Tree Indexing

Assume that the block size is 30 bytes. In this question, each node in a B+ tree must fit in a block and its size must be as close as possible to the size of a block. Answer the following parts using B+ trees.

(a) Assume that all data values are integers with the fixed size of 8 bytes and each record pointer takes at most 4 bytes. Find a B+ tree whose height changes from 2 to 3 when the value 20 is inserted. Note that the height of a tree is depth of the deepest node plus one. For example, the height of a tree with a single node is 1. Show your structure before and after the insertion.

(b) Assume that all data values are integers with the fixed size of 4 bytes and each record pointer takes at most 4 bytes. Find a B+ tree in which the deletion of the value 40 leads to a redistribution. Show your structure before and after the deletion. Your example could be different from the answer given for part a.