Tarjan algorithm and undirected graph connectivity

One, the cut point and the bridge of the non-direction graph

For g= (v,e)

1. Cut point: xξv If you delete X and the edge with X, the graph is split into multiple unicom diagrams, then X is the cut point of the graph.

2. Bridge (cut edge): eξe If you delete the E-map, the graph is split into multiple unicom diagrams, then E is the cut point of the graph.

How to find the cutting point and cutting edge

Tarjan algorithm

It's him.

First we introduce the concept of time stamp

Set Dfsn[x] Indicates the first access to the source node Y

That is to say we assume dfsn[y]=1, then we use the depth-first search tree to access the graph

Mark the order in which the graphs are accessed sequentially

The red number in the figure left represents the low[x] value and the right represents the dfsn[x] value

What is low[x], the value?

We define LOW[X] to represent the number of the earliest numbered nodes that x can reach through its subtree

How do I update the low[x] value?

We are in the DFS process, first let Low[x]=dfsn[x]

It is defined that Y is the X child node, then Low[x]=min (Low[x],low[y]);

, we find that node 5 can reach node 1 without its parent node

So, the same low[x]=min (Low[x],dfsn[y])

How to tell if a point is a cut point?

DFSN[X]<=LOW[X]

How to tell if the edge is cutting edge?

Dfsn[x]<low[y]

(x, y) for cutting edges

Cut Point Code

Tarjan algorithm and undirected graph connectivity