图的连通_Tarjan

强连通分量

http://blog.csdn.net/xinghongduo/article/details/6195337
http://www.cnblogs.com/shadowland/p/5872257.html
http://blog.csdn.net/jeryjeryjery/article/details/52829142?locationNum=4&fps=1
https://www.byvoid.com/zht/blog/scc-tarjan/

 

题目

bzoj1051 缩点

被所有的牛认为受欢迎，也就意味着缩点之后，该牛所在的点的出度为0（否则其他点不可能全部通往该点）

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int Maxn=10000;
const int Maxe=50000;
int n,e,tot=0,num=0;
int top;
int Cnt[Maxn+50],Outdegree[Maxn+50];
int Low[Maxn+50],Dfn[Maxn+50],Fir[Maxe+50],Stack[Maxn+50],Belong[Maxn+50];
bool Vis[Maxn+50];
struct Edge{
    int u,v,next;
}E[Maxe+50];

int read(){
    char ch=getchar();
    int x=0,f=1;
    while (ch<'0'||ch>'9') {
        if (ch=='-') f=-1;
        ch=getchar();        
    }
    while (ch>='0'&&ch<='9'){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return  x*f; 
}
void Insert(int x,int y){
    tot++;
    E[tot].u=x;
    E[tot].v=y;
    E[tot].next=Fir[x];
    Fir[x]=tot;
}
void Tarjan(int u){
    Low[u]=Dfn[u]=++tot;
    Stack[++top]=u;
    Vis[u]=1;
    for (int p=Fir[u];p!=-1;p=E[p].next){
        int v=E[p].v;
        if (!Dfn[v]){
            Tarjan(v);
            Low[u]=min(Low[u],Low[v]);
        }
        else if (Vis[v])
            Low[u]=min(Low[u],Dfn[v]);
    }
    if (Dfn[u]==Low[u]){
        num++;
        int v=-1;
        while (u!=v){
            v=Stack[top--];
            Belong[v]=num;
            Cnt[num]++;
            Vis[v]=0;
        }
    }
}
int main(){
    memset(Fir,-1,sizeof(Fir));
    n=read();e=read();
    for (int i=1;i<=e;i++){
        int u=read(),v=read();
        Insert(u,v);
    }
    memset(Low,0,sizeof(Low));
    memset(Dfn,0,sizeof(Dfn));
    memset(Vis,0,sizeof(Vis));
    for (int i=1;i<=n;i++)
      if (!Dfn[i])
        Tarjan(i);
    for (int i=1;i<=e;i++)
      if (Belong[E[i].u]!=Belong[E[i].v])
        Outdegree[Belong[E[i].u]]++;
    int res=0,ans=0;
    for (int i=1;i<=num;i++)
      if (Outdegree[i]==0){
          res++;
          ans=i;
      }
    if(res==1) printf("%d
",Cnt[ans]);
    else printf("0
");
    return 0;
}

poj1236 缩点

题意+题解

第一问求缩点之后入度为0的点数（只要入度不为0，就可从其他点处得到软件）；

第二问答案为max（入度为零的点数，出度为0的点数）

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int Maxn=100; 
const int Maxe=10000;
struct Edge{
    int from,u,v;
}E[Maxe];
int n;
int tot_e=0,top=0,ans1,ans2,cnt=0;
int Fir[Maxn+50]={0},dfn[Maxn+50],low[Maxn+50],Stack[Maxn+100],Belong[Maxn+50];
int time=0;
int V[Maxn+50],Indegree[Maxn+50],Outdegree[Maxn+50];
int read(){
    int x=0,f=1;
    char ch=getchar();
    while (ch<'0'||ch>'9'){
        if (ch=='-') f=-1;
        ch=getchar();
    }
    while (ch>='0'&&ch<='9'){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x*f;
}
void Insert(int u,int v){
    tot_e++;
    E[tot_e].u=u;E[tot_e].v=v;
    E[tot_e].from=Fir[u];Fir[u]=tot_e;
}
void Tarjan(int x){
    int y;
    dfn[x]=low[x]=++time;
    V[x]=1;
    Stack[++top]=x;
    for (int i=Fir[x];i;i=E[i].from){
        y=E[i].v;
        if (!V[y]){
            Tarjan(y);
            low[x]=min(low[x],low[y]);
        }
        if (V[y]==1)
          low[x]=min(low[x],dfn[y]);
    }
    if (dfn[x]==low[x]){
        cnt++;
        do{
            y=Stack[top--];
            Belong[y]=cnt;V[y]=2;
        }while (y!=x);
    }
}
int main(){
    n=read();
    memset(V,0,sizeof(V));
    for (int i=1;i<=n;i++){//build the graph
        int j=read();
        while(j){
            Insert(i,j);
            j=read();
        }
    }
    for (int i=1;i<=n;i++)
      if (!V[i])
        Tarjan(i);
    if (cnt==1){
        printf("1
0");
        return 0;
    }
    for (int i=1;i<=tot_e;i++)
      if (Belong[E[i].u]!=Belong[E[i].v]){
          Outdegree[Belong[E[i].u]]++;
          Indegree[Belong[E[i].v]]++;
    }
    ans1=ans2=0;
    for (int i=1;i<=cnt;i++){
      if (Indegree[i]==0) ans1++;
      if (Outdegree[i]==0) ans2++;
    }
    printf("%d
%d",ans1,max(ans1,ans2));
    return 0;
}

poj3177 边双联通分量

题意+题解

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int Maxn=5000;
const int Maxe=10000;
struct edge{
    int u,v,from;
}E[Maxe+100];
int n,e;
int tot=0,T=0,ccnum=0;
int Fir[Maxn+50],dfn[Maxn+50],low[Maxn+50],cc[Maxn+50],Degree[Maxn+50];
bool Is_cut[Maxn+50]={0};
int read(){
    char ch=getchar();
    int x=0,f=1;
    while (ch<'0'||ch>'9'){
        if (ch=='-') f=-1;
        ch=getchar();
    }
    while (ch>='0'&&ch<='9'){
        x=x*10+ch-'0';
        ch=getchar();
    }
    return x*f;
}
void Insert(int x,int y){
    tot++;
    E[tot].u=x;E[tot].v=y;
    E[tot].from=Fir[x];Fir[x]=tot;
}
void Tarjan(int x,int fa){
    dfn[x]=low[x]=++T;
    for (int i=Fir[x];i;i=E[i].from)
      if (E[i].v!=fa){
          int y=E[i].v;
          if (!dfn[y]){
              Tarjan(y,x);
              low[x]=min(low[x],low[y]);
              if (low[y]>dfn[x]) Is_cut[i]=1,Is_cut[i%2?i+1:i-1]=1;
          }
        else low[x]=min(low[x],dfn[y]);
      }
}
void dfs(int x,int fa){
    cc[x]=ccnum;
    for (int i=Fir[x];i;i=E[i].from)
      if (E[i].v!=fa&&!Is_cut[i]&&!cc[E[i].v])
        dfs(E[i].v,x);
}
int main(){
    n=read();e=read();
    memset(Fir,0,sizeof(Fir));
    for (int i=1;i<=e;i++){
        int u=read(),v=read();
        Insert(u,v);
        Insert(v,u);
    }
    for (int i=1;i<=n;i++)
      if (!dfn[i]) Tarjan(i,-1);
    for (int i=1;i<=n;i++)
      if (!cc[i]){
        ccnum++;
        dfs(i,-1);
    }
    int ans=0;
    for (int i=1;i<=tot;i++)
      if (cc[E[i].u]!=cc[E[i].v]){
          Degree[cc[E[i].u]]++;
          Degree[cc[E[i].v]]++; 
      }
    for (int i=1;i<=ccnum;i++)
      if (Degree[i]==2)ans++;
    printf("%d",(ans+1)/2);
    return 0;
    return 0;
}