Problem 1. (13 marks) On sorting lower bound. a. (5 marks) Consider the Searching problem which takes as input a sorted array A with n elements and a key k, and we return the largest element in A that is less than or equal to k. From Exercise I of Assignment #1, we know that it can be solved by binary-search in O (log n) time. Show that any algorithm for solving this Searching problem that accesses the array only via comparisons (that is, only by checking whether Ali k must take S2(log n) time. b. (8 marks) Given an array A of n integers, propose an algorithm that can sort array A in O(n +y - ) time, where r is the minimum integer in A and y is the maximum integer in A. Prove the running time of uur