The CC class represents a data type for determining the connected components in an undirected graph. The Id operation determines in which connected component a given vertex lies; the Connected operation determines whether two vertices are in the same connected component; the Count operation determines the number of connected components; and the Count operation determines the number of vertices in the connect component containing a given vertex. The Component identifier of a connected component is one of the vertices in the connected component: two vertices have the same component identifier if and only if they are in the same connected component.

This implementation uses depth-first search. The constructor takes time proportional to V + E (in the worst case), V is the number of vertices and E is the number of edges. Afterwards, the Id, Count, Connected, and Count operations take constant time.