1. [10 pts.] AVL Trees: Example Operations

(a) [5 pts.] Draw the AVL tree that results from inserting key 45 into the following AVL tree.

(b) [5 pts.] Draw the AVL tree that results from deleting key 70 from the following AVL tree. NOTE: When deleting a key from an AVL tree, please follow the textbook approach of finding the node with the key using the function for standard binary search trees. If the key is in the tree and the node w where the key is found does not have any child pointing to NULLone, then use the implementation of the algorithm that finds the successor node x to node w in an inorder traversal of the binary search tree, and copies the entry information (i.e., not including the children or parent pointers) from x to w (e.g., the key and value stored at node x becomes that of node w). That algorithm then deletes node x from the AVL tree and perform any required balancing by properly restructuring the tree.

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