Please answer the following questions.

Table $4$ shows a transaction database with $6$ transaction records and $4$ different items A$,$ B$,$ C$,$ D$.$

Assume that the minimum support $($denoted as minsup $=\frac{1}{3})$ and the minimum confidence $($denoted as

minconf$=0\mathrm{.}5$;

Table $4.$ A set of transactions

$($a$)$ Adapt FP$-$growth algorithm to construct FP$-$tree to find all frequent itemsets. Write the details of

key steps.

$($b$)$ List all maximal frequent itemsets and all closed frequent itemsets.

$($c$)$ Find one qualified rule $xY($satisfying the minimum support and confidence$)$ with the largest

interest, and calculate its confidence and interest.

$($d$)$ Compared the closed frequent itemsets and the classical definition of frequent itemsets. Use your

own words to describe what are their advantages and the disadvantages.

$($e$)$ Compared the closed frequent itemsets and the maximal frequent itemsets. Use your own words to

describe what are their advantages and the disadvantages.