Weight-Based to Value-Based

Your $O(n \cdot W)$ solution works great when $W$ is small. But what if $W = 10^9$? You can't create an array of size $10^9$. The solution crashes before it starts.

But notice something: even with huge weights, the total value might be bounded. If $n = 100$ and each value is at most $1000$, the maximum possible value is $100{,}000$. What if you flipped the problem? Instead of "max value for this weight," ask "min weight for this value." That's the observation for the next problem.