HDU4612Warm up 边双连通 Tarjan缩点

　N planets are connected by M bidirectional channels that allow instant transportation. It's always possible to travel between any two planets through these channels. 
　　If we can isolate some planets from others by breaking only one channel , the channel is called a bridge of the transportation system. 
People don't like to be isolated. So they ask what's the minimal number of bridges they can have if they decide to build a new channel. 
　　Note that there could be more than one channel between two planets. 

Input　　The input contains multiple cases. 
　　Each case starts with two positive integers N and M , indicating the number of planets and the number of channels. 
　　(2<=N<=200000, 1<=M<=1000000) 
　　Next M lines each contains two positive integers A and B, indicating a channel between planet A and B in the system. Planets are numbered by 1..N. 
　　A line with two integers '0' terminates the input.Output　　For each case, output the minimal number of bridges after building a new channel in a line.Sample Input

4 4
1 2
1 3
1 4
2 3
0 0 

Sample Output

0

要求：树的直径+缩点

和上一道题纠结了好久，到底怎么加入一个块。

首先要明确边双连通分量和点双连通分量的区别与联系

1.二者都是基于无向图

2.边双连通分量是删边后还连通，而后者是删点

3.点双连通分量一定是边双连通分量（除两点一线的特殊情况），反之不一定，见HDU3749

4.点双连通分量可以有公共点，而边双连通分量不能有公共边

 

     最后补充：

               点的双连通存桥（边），每访问一条边操作一次。 

            边的双连通存割点（点），访问完所有边后操作。

此题是边双连通，所以属于后者。yeah~~·

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<cstdio>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<cstring>
#include<vector>
using namespace std;
const int maxn=200010;
const int maxm=2000010;
int Laxt[maxn],Next[maxm],To[maxm],cnt,vis[maxn];
int dfn[maxn],low[maxn];
int times,ans,cut_cnt,n,m; 
int scc[maxn],scc_cnt;
int dis[maxn],S;
int stk[maxn],top,Maxdis,Maxpos;
vector<int>G[maxn];
void _init()
{
    memset(Laxt,0,sizeof(Laxt));
    memset(dfn,0,sizeof(dfn));
    memset(scc,0,sizeof(scc));
    memset(vis,0,sizeof(vis));
    ans=cut_cnt=top=scc_cnt=cnt=times=0;    
}
void _add(int u,int v)
{
      Next[++cnt]=Laxt[u];
      Laxt[u]=cnt;
      To[cnt]=v;    
}
void _tarjan(int u,int v){
    dfn[u]=low[u]=++times;
    int num_v=0;
    stk[top++]=u;
    for(int i=Laxt[u];i;i=Next[i]){
        if(To[i]==v){
            num_v++;
            if(num_v==1) continue;//保证重边
        }
        if(!dfn[To[i]]){
            _tarjan(To[i],u);
            if(low[u]>low[To[i]])  low[u]=low[To[i]];
            if(dfn[u]<low[To[i]])  cut_cnt++;//割边,对应缩点后是边 
        }
        else if(dfn[To[i]]<low[u]) low[u]=dfn[To[i]];
    }
    if(dfn[u]<=low[u]){//割点或者环里面第一个访问到的点（点连通缩点）
         G[++scc_cnt].clear();
         for(;;){
             int tmp=stk[--top];
             scc[tmp]=scc_cnt;
             if(tmp==u) break;
         }    
    }
}
void _rebuild()//重建无环图 
{
     for(int i=1;i<=n;i++)
     for(int j=Laxt[i];j;j=Next[j])
       if(scc[i]!=scc[To[j]])
       G[scc[i]].push_back(scc[To[j]]);
}
void _dfs(int u)
{    
    int i,L=G[u].size();
    for(int i=0;i<L;i++)
     if(!dis[G[u][i]]){
       dis[G[u][i]]=dis[u]+1;
       _dfs(G[u][i]);
     }
}
void _findR()
{
        memset(dis,0,sizeof(dis));
        dis[1]=1;S=1;Maxdis=1;
        _dfs(1);
        for(int i=1;i<=scc_cnt;i++)
            if(dis[i]>dis[S]) S=i;
        memset(dis,0,sizeof(dis));
        dis[S]=1;
        _dfs(S);
        for(int i=1;i<=scc_cnt;i++)
            if(dis[i]>Maxdis) Maxdis=dis[i];
        Maxdis--;
}
int main()
{                    
    int i,j,k,u,v;
    while(~scanf("%d%d",&n,&m)){
        if(n==0&&m==0) return 0; 
        _init();
        for(i=1;i<=m;i++){
            scanf("%d%d",&u,&v);
            _add(u,v);
            _add(v,u);
        }
        for(i=1;i<=n;i++)
          if(!dfn[i])  _tarjan(i,-1);
        _rebuild();
        _findR();
        printf("%d\n",cut_cnt-Maxdis);
    }
    return 0;
}