It is possible to implement AVL trees such that the nodes store only the balance factor {1,0,1} at each node instead of the height of the subtree rooted at the node. a) Starting from an empty AVL tree, insert the following keys in order. You should obtain the tree shown in the figure. 41,72,33,45,60,25,3,12,17,47 b) Show the process of inserting the key 15 into the tree in figure 1. Specifically, draw the tree, with balance factors, after the initial BST insert and after each call to restructure. c) Suppose the key 41 were deleted from the original tree in figure 1 . Would this cause a tree rotation? Briefly justify. d) Show the process of deleting the key 72 from the original tree in figure 1. Specifically, draw the tree, with balance factors, after the initial BST delete and after each call to restructure. Figure 1