending order. Give a divide-and-conquer algorithm that counts the number of exchanged pairs in X in O(nlogn) time.

Given an array of numbers X₁ = {x₁, x2, ..., n } an exchanged pair in X is a pair xi, xj such that i < j and xį > x¡ . Note that an element x; can be part of up to n - 1 exchanged pairs, and that the maximal possible number of exchanged pairs in X is n(n − 1)/2, which is achieved if the array is sorted in descending order. Give a divide-and-conquer algorithm that counts the number of exchanged pairs in X in O(nlogn) time.