Show that we can use a depth-first search of an undirected graph G to identify the connected components of G, and that the depth-first forest contains as many trees as G has connected components. More precisely, show how to modify depth-first search so that it assigns to each vertex ν an integer label ν.cc between 1 and k, where k is the number of connected components of G, such that u.cc = ν.cc if and only if u and ν are in the same connected component.