Given an array of integers, do the following (SHOW ALL THE STEPS: just writing the final answer will get only ZERO) Clear label your answers for each of the sub parts (a)- (), in the space provided. (a - 12 pts) Construct a max heap of the array. Show the initial essentially complete binary tree and the transformation of the binary tree to a max heap via the reheapify operations at the indices of the internal nodes (as shown in the slides) (b-12 pts) Sort the max heap version of the array obtained from (a) to obtain a sorted array of integers. Show the structural changes of the max heap in each iteration. (c -7 pts) Transform the max heap of (a) to a binary search tree. (d-8 pts) For the binary search tree obtained in (c, determine the average number of comparisons fora successful search and the average number of comparisons for an unsuccessful search. (e-8 pts) Use the sorted array of (b) to construct a binary search tree. (f-7 pts) For the binary search tree obtained in (e), determine the average number of comparisons for a successful search and the average number of comparisons for an unsuccessful search. (g-7 pts) Construct a hash table of the given array using a hash function H(K) - K mod 5. (h-7 pts) For the hash table of (g), determine the average number of comparisons for a successful search and the worst case number of comparisons for an unsuccessful search. G- 14 pts) Consider the elements of the array assigned to you are known only one at a time. Construct a sequence of priority queues (as max heaps) with the insertion (enqueue) of one element at a time, as shown in the slides. G-7 pts) Transform the binary search tree of (c) to a min heap. (k -7 pts) Transform the max heap of (a) to a min heap via reheapify operations at the internal nodes (1- 4 pts) Are the min heaps of G) and (k) the same or not? What can you say about the distribution of the data in the min heaps of (G) and (k)