onsider the join R $\{$R$.$a $=$ S$.$b$\}$ S$,$ given the following information about R and S$.$ The cost metric is the number of page I$/$Os$,$ and the cost of writing out the final result is ignored.

R contains $200,000$ tuples and has $20$ tuple per page.

S contains $4,000,000$ tuples and also has $20$ tuples per page.

R$.$a is the primary key for R$.$

Each tuple of R joins with exactly $20$ tuples of S$.$

$1,002$ pages available in the buffer pool.

What is the cost of the join using a page$-$oriented nested loop joins $($that is$,$ to use one page to load outer relation in each iteration$)?$

What is the cost of the join using a block nested loop joins?$$

What is the cost of the join using a sort$-$merge join?$$

What is the minimum number of buffer pages required for the sort$-$merge join? Suppose we use heap sort to increase initial run size in the sort phase.$$

What is the cost of the join using a hash join?