Bulk Loading a B+Tree

Suppose we are bulk-loading an initially empty B+-Tree. Pages have 28 bytes to store information. A key value takes 8 bytes, and a pointer to a tree node or row takes 4 bytes. Bulk load the B+ tree with data entries 1*, 2*, ., 12* so that each leaf is at least half full using the algorithm outlined in Section 10.8.2 (Page 360) of the textbook.

Q2.1. What is the order of the B+ tree? Also, how many keys and pointers per node can it hold? (Note: Recall that each node in a B+ tree is a page).

Q2.2. How many levels are in the resulting tree? (e.g. The B+Tree in Figure 1 has 2 levels). Q2.3.Sketch the final B+ tree after bulk loading. No need to show each node, just enough for us to be convinced you have the right tree.

Q2.4.Is this the densest possible (i.e. the most filled) B+-Tree tree with these keys? If not, sketch the densest possible tree.

Q2.5. What is the minimum number of keys that must be added so that the height of the tree increases by 1? List these keys. Note1: There may be more than one correct answer. Note2: Please use the algorithm outlined in section 10.6 (page 353) of the textbook.