Explain why routing a BST left or right does not destroy the BST property. Use left child, right child, and subtrees in your explanation. A diagram would be useful. What is the minimum height of a BST with 128 entries? What is the maximum height of a BST with 128 entries? After rotating a BST Node alpha right, where will alpha's right subtree be located? Explain why rotating a BST left or right does not destroy the BST property. Use left child, right child, and subtrees in your explanation. A diagram would be useful. The following integers are inserted into an empty BST in this order 23, 45, 1, 6, 37, 19, 51, 47, 48, and 44. Draw the resulting BST after all the inserts. Delete 45 and draw the resulting BST (use successor over predecessor). Given the BST after the deletion, what insertions into an empty BST would result the same tree. Explain why AVL trees are not exactly log N for all operations (~1.44log N). What is the minimum height of an AVL tree with 57 entries? What is the maximum height of an AVL tree with 57 entries? Give an approximate max height of an AVL tree with N entries, where N is any positive integer. The following integers are inserted into an empty AVL tree in this order 23, 45, 1, 6, 37, 49, 51, 47, 48, and 44. Draw the resulting AVL tree after all the inserts. Delete the root (use successor over predecessor) and draw the resulting AVL tree. Explain why Splay tree operations are O(log N) on average. The following integers are inserted into an empty Splay tree in this order 23, 45, 1, 6, 37, 49, 51, 47, 48, and 44. Draw the resulting Splay tree after all the inserts. Find min and draw the resulting Splay tree. Delete the root (use successor over predecessor) and draw the resulting Splay tree. Provide an example of the wont case for a Splay Tree using ten integers inserted into an empty Splay tree. Find the value with the lowest node height and then draw the resulting Splay tree after the And operation Design the Trie Node class in Java. Explain how it works for find, insert, and delete. What are some advantages, and disadvantages of Trie over Hash tables? Insert the following Strings into an empty Trie: " apple", "dog", "dogma", "man", middot mandate", "mandamus", and "apogee". Draw the resulting Trie. Delete "mandate" and draw the resulting Trie. Delete "apogee" and draw the resulting Trie