4. Suppose 1 wanted to implement a binary seatch tree using af arny in a simile maner to the wiy Heapsort uses an artay to create a heap. The artay would be structured such that the rook of the itar is A(0), the left child of node A(n) is A(2n+1], the right cilld of A(n) is A2n+2, and the purne of sode A A al is A[n1/2]. As we cannot guarantee that the tre be NULL, this indicates that no node exists there- . Wet-rotation on igive pade sith inder an in this artay-based tree. (300pt) b. Argue the correctness of this algorithm, and provide a Big. eqression for tos runtimen is terms of the size of the tre