Exercise 3.3.5 : The figure at right shows all the structurally different 2-3 trees with N keys, for N from 1 up to 6 (ignore the order of the subtrees). Draw all the structurally different trees for N = 7, 8, 9, and 10.

Show also an example of tree for each different structure.

3.3.4 Prove that the height of a 2-3 tree with N keys is between log, N 63 lg N (for a tree that is all 3-nodes) and g N] (for a tree that is 2-nodes) R dh hand-h 3.3.5 The figure at right shows all the structurally different 2-3 trees with N keys, for N from 1 up to 6 (ignore the order of the subtrees). Draw all the structurally different trees for N-7,8, 9, and 10. 3.3.6 Find the probability that each of the 2-3 trees in EXERCISE 3.3.5 sthe result of the insertion of N random distinct keys into an initially empty tree. 3.3.7 Draw diagrams like the one at the top ofpage 428 for the other five cases in the diagram at the bottom of that page 3.3.8 Show all possible ways that one might represent a 4-node with three 2-nodes bound together with red links (not necessarily left-leaning)