Let A[0..n − 1] be an array of n sortable elements. (For simplicity, you may assume that...

Let A[0..n − 1] be an array of n sortable elements. (For simplicity, you may assume that all the elements are distinct.) A pair (A[i], A[j ]) is called an inversion if i < j and A[i]>A[j ].

a. What arrays of size n have the largest number of inversions and what is this number? Answer the same questions for the smallest number of inversions.

b. Show that the average-case number of key comparisons in insertion sort is given by the formula