$(35$ points$)$ Consider a disk with a block size of $2000$ bytes, block transfer time of $0\mathrm{.}5$ milliseconds,

average rotational delay of $7$ milliseconds, and average seek time of $10$ milliseconds. Suppose that a

file containing $150000$ records of $300$ bytes each is to be stored on such disk and that no record is

allowed to span two blocks.

a$)$ Compute number of passes, number of disk accesses, and time $($in milliseconds$)$ required to sort

this file using general external merge sort $($without any improvement$)$ algorithm assuming

that $11$ buffer pages are available in the memory.

b$)$ Assume that an unclustered $B+$ tree index using Alternative $2$ is constructed on the file. In this

index, you can assume that the key field and address pair occupy $100$ bytes for each record, and

each leaf node is $60\%$ full. Only the leaf nodes and the file are stored on disk. Compute time

required for sorting the file by using the unclustered $B+$ tree index.