Explain and solve this step by step

Nested$-$Loop Join

Consider relations V$($i$,$k$,$I$)$ and U$($i$,$j$)$ to be joined on the common attribute i$.$ Assume that there are no indexes available on the tables to speed up the join algorithms.

$-$There are D$=50$ blocks in the buffer.

$-$Table V spans R $=900$ blocks with $120$ tuples per block.

$-$ Table U spans Q$=1,800$ blocks with $40$ tuples per block.

Answer the following questions on computing the I$/$O costs for the joins, using a simple cost model where blocks are read and written one at a time. Assume that one buffer block is used to hold the evolving output block and one input block to hold the current input block of the inner relation. You may ignore the cost of writing the final results.

$($a$)$ Nested loop join with V as the outer relation and U as the inner relation.

I. What is the cost of the join without any optimization techniques? Hint: Consider

the cost of reading each block of V and for each block of V$,$ reading all blocks of U$.$

II$.$ Assume that a selection operation is performed on U before the join, reducing

its size by half. What is the new I$/$O cost of the join? Hint: First, calculate the cost

of applying the selection operation on U $($considering that every block of U must be

read$).$ Then, calculate the cost of the join, taking into account the reduced size of U$.$