Draw the diagrams of an 2-3 tree as the following items are inserted into an empty tree in the specified order: 8, 71, 90, 80, 84, 75, 76, 70, 10, 1, 2, 3, 4, 5, 6. To simplify the diagrams, you only have to draw the diagrams before and after each split/promotion operation. If a split/promotion has to be done recursively, only draw the diagram after all recursive splits/promotions have been done.

Recursively, a complete binary tree is a graph. Basis step: One vertex forms a binary tree. Inductive step: If T1 and T2 are disjoint complete binary trees with roots r1, r2, respectively, the graph produced by starting with a root r and adding an edge from r to each of the vertices r1, r2 is also complete. Recursively define a complete binary tree's leaves. Base step: The full binary tree has one root, r. Inductive step: T's leaves are the union of T1's and T2's.       Class defines binary tree height h(T). Use structural induction to prove that `(T), the number of leaves of a complete binary tree T, is less than 2 h(T).

What is the Postorder Traversal of the following tree E H I) F, J, I, H, G, E, D II) G, H, I, J, E, D, F III) D, F, E, H, I, J, G IV) D, E, G, H, I, J, F V) G, J, I, H, E, F, D (F)