This question deals with AVL trees. You must use mutable pairs/lists to implement this data structure:

(a) Define a procedure called make-avl-tree which makes an AVL tree with one node. Also create another constructor build-avl-tree that creates an AVL tree from a root, left subtree and right subtree. The constructors return an AVL tree object.

(b) Create procedures for accessing the root, left subtree and right subtree, and also mutators for changing the root, left subtree and right subtree of an avl argument.

(c) Write a procedure called (insert n t). This procedure has 2 arguments: n is the value being inserted, t is the AVL tree.

(d) Write a procedure called (lookup n t). This procedure has 2 arguments: n is the value being looked up, t is the AVL tree. The subtree with n as its root is returned (or '() if no such node is found).

(e) Write a procedure called (print-as-list t). This procedure prints the AVL tree passed in t as a regular list (not a mutable list).

(f) Write a procedure called (print-inorder t). This procedure prints the AVL tree passed in t in inorder traversal form.