Exercise 10.2 Consider the B+ tree index shown in Figure 10.10, which uses Alternative (1)...

Exercise 10.2 Consider the B+ tree index shown in Figure 10.10, which uses Alternative (1) for data entries. Each intermediate node can hold up to five pointers and four key values. Each leaf can hold up to four records, and leaf nodes are doubly linked as usual, although these links are not shown in the figure. Answer the following questions.

1. Name all the tree nodes that must be fetched to answer the following query: “Get all records with search key greater than 38.”
   
   Figure 10.11
2. Show the B+ tree that would result from inserting a record with search key 109 into the tree.
3. Show the B+ tree that would result from deleting the record with search key 81 from the original tree.
4. Name a search key value such that inserting it into the (original) tree would cause an increase in the height of the tree.
5. Note that subtrees A, B, and C are not fully specified. Nonetheless, what can you infer about the contents and the shape of these trees?
6. How would your answers to the preceding questions change if this were an ISAM index?
7. Suppose that this is an ISAM index. What is the minimum number of insertions needed to create a chain of three overflow pages?