1. **Problem statement:** We want to analyze the running time of a dynamic programming algorithm Alg that fills a table of size $n^2$ for an input array of size $n$. 2. **Understanding the problem:** The algorithm fills every entry in a table of size $n^2$. This means it performs some computation for each of the $n^2$ entries. 3. **Time complexity basics:** - $O(f(n))$ means the running time is at most proportional to $f(n)$ for large $n$. - $\Omega(f(n))$ means the running time is at least proportional to $f(n)$ for large $n$. - $\Theta(f(n))$ means the running time is both $O(f(n))$ and $\Omega(f(n))$, i.e., tightly bounded by $f(n)$. 4. **Applying to Alg:** Since Alg fills all $n^2$ entries, it must take at least $\Omega(n^2)$ time. 5. **Is it $O(n^2)$?** Usually, filling each entry takes constant or bounded time, so the total time is at most proportional to $n^2$, i.e., $O(n^2)$. 6. **Is it $\Theta(n^2)$?** If each entry requires a constant amount of work, then the running time is exactly proportional to $n^2$, so $\Theta(n^2)$. 7. **Conclusion:** The running time of Alg is $\Theta(n^2)$. **Final answer:** c. Alg runs in $\theta(n^2)$.