Knapsack 2 - The Observation

Instead of asking "What's the max value for capacity $w$?", ask "What's the min weight to achieve value $v$?" If you can compute the minimum weight needed for every possible value from $0$ to $V_{max}$, you can find the largest $v$ where that minimum weight is at most $W$.

Same problem, different angle. The dimension that was $10^9$ becomes the answer you're searching for. The dimension that was at most $100{,}000$ becomes your DP index.