Answer: (iii) FP-growth

FP-growth mines frequent patterns by first compressing the transaction database into a compact FP-tree (frequent-pattern tree) and then mining that tree with a divide-and-conquer strategy. It never materialises any candidate itemsets at all, so the number of candidate itemsets generated is zero — the minimum possible for any frequent-pattern technique.

Apriori is the natural comparison: at each level it joins the frequent (k-1)-itemsets to generate candidate k-itemsets and then prunes them, and this candidate generation is exactly the bottleneck FP-growth was designed to remove. Partitioning and dynamic itemset counting both follow the same Apriori-style generate-and-test paradigm, so they do generate candidate itemsets. Hence (iii) is correct.