Tall Barn - Penalized DP

Add penalty $\lambda$ per cow. New goal: reduce $\sum_{i=1}^{N} a_i / c_i + \lambda \cdot K_{used}$. For each floor $i$ with work $a_i$, compute the optimal number of cows to assign if each cow costs $\lambda$.

This is a separate improvement per floor! For floor $i$: reduce $a_i / c + \lambda \cdot c$ over positive integers $c$. The optimal $c$ is around $\sqrt{a_i / \lambda}$. Try $c = \lfloor\sqrt{a_i / \lambda}\rfloor$ and $c+1$, take the better one.