Side double Unicom component and cutting edge

Objective

In graph theory, in addition to the strongly connected components in the undirected graph, there is a class of double-link components in undirected graphs.

The dual-link component is usually the point of two connected components

Of course, there is also a two-connected component called Edge

Side Double Unicom component

For a connected graph, if any two points have at least two "edge not repeat" path, then the graph is a point double connected, the edge of the double-connected maximum sub-graph is called the edge of the two connected components.

The calculation method of side-double-link component is relatively simple

The only difference between the analogy Tarjan and the algorithm of the strong Unicom component is that it is not possible to walk back along the DFS side.

Which means we need to record the father's node in Tarjan.

The rest is just like the normal Tarjan.

Examples

Exercises

Cutting Edge (bridge)

Cutting edge: For the side of the graph (i\), if removed \ (i\), the non-graph of the number of Unicom will increase, then the point \ (i\) for Cutting Edge (bridge)

Calculation method

It is not difficult to find that an edge is a cutting edge when and only if he is not on either side of the double.

This means that when \ (low[v]>dfn[u]\) \ ( (u,v) \) is a cut edge.

Examples

Exercises

Side double Unicom component and cutting edge