Part A. 1. Starting with the following binary search tree, draw the final BST obtained by first deleting the node with key 6 and then inserting a new node with key 12. (Show the intermediate BST after the deletion to receive partial credit in case your final tree is incorrect after the insertion.) i3 15 18 17 13 The initial BST for Problem 5. 2. Show that the longest simple path from a node x in a red-black tree to a descendant leaf has length at most twice that of the shortest simple path from node x to a descendant leaf