$2.(60\text{'})$ Consider a database with a single table T$($song id$,$song name,artist id$,$duration number of streams$),$ where song id is the primary key, and all attributes are the same fixed width. Suppose T has $10,000$ tuples that fit into $500$ pages, Ignore any additional storage overhead for the table $($e$.$g$.,$ page headers, tuple headers$).$ Additionally, you should make the following assumptions:

$-$ The DBMS does not have any additional meta$-$data $($e$.$g$.,$ sort order, zone maps$).$

$-$ T does not have any indexes $($including for primary key song id$).$

$-$ None of T$\text{'}$s pages are already in the buffer pool. The DMBS has an infinite buffer pool.

$-$ Content$-$wise, the tuples of T will always make each query run the longest possible and do the most page accesses.

$-$ The tuples of T can be in any order $($keep this in mind when computing minimum versus maximum number of pages that the DBMS will potentially have to read and think of all possible orderings$)$

$-$ There are $100$ pages per attribute.

Part a$.$

SELECT MAX$($number$\_$of$\_$streams$)$ FROM T

WHERE duration $>100$ AND artist$\_$id $==123321$ ;

i$.$ Suppose the DBMS uses the decomposition storage model $($DSM$)$ with implicit offsets. How many pages will the DBMS potentially have to read from disk to answer this query? $($should be a range between the best case and the worst case, and why$)$

ii$.$ Suppose the DBMS uses the N$-$ary storage model $($NSM$).$ How many pages will the DBMS potentially have to read from disk to answer this query? $($should be a range between the best case and the worst case, and why$)$

Part b$.$

SELECT song$\_$name, artist$\_$id FROM T

WHERE song$\_$id $=15445$ OR song$\_$id $=15645$ OR song$\_$id $=15721$;

i$.$ Suppose the DBMS uses the decomposition storage model $($DSM$)$ with implicit offsets. What is the minimum and maximum number of pages that the DBMS will potentially have to read from disk to answer this query?

ii$.$ Suppose the DBMS uses the N$-$ary storage model $($NSM$).$ What is the minimum and maximum number of pages that the DBMS will potentially have to read from disk to answer this query?

Part c$.$

$```$

SELECT song$\_$id$,$ number$\_$of$\_$streams FROM T

WHERE duration $=($SELECT MIN$($duration$)$ FROM T$)$;

$```$

i$.$ Suppose the DBMS uses the decomposition storage model $($DSM$)$ with implicit offsets. What is the minimum and maximum number of pages that the DBMS will potentially have to read from disk to answer this query?

ii$.$ Suppose the DBMS uses the N$-$ary storage model $($NSM$).$ What is the minimum and maximum number of pages that the DBMS will potentially have to read from disk to answer this query?