Assume you have a table that contains 27,000 records, and you have an unclustered B+-tree index on the table. Assume further that each index node can contain up to 100 pointers.
(a) What is the maximum possible number of levels in the B+-tree index for this table? Draw a sketch of this ”maximal height” B+-tree for the 27,000 record table.
(b) What is the minimum possible number of levels in the B+-tree index for this table? Draw a sketch of this ”minimal height” B+-tree for the 27,000 record table.
(a) What is the maximum possible number of levels in the B+-tree index for this table? Draw a sketch of this ”maximal height” B+-tree for the 27,000 record table.
Solution:
Since the index is unclustered, it requires one pointer per record in the data file. The tree will have the maximal depth is the nodes of the tree are minimally packed. This means that the root has only 2 pointers and the rest of the nodes have 50 pointers. So, the maximal depth will be 1 + ceiling(log5013500) = 4
(b) What is the minimum possible number of levels in the B+-tree index for this table? Draw a sketch of this ”minimal height” B+-tree for the 27,000 record table.
Solution:
Again, the index needs 27,000 pointers. The tree has minimal depth if the nodes are maximally packed. Therefore, the min depth is ceiling(log10027000) = 3.
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