Problem 7. (10 points) Suppose we run the Multistage Algorithm on the data of Problem 6, with the same support threshold of 4. The first pass is the same as in that problem, and for the second pass, we hash pairs to nine buckets, using the hash function that hashes {i, j} to bucket i+j mod 9. (a) Determine the counts of the buckets on the second pass. (b) Does the second pass reduce the set of candidate pairs? Note that all items are frequent, so the only reason a pair would not be hashed on the second pass is if it hashed to an infrequent bucket on the first pass. Problem 7. (10 points) Suppose we run the Multistage Algorithm on the data of Problem 6, with the same support threshold of 4. The first pass is the same as in that problem, and for the second pass, we hash pairs to nine buckets, using the hash function that hashes {i, j} to bucket i+j mod 9. (a) Determine the counts of the buckets on the second pass. (b) Does the second pass reduce the set of candidate pairs? Note that all items are frequent, so the only reason a pair would not be hashed on the second pass is if it hashed to an infrequent bucket on the first pass