Near the end of class, we discussed the book's TransitiveClosure
algorithm (from end of Section 4.2). It does a DFS from every
vertex v, and then stores the "marked" array from each.  Then
in constant time, we can answer, for a given v and w, whether
there is a path from v to w.

Single DFS:
  Time  O(V+E)
  Space O(V)

Transitive Closure (one DFS per vertex):
  Time  O(V*(V+E))
  Space O(V*V)

Next we observed that we might use SCC's to speed this up.  Suppose
digraph G has only S strongly-connected components.  S may be quite a
bit smaller than V, the number of vertices.

Idea: if u and v are in the same SCC, then the set of reachable
vertices for u is exactly the same as the set for v.

So, we could speed up TransitiveClosure as follows:
  * compute the SCC's, in O(V+E) time
  * do a DFS from only one vertex u per SCC
  * reuse u's "marked" array for every other vertex
    in its component

In this way, we get:
  Time  O(S*(V+E))
  Space O(S*V)

If S is small, that is a big improvement.  But this is not in the
book.  (With more work, we might improve the space further to
O(S*S+V), do you see how?)