3. 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 sx and all elements in the right portion Alm:hi] are zx) is the penultimate element of the array to be split (i. e., A[hi-1]). 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. 3. 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 sx and all elements in the right portion Alm:hi] are zx) is the penultimate element of the array to be split (i. e., A[hi-1]). 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