For the B+tree in Question 1, what is the worst I/O cost for finding the records with the search key value k? You can assume that each disk page contains 20 records, contains 40 data entries, and at most 100 records match the search key value k. question 1

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. answer to this

he worst-case I/O cost of inserting a record r into the file F with a 5-level clustered B+tree with Alternative 2 for data entries is 6 disk I/Os.

To explain how this is derived:

1 disk I/O is required to retrieve the root node of the B+tree.

2 disk I/Os are required to traverse the B+tree to find the leaf node where the data entry k* of r should be inserted. This involves reading the non-leaf nodes at levels 2 through 4 and the leaf node at level 5.

1 disk I/O is required to insert the data entry k* of r into the leaf node. This may cause the leaf node to split, requiring an additional disk I/O to write the split node to disk.

1 disk I/O is required to update the parent node of the split leaf node, if the leaf node split. This may cause the parent node to split, requiring another disk I/O to write the split node to disk.

1 disk I/O is required to insert the record r into the file F.

Therefore, the total I/O cost of inserting a record r into the file F with a 5-level clustered B+tree with Alternative 2 for data entries is 6 disk I/Os.