Unbounded Knapsack - Walkthrough

Trace unbounded Knapsack with items $[(w=2, v=3), (w=3, v=5)]$ and capacity $W=7$. Unlike 0/1 Knapsack, we can reuse items. The DP is $dp[w]$ = max value with capacity $w$. Process each capacity, trying all items. $dp[2]=3$ (one of item 1). $dp[3]=5$ (one of item 2). $dp[4]=6$ (two of item 1). $dp[5]=8$ (item 1 + item 2). $dp[6]=10$ (two of item 2). $dp[7]=11$ (two of item 1 + one of item 2).

Answer: $dp[7]=11$. The key difference from 0/1: each item can contribute multiple times, so we don't track which items were used, just the capacity.