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Limited quantities
Trace Bounded Knapsack with items and capacity . Item 1 has copies. Using binary representation: split into pseudo-items of count and (since ).
Now run 0/1 Knapsack on pseudo-items: , , . Result: take both copies of item 1 (, ) plus item 2 (, ). Total: , . Track remaining copies carefully to avoid exceeding the limit. The state space grows but the logic stays similar.
