牛客练习赛56 E 小雀和他的王国

题目链接：https://ac.nowcoder.com/acm/contest/3566/E

思路：tarjan缩点，桥重建图，dfs跑树的直径。

 #include <iostream>
 #include <cstdio>
 #include <vector>
 #include <algorithm>
 using namespace std;
 typedef long long ll;

 const int N = (int)2e5+,mod = (int)1e9+;
 struct node{
     int to,nxt;
 }e[N<<];
 vector<pair<int,int> > cut;
 int n,m,u,v,tot,tim,top,scc_num,bridge;
 int head[N],dfn[N],low[N],s[N],scc_no[N],d[N];
 bool vis[N];

 ll quick(ll a,ll b){
     ll ans=;
     a=a%mod;
     while(b!=){
         if(b&) ans=(ans*a)%mod;
         b>>=;
         a=(a*a)%mod;
     }
     return ans;
 }

 inline void add(int u,int v){
     e[tot].to = v; e[tot].nxt = head[u]; head[u] = tot++;
     e[tot].to = u; e[tot].nxt = head[v]; head[v] = tot++;
 }

 void tarjan(int now,int pre){
     dfn[now] = low[now] = ++tim;
     s[top++] = now;
     int pre_cnt = ;
     for(int o = head[now]; ~o; o = e[o].nxt){
         int to = e[o].to;
         if(to == pre && pre_cnt == ){ pre_cnt = ; continue; }
         if(!dfn[to]){
             tarjan(to,now);
             low[now] = min(low[now],low[to]);
             if(dfn[now] < low[to]) cut.push_back(make_pair(now,to));
         }else low[now] = min(low[now],dfn[to]);
     }

     if(dfn[now] == low[now]){
         ++scc_num;
         int tmp;
         do{
             tmp = s[--top];
             scc_no[tmp] = scc_num;
         }while(now != tmp);
     }
 }

 void dfs(int now,int pre){
     vis[now] = ;
     d[now] = d[pre]+;
     for(int o = head[now]; ~o; o = e[o].nxt){
         int to = e[o].to;
         if(vis[to]) continue;
         dfs(to,now);
     }
 }

 void rebuild(){
     for(int i = ; i <= scc_num; ++i) head[i] = -; tot = ;
     bridge = cut.size();
     for(int i = ; i < bridge; ++i){
     //    printf("%d %d\n",scc_no[cut[i].first],scc_no[cut[i].second]);
         add(scc_no[cut[i].first],scc_no[cut[i].second]);
     }
     /*
     for(int i = 1; i <= scc_num; ++i){
         printf("u = %d\t",i);
         for(int o = head[i]; ~o; o = e[o].nxt) printf("%d ",e[o].to);
         cout << endl;
     }*/
 }

 void show_info(){
     for(int i = ; i <= n; ++i){
         printf("loc = %d scc_no = %d\n",i,scc_no[i]);
     }
 }

 void solve(){

     for(int i = ; i <= n; ++i) head[i] = -; tot = ;
     for(int i = ; i <= m; ++i){
         scanf("%d%d",&u,&v);
         add(u,v);
     }
     tarjan(,);
     rebuild();
     int s = ;
     for(int i = ; i <= scc_num; ++i){
         d[i] = -; vis[i] = ;
     }
     dfs(s,);
     for(int i = ; i <= scc_num; ++i){
         if(d[s] < d[i]) s = i;
     }
     for(int i = ; i <= scc_num; ++i){
         d[i] = -; vis[i] = ;
     }
     dfs(s,);
     int max_len = ;
     for(int i = ; i <= scc_num; ++i) max_len = max(max_len,d[i]);
    // printf("max_len = %d\n",max_len);
    //printf("%lf\n",(double)(bridge-max_len)/(m+1));
    printf("%lld\n",1ll*(bridge-max_len)*quick(m+,mod-)%mod);
 }

 int main(){

     scanf("%d%d",&n,&m);
     solve();
     //show_info();

     return ;
 }