The maximum number of records in a B-tree of degree 5 and height 2 is ______.
A)10
B)20
C)24
D)30

Question

Quizplus · Accepted Answer

A B-tree of degree 5 means each node can have at most 5 children. At height 0, there is only the root node. At height 1, there can be at most 5 children of the root node. At height 2, each child of height 1 can have at most 5 children which gives a maximum of 5*5 = 25 children for each child of the root. However, we must consider that the children of the root may not be all full, hence we must take the floor division of (5*5) / 2 which gives us 12. This means that each child of the root can have 12 children at most. Since there can be at most 5 children of the root node, the total number of nodes at height 2 is 5*12 = 60. But, we need to have at most 24 records in total. This means that each node of height 2 must have at most ceil(24/60) = 1 record. Hence, the maximum number of records in a B-tree of degree 5 and height 2 is 24.

The Maximum Number of Records in a B-Tree of Degree