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2 Heaps and Heapsort (25 points) 2.1 Is the sequence a max-heap? Why or why not? 2.2 Illustrate the operation of MAX-HEAPIFY(43) on the array A=, using the binary trees as we did in class 2.3 Illustrate the operation of BUilD-Max-HEAP(A) on the array A , using the binary trees as we did in class. 2.4 You are given a list of numbers for which you need to construct a min-heap. How would you use an algorithm for constructing a max-heap to construct a min-heap? Explain in your own words 2.5 Argue the correctness of Heapsort using the following loop invariant: At the start of each iteration of the for loop, the subarray A. i is a max-heap containing the i smallest elements of A1,. ,n] and the subarray A[i + 1, , n] contains the n-i largest elenents of A[1, , n]