B Trees - A) For a sequence of keys {a, j, b, i, c, h, d, g, e, f}, suppose we would like to construct a B-Tree, with degree 2, by successively inserting those keys, one at a time, into an initially empty tree. Please draw the sequence of B-Trees after inserting each of the 10 keys.
Note: please draw only one tree after each insertion.
B) Let t be the (minimal) degree of a BTree. Suppose the size of each object, including the key, stored in the tree is 40 bytes. Also, suppose the size of a BTreeNode pointer is 4 bytes. In addition, 100 bytes of meta-data is required for each BTree node to keep track of some useful information. Suppose each BTreeNode has only the meta- data, a parent pointer, a list of objects, and a list of child pointers. What is the optimal (minimal) degree for this BTree if a disk block is 4096 bytes?
C) For a BTree with height 4 (or 5 levels), what is the maximal number of objects can be stored if the (minimal) degree t = 51?