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 a table of size $n^2$, which means it performs some computation for each of the $n^2$ entries. 3. **Time complexity notation:** - $O(f(n))$ means the running time is at most proportional to $f(n)$ for large $n$ (upper bound). - $\Omega(f(n))$ means the running time is at least proportional to $f(n)$ for large $n$ (lower bound). - $\Theta(f(n))$ means the running time is both $O(f(n))$ and $\Omega(f(n))$, i.e., tightly bounded. 4. **Analyzing Alg:** Since Alg fills a table of size $n^2$, it must perform at least $n^2$ operations, so the running time is at least $\Omega(n^2)$. 5. **Upper bound:** Usually, filling each entry takes constant or bounded time, so the running time is at most $O(n^2)$. 6. **Conclusion:** Because the running time is both $\Omega(n^2)$ and $O(n^2)$, it is $\Theta(n^2)$. 7. **Answer:** The correct statement is (c) Alg runs in $\Theta(n^2)$.