Consider a valleyed array A[1, 2, · · · , n] with the property that the subarray A[1..i] has the property that A[j] > A[j + 1] for 1 ≤ j < i, and the subarray A[i..n] has the property that A[j] < A[j + 1] for i ≤ j < n. For example, A = [16, 15, 10, 9, 7, 3, 6, 8, 17, 23] is a valleyed array.
(a) What is a recursive algorithm that takes asymptotically sub-linear time to find the minimum element of A.