Let there be I items in a market-basket data set of B baskets. Suppose that every basket contains exactly K items. As a function of I, B, and K:
(a) How much space does the triangular-matrix method take to store the counts of all pairs of items, assuming four bytes per array element?
(b) What is the largest possible number of pairs with a nonzero count?
(c) Under what circumstances can we be certain that the triples method will use less space than the triangular array?