minimum number of nodes that traverse all the graph In the following graph, we can traverse entire graph if we select the nodes 0 and 2. I am looking for an efficient algorithm which returns this two nodes. Note that this is neither vertex-cover problem nor dominating-set problem since we don't need to select node 3. We say that, if we select node 0, we can go to node 1 from there and if we select node 2, we can go to node 3 and then node 4 from there.

Also, the number of nodes can be up to 10^5 and the algorithm's runtime must be 1 second or less. Any suggestion would be useful.
Try combining Tarjan's strongly connected components algorithm with a topological sort.