$($a$)[10$ pts$]$ Give an asymptotically tight lower bound on the number of calls to contains$($u$,$ v$)$ required to find a topological sort of G$.$

$($b$)[10$ pts$]$ Prove that the bound is tight, i$.$e$.,$ that no algorithm can find a topological sort of G with fewer than that many calls to contains$($u$,$ v$).$

$($c$)[10$ pts$]$ Describe an algorithm that achieves this bound. No need for a correctness or runtime proof.