Room Test 2: home (tarjan will seek through point)

topic:

Seeking an undirected graph will go through from point N 1

n<=2e5   m<=4e5

analysis:

A necessary point means: After deleting the entire graph is not connected, but can not find a cut point directly. Because the deleted point can not communicate FIG, 1 and n can not be guaranteed but not in communication.

So you want to delete that point on the path 1 to n. That is, points can be deleted and n 1 are separated.

Method 1:

tarjan sentenced to ring when starting at 1, and maintains an array siz [v]: at this point there is no representation v n at this point in the sub-tree search, every time back when the flag back to u (u is v's father).

In the cut point judgment conditions: low [v] <= dfn [u] (u subtree than can not reach the point u) plus a limit: siz [v] == 1 (v subtree has n )

Why not siz [u] == 1?

V u possible non subtree has n, u 1 and n after removing still connected.

Method 2:

When this loop judgment condition to pay more: dfn [v] <= dfn [n] (n v ratio after traversed)

Paint, the requirement that Italy

#include<bits/stdc++.h>
using namespace std;
#define N 200005
#define ri register int
int siz[N],low[N],nex[N<<2],head[N],to[N<<2],dfn[N],cut[N];
int Ti=0,tot=0,n,m,ans=0;
int read()
{
    int x=0,fl=1; char ch=getchar();
    while(ch<'0'||ch>'9') { if(ch=='-') fl=-1; ch=getchar(); }
    while(ch<='9'&&ch>='0') x=x*10+ch-'0',ch=getchar();
    return x*fl;
}
void add(int a,int b)
{
    to[++tot]=b; nex[tot]=head[a]; head[a]=tot;
    to[++tot]=a; nex[tot]=head[b]; head[b]=tot;
}
void dfs(int u,intFA) 
{ 
    DFN [U] = Low [U] = ++ of Ti;
     IF (n-== U) SIZ [U] = . 1 ;
     BOOL Flagg = 0 ;
     for (I = RI head [U]; I; I = NEX [I]) {
         int V = to [I];
         IF (DFN [V] && V =!! FA) { 
            DFS (V, U); 
            Low [U] = min (Low [U], Low [V ]); 
            SIZ [U] | = siz [v];
             IF (siz [v] && Low [V]> = DFN [U]) = Flagg . 1 ;
             // this must siz [v] In order to guarantee from v subtree pass up tags instead transmitted from another subtree of up tag u
             //U is a judgment because there is a cut point subtree judged v
             // That is cut off after the u and v sub-tree split other portions will be just n subtrees without the v 1 and in a block
             / / there is a play: dfn [v] <= dfn [n] ( n after that is traversed v)
             // 1. v n in the subtree 2.n another non u v in the sub-tree (since n must traverse dfn advance value so that the accuracy can be guaranteed only) 
        }
         the else  IF (FA = V!) Low [U] = min (Low [U], dfn [V]); 
    } 
    IF ( ! U = . 1 && Flagg) ANS ++, Cut [U] = . 1 ; 
} 
int main () 
{ 
    // The freopen ( "home.in", "R & lt", stdin);
     // The freopen ( "home.out", " W ", stdout); 
    int T = Read ();
    while(T--){
        n=read(); m=read();
        while(m--) add(read(),read());
        dfs(1,0);
        printf("%d\n",ans);
        for(ri i=1;i<=n;++i) if(cut[i]) printf("%d ",i);
        printf("\n");
        for(ri i=1;i<=n;++i) dfn[i]=nex[i]=to[i]=head[i]=low[i]=siz[i]=cut[i]=0; 
        Ti=0; tot=0; ans=0;
    }
}
/*
1
10 11
1 10
10 6
6 7
7 8
8 5
5 3
3 9
9 4
4 2
6 2
8 7
*/

View Code