Suppose we have a B-Tree that holds keys and leaves. There are 100 million data records (N), and they are stored in the leaves (lowest level) of the B-Tree. Each leaf contains 100 data records. Like the example B Tree below (which has M = 5), the leaves are stored only at the bottom level of the tree (below the keys), and each key at the bottom level of keys points to one leaf. The B-Tree has 4 levels of keys counting the root level which has m keys. Except for the bottom level, each key has m child keys. The bottom level keys have leaves (one leaf per key).

a) Sketch a simple tree like the one on the next page (this is not the same tree you have to do, its just a similar example)

b) What is the branching factor (M) of the B-Tree. Show your work.

c) If the root level contains 1 key (instead of m), and the tree has 4 more levels under the root (each with M branches), the root being level 1, and the levels under the root being 2 - 5, then what is M?

Question 2 figure Trees Simple B Tree (no root) # keys Keys M 5 M-125 etc Leaves, one per key (there are 125 leaves) Data is stored in the leaves. The keys point to other keys on the next level, or to leaves (if on the bottom level)