Software Design:

A) For an unsorted numeric array A of size N, given that A[1]>A[N], develop an efficient algorithm to find one index i such that A[i]>A[i+1], an algorithm description is adequate. Provide justifications about whether this algorithm can always return one such index successfully.

B) In QuickFind algorithm, in a manner similar to quicksort algorithm, based on the ranking of a random anchor value we recursively zero in on of the two sub-arrays to find the grand median value of the original array. Analyze the time complexity of this algorithm via mathematical/statistical reasoning.