Unbounded Knapsack - State Design

Here's the simplification: you don't need to track which items you've processed. Since items can repeat, the order doesn't matter.

Define $dp[w]$ as the maximum value achievable with capacity $w$. That's it. One dimension instead of two. For each capacity, you consider all items and decide whether to add one more copy of each. Base case: $dp[0] = 0$ (zero capacity means zero value).