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zc
2019-12-31 20:01:00
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分类讨论:

Tarjan跑出割点,然后DFS搜索所有的联通快

计算每一个联通快中的割点数目

分类讨论:

  1. 没有割点

    至少需要建立两个出口

    从任意非割点的地方选择两个点建立

  2. 这个分组只有一个割点

    只需要在分组内设立一个出口

    可以设立在任意一个非割点的地方

  3. 有两个及以上个割点,则无需建立,可以直接到达其他联通块

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i(x);i<=y;++i)
    #define Fdr(i,x,y) for(int i(x);i>=y;--i)
    #define fl(i,x) for(int i(head[x]),to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) ((int)(log2(n)))
    #define inf 2122219134
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const int str=1<<20;static char in_buf[str],*in_s,*in_t;bool __=0;il char gc(){return (in_s==in_t)&&(in_t=(in_s=in_buf)+fread(in_buf,1,str,stdin)),in_s==in_t?EOF:*in_s++;}il void in(string &ch){ch.clear();if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)__=1;}il void in(char &ch){if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)__=1;else ch=c;}il void in(char *ch){*ch='\0';if(__)return;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF){__=1;return;}*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)__=1;*ch='\0';}template<typename T>il void in(T &x){if(__)return;char c=gc();bool f=0;while(c!=EOF&&(c<'0'||c>'9'))f^=(c=='-'),c=gc();if(c==EOF){__=1;return;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=x*10+c-48,c=gc();if(c==EOF)__=1;if(f)x=-x;}template<typename T,typename ... arr>il void in(T &x,arr & ... y){in(x),in(y...);}const char ln='\n';static char out_buf[str],*out_s=out_buf,*out_t=out_buf+str;il void flush(){fwrite(out_buf,1,out_s-out_buf,stdout);out_s=out_buf;}il void pt(char c){(out_s==out_t)?(fwrite(out_s=out_buf,1,str,stdout),*out_s++=c):(*out_s++=c);}il void out(const char* s){while(*s)pt(*s++);}il void out(char* s){while(*s)pt(*s++);}il void out(char c){pt(c);}il void out(string s){for(int i=0;s[i];i++)pt(s[i]);}template<typename T>il void out(T x){if(!x){pt('0');return;}if(x<0)pt('-'),x=-x;char a[50],t=0;while(x)a[t++]=x%10,x/= 10;while(t--)pt(a[t]+'0');}template<typename T,typename ... arr>il void out(T x,arr & ... y){out(x),out(y...);}}using namespace IO;
#define N 50011
int n,m,cnt=0,head[N];
struct edge{
    int to,nxt;
}e[100011];
il void add(int x,int y){
    e[++cnt].to=y;e[cnt].nxt=head[x];head[x]=cnt;
}
int dfn[N],low[N],sz=0,rt,rs,v[N],tt,num,cuts=0;
bool cut[N];
void tarjan(int x,int f){
    dfn[x]=low[x]=++sz;
    fl(i,x)
    if(!dfn[to]){
        tarjan(to,x);
        low[x]=MIN(low[x],low[to]);
        if(low[to]>=dfn[x]){
            if(x!=rt)cut[x]=1;
            else ++rs;
        }
    }
    else if(to!=f)low[x]=MIN(low[x],dfn[to]);
}
void dfs(int x){
    v[x]=tt;
    ++num;
    fl(i,x){
        if(cut[to]&&v[to]!=tt){
            ++cuts;
            v[to]=tt;
        }
        if(!v[to])dfs(to);
    }
}
int CASE=0;
void work(){
    in(m);
    if(!m)flush(),exit(0);
    clr(head,0);sz=cnt=tt=0;
    clr(cut,0);clr(v,0);
    clr(dfn,0);clr(low,0);

    int x,y;
    ll ans1=0,ans2=1;
    n=0;
    Fur(i,1,m){
        in(x,y);
        add(x,y),add(y,x);
        n=MAX(n,MAX(x,y));
    }
    Fur(i,1,n)
    if(!dfn[i]){
        rt=i;rs=0;
        tarjan(i,i);
        if(rs>=2)cut[i]=1;
    }
    Fur(i,1,n)
    if(!v[i]&&!cut[i]){
        ++tt;
        num=cuts=0;
        dfs(i);
        if(!cuts)
            ans1+=2ll,
            ans2*=1ll*(num-1)*num/2;
        if(cuts==1)
            ++ans1,
            ans2*=1ll*num;
    }

    out("Case ",++CASE,": ",ans1," ",ans2,ln);
}
int main(){
    while(1)work();
}
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