1. Consider the following sequence of operations on an initially empty search tree: Insert 10 Insert 100 Insert 30 Insert 80 Insert 50 Remove 10 Insert 60 Insert 70 Insert 40 Remove 80 Insert 90...

1. Consider the following sequence of operations on an initially empty search tree:

Insert 10

Insert 100

Insert 30

Insert 80

Insert 50

Remove 10

Insert 60

Insert 70

Insert 40

Remove 80

Insert 90

Insert 20

Remove 30

Remove 70

What does the tree look like after these operations execute if the tree is

a. A binary search tree?                                d. A red-black tree?

b. A 2-3 tree?                                     e. An AVL tree?

c. A 2-3-4 tree?

2. What are the advantages of implementing the ADT dictionary with a 2-3 tree instead of a binary search tree? Why do you not, in general, maintain a completely balanced binary search tree?