Problem 1:"Creamed Root Entree-All Mashed. (20pt) Explore these tragically True or frighteningly False statements. fill in the circle corresponding to the appropriate choice (True or False). For example, if any given statement is True, you should fill in the first circle, such that becomes Otherwise, fill in the second circle FALSE. Zero points for a blank answer. Two points per correct action, and no partial credit. If you feel the need to justify your answer, then the statement as given is probably false. True False Statement (a) All red-black trees are full by construction o o (b) The rightmost leaf of a 2-3 tree contains the largest key in the structure. O o (c) Asymptotic analysis can be used to determine the growth rate of the storage o space required by a given data structure when the problem size grows. o (a) Each node in a treap contains a key and a randomly generated priority. o O (e) AVL tree rotations are used to restore the BST property after insertion of a new key. o (f) The root of a red-black tree is always red. O o (8) In a binary min heap, the largest key will always be found in a leaf. O (h) According to Dr. Mount's notes, the expected height of a BST created by inserting n random keys is O(logn). O (1) The height of a red-black tree that is the encoding of a (2-3) tree is at least o twice the height of the 2-3) tree. O