We can build a heap by repeatedly calling MAX-HEAP-INSERT to insert the elements into the heap. Consider the following variation on the BUILD-MAX-HEAP procedure: BUILD-MAX-HEAP'(A) 1 A.heap-size = 1 2 for i = 2 to A.length MAX-HEAP-INSERT(A, A[i]) a. Do the procedures BUILD-MAX-HEAP and BUILD-MAX-HEAP' always create the same heap when run on the same input array? Prove that they do, or provide a counterexample. b. Show that in the worst case, BUILD-MAX-HEAP' requires O(n lg n) time to build an n-element |heap