Q52

Consider a database of fixed-length records, stored as an ordered file. The database has $25,000$ records, with each record being $100$ bytes, of which the primary key occupies $15$ bytes. The data file is block-aligned in that each data record is fully contained within a block. The database is indexed by a primary index file, which is also stored as a block-aligned ordered file. The figure below depicts this indexing scheme.

Suppose the block size of the file system is $1024$ bytes, and a pointer to a block occupies $5$ bytes. The system uses binary search on the index file to search for a record with a given key. You may assume that a binary search on an index file of $b$ blocks takes $\left\lceil\log _{2} b\right\rceil$ block accesses in the worst case. Given a key, the number of block accesses required to identify the block in the data file that may contain a record with the key, in the worst case, is _____________.