A file F is indexed by a clustered B+tree with Alternative 2 for data entries, and the B+tree has 5 levels with the root at level 1. What is the worst I/O cost of inserting a record r into the file F? Explain how you derive your I/O cost by describing the disk read and writes needed for the insertion. Note that the I/O cost should include the cost for inserting the record r into the file F and the cost for inserting the data entry k* of r into the B+tree.

This is wrong answer

A B+tree with 5 levels has a maximum of 31=(100^(5-1))-1 index entries (excluding the root). So, it can index a maximum of 31 * 1000 = 31000 data entries, which correspond to 31000 / 100 = 310 data pages.

Without the B+tree, the worst I/O cost of finding a record with search key value k would be O(n), where n is the number of data pages in the file. In this case, the cost would be O(310) = 310 I/Os, as we would need to scan every data page to find the record with the search key value k.