Consider QuickSort on the array A[1:n] and assume that the pivot element x (used to split the array A[lo:hi] into two portions such that all elements in the left portion A[lo:m] are ≤x and all elements in the right portion A[m:hi] are ≥x) is the last element of the array to be split (i. e., A[hi]). Construct an infinite sequence of numbers for n and construct an assignment of the numbers 1...n to the n array elements that causes QuickSort, with the stated choice of pivot, to
(a) execute optimally (that is A[lo:m] and A[m:hi] are always of equal size)
(b) execute in the slowest possible way.