Strongly connected

  1 #include<iostream>
  2 #include<cstdio>
  3 #include<cstring>
  4 #include<algorithm>
  5 using namespace std;
  6 const int N=200010;
  7 const int M=400010;
  8 const int INF=0xffffffff;
  9 struct Edge{
 10     int to,next;
 11 } edge[M];
 12 
 13 int  n,m,cnt,dep,top,atype;
 14 int  dfn[N],low[N],vis[N],head[N],st[N],belong[N],in[N],out[N],sum[N];
 15 //sum[i]记录第i个连通图的点的个数,in[i],out[i],表示缩点之后点的入度和初度。
 16 void init(){
 17       cnt=dep=top=atype=0;
 18     memset(head,-1,sizeof(head));
 19     memset(dfn,0,sizeof(dfn));
 20     memset(low,0,sizeof(low));
 21     memset(vis,0,sizeof(vis));
 22     memset(belong,0,sizeof(belong));
 23     memset(in,0,sizeof(in));
 24     memset(out,0,sizeof(out));
 25     memset(sum,0,sizeof(sum));
 26 }
 27 void addedge(int u,int v){
 28     edge[cnt].to=v;
 29     edge[cnt].next=head[u];
 30     head[u]=cnt++;
 31 }
 32 
 33 void Tarjan(int u){
 34     dfn[u]=low[u]=++dep;
 35     st[top++]=u;
 36     vis[u]=1;
 37     for(int i=head[u]; i!=-1; i=edge[i].next){
 38         int v=edge[i].to;
 39         if(!dfn[v]){
 40             Tarjan(v);
 41             low[u]=min(low[u],low[v]);
 42         }
 43         else if(vis[v]){
 44             low[u]=min(low[u],dfn[v]);
 45         }
 46     }
 47     int j;
 48     if(dfn[u]==low[u]){
 49         atype++;
 50         do{
 51             j=st[--top];
 52             belong[j]=atype;
 53             sum[atype]++;   //记录每个连通分量中点的个数
 54             vis[j]=0;
 55         }
 56         while(u!=j);
 57     }
 58 }
 59 
 60 long long solve(){
 61     if(n==1){
 62         return -1;
 63     }
 64     init();
 65     int u,v;
 66     for(int i=0; i<m; i++){
 67         scanf("%d%d",&u,&v);
 68         addedge(u,v);
 69     }
 70     for(int i=1; i<=n; i++)
 71         if(!dfn[i])
 72             Tarjan(i);
 73     if(atype==1){
 74         return -1;
 75     }
 76     for(int u=1; u<=n; u++)
 77         for(int i=head[u]; i!=-1; i=edge[i].next){
 78             int v=edge[i].to;
 79             if(belong[u]!=belong[v]){
 80                 out[belong[u]]++;
 81                 in[belong[v]]++;
 82             }
 83         }
 84     long long  tmp=100000000;
 85     for(int i=1; i<=atype; i++)
 86         if(in[i]==0 || out[i]==0){
 87          tmp=min(tmp,(long long)sum[i]);
 88         }
 89     return  tmp*(tmp-1)+(n-tmp)*(n-tmp-1)+tmp*(n-tmp)-m;
 90 }
 91 int cas;
 92 int main(){
 93     scanf("%d",&cas);
 94     int tt=1;
 95     while(cas--){
 96         scanf("%d%d",&n,&m);
 97         printf("Case %d: %I64d\n",tt++,solve());
 98     }
 99     return 0;
100 }