POJ 2553 - The Bottom of a Graph
Problem : Find all the vertices that, if it can reach a vertice, the corresponding vertice can also reach it.
Solution : Merge the graph by strongly connected set, and get DAG G'. If a vertice in G is merged into a vertice with no out-degree in G', it is available in answer.
Proof : All the vertices no be chosen is not available, because it can go to one of the available vertice, but the available vertice cannot reach it.