Assume a relation prod$($pid$,$ category, price, $...)$ with $600,000$ tuples, where

each tuple is $100$ bytes. The product ID pid is a key and is equally distributed

between $1$ and $3,000,000.$ The block size is $2,000$ bytes.

Consider a $B^{+}-$tree index on the product ID pid, where the pid requires $4$

bytes and a pointer requires $6$ bytes; a tree node occupies an entire block.

The minimal and maximal number of blocks used for the tree are

and respectively.

Consider the $B^{+}-$tree from a$)$ with the minimal number of blocks and as$-$

sume that it is a primary index. The following two queries are run:

Q$1$: SELECT $*$ FROM prod WHERE pid BETWEEN $10000$ AND $20000$

Q$2$: SELECT CNT$(*)$ FROM prod WHERE pid BETWEEN $10000$ AND

$20000$

The number of IOs $($data blocks $+$ index blocks$)$ are and respectively.

Repeat the query Q$1$ in part $b$ with $B^{+}-$tree index as a secondary index.

The number of IOs $($data blocks $+$ index blocks$)$ are