Bounded Knapsack - Walkthrough

Trace Bounded Knapsack with items $[(w=2, v=3, c=2), (w=3, v=4, c=1)]$ and capacity $W=7$. Item 1 has $2$ copies. Using binary representation: split into pseudo-items of count $1$ and $1$ (since $2 = 1 + 1$).

Now run 0/1 Knapsack on pseudo-items: $(w=2, v=3)$, $(w=2, v=3)$, $(w=3, v=4)$. Result: take both copies of item 1 ($w=4$, $v=6$) plus item 2 ($w=3$, $v=4$). Total: $w=7$, $v=10$. Track remaining copies carefully to avoid exceeding the limit. The state space grows but the logic stays similar.