Let A[1..n] be an array of n distinct real numbers. A pair (A[i],A[j]) is said to be an inversion if i < j but A[i] > A[j].

(a) Suppose we exchange elements A[i] and A[i+k] in an array, which were originally out of order. Find out how many inversions can be removed. You need to give a lower bound and an upper bound and show why;

(b) Design an O(n logn) algorithm for counting the number of inversions in A[1..n]. This means that you need to design an algorithm and show why it takes the specied time.

PLEASE SHOW FULL STEPS SHOW THINKING PLEASE AND THANK YOU! AND ANSWER A AND B SEPERATELY!