Let relations r$1($A$,$ B$,$ C$)$ and r$2($C$,$ D$,$ E$)$ have the following properties: r$1$ has $20,000$ tuples, r$2$ has $45,000$ tuples, $25$ tuples of r$1$ fit on one block, and $30$ tuples of r$2$ fit on one block. Estimate the number of block transfers and seeks required using each of the following join strategies for r$1$ r$2.$

$**$ Consider the following assumptions:

$1.$ Memory size M$=600$ blocks.

$2.$ For Hash join, assuming $3$ blocks $($bb $=3)$ are allocated for the input buffer and each output buffer. Number of partitions nh $=20.$

$**$ You may use the following expressions to estimate required block transfers and seeks for a hash join:

a$.$ # of block transfers: $3($br $+$ bs$)+4$nh

b$.$ # of seeks: $2($ br $/$ bb $+$ bs $/$ bb$)+2$nh

a$.$ Nested$-$loop join.

b$.$ Block nested$-$loop join.

c$.$ Merge join.

d$.$ Hash join.