Consider the natural join of the relation R(A,B) and S(A,C) on attribute A. Neither relations have any indexes built on them. Assume that R and S have 80000 and 20000 blocks, respectively. The cost of a join is the number of its block I/Os accesses. When sorting is needed, you are only allowed to use two passes, multi-way merge sort algorithm.

(a) Assume that there are 120000 buffer blocks available in the main memory. We would like to have the output of join sorted according to attribute A. What is the fastest join algorithm for computing the join of R and S? What is the cost of this algorithm?

(b) Assume that there are 400 buffer blocks available in the main memory. What is the fastest join algorithm to compute the join of R and S? What is the cost of this algorithm?

(c) Assume that there are 200 buffer blocks available in the main memory. What is the fastest join algorithm to compute the join of R and S? What is the cost of this algorithm?