1. A computer system comprising: a computer processor configured to execute a fast algorithm for mining utility itemsets, comprising: Step (a): undertaking a first database scanning process to compute a transaction weighted utility (TWU) of each item at least one transaction database and a count of appearances of each item, and sorting said items having TWU greater than a minimal utility (MU) according to said counts of appearances from large to small; Step (b): undertaking a second database scanning process to resort items according to a sequence of said items in a new transaction, computing a utility of each item in said new transaction, deleting items whose TWU is smaller than said MU, recording all items of said new transaction and their utilities, and defining an itemset as a set of said items; Step (c): establishing an initial absorptive mining (AM) tree, outputting itemsets whose utilities are no less than MU as high utility itemsets; Step (d): defining a itemset having a closure utility no less than said MU as a high closure utility itemset, checking whether there is a high closure utility itemset whose conditional AM-tree has not been constructed yet; if there is a high closure utility itemset whose conditional AM-tree has not been constructed, executing Step (e); if there is no high closure utility itemset whose conditional AM-tree has not been constructed, executing Step (f); Step (e): establishing a conditional AM-tree for said high closure utility itemset, outputting all said high utility itemsets in said conditional AM-tree, generating other possible high closure utility itemsets, and returning to Step (d); and Step (f): completing generation of all said high utility itemsets and terminating the process.