【APIO2018】铁人两项

题面

https://www.luogu.org/problem/P4630

题解

// luogu-judger-enable-o2
#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#define ri register int
#define LL long long
#define N 200500
#define M 250000
using namespace std;

inline int read() {
  int f=0,ret=0; char ch=getchar();
  while (ch<'0' || ch>'9') f|=(ch=='-'),ch=getchar();
  while (ch>='0'&& ch<='9') ret=ret*10+(ch-'0'),ch=getchar();
  return f?-ret:ret;
}

int n,m,tn;
LL ans=0;

struct tree {
  vector<int> to[N];
  LL s1[N],s2[N]; LL siz[N];
  void add_edge(int a,int b) {
    //printf("%d %d
",a,b);
    to[a].push_back(b);
    to[b].push_back(a);
  }
  void tonji(int x,int ff,int &tot) {
    if (x<=tn) tot++;
    for (ri i=0;i<to[x].size();i++) {
      int y=to[x][i];
      if (y==ff) continue;
      tonji(y,x,tot);
    }
  }
  void dp(int x,int ff,int pa,int tot) {
    siz[x]=(x<=tn);
    for (ri i=0;i<to[x].size();i++) {
      if (to[x][i]==ff) continue;
      dp(to[x][i],x,pa,tot);
      siz[x]+=siz[to[x][i]];
    }
    if (x>tn) {
      s1[x]=0LL;
      s2[x]=0LL;
      for (ri i=0;i<to[x].size();i++) {
        if (to[x][i]==ff) continue;
        s1[x]+=siz[to[x][i]];
        s2[x]+=siz[to[x][i]]*siz[to[x][i]];
      }
      s1[x]+=(tot-siz[x]);
      s2[x]+=(tot-siz[x])*(tot-siz[x]);
    }
  }
  void getans(int x,int ff,int pa) {
    for (ri i=0;i<to[x].size();i++) {
      int y=to[x][i];
      if (y==ff) continue;
      getans(y,x,pa);
    }
    if (x<=tn) {
      s1[x]=0LL;
      s2[x]=0LL;
      for (ri i=0;i<to[x].size();i++) {
        s1[x]+=s1[to[x][i]];
        s2[x]+=s2[to[x][i]];
      }
      for (ri i=0;i<to[x].size();i++) {
        if (to[x][i]==ff) continue;
        s1[x]-=(siz[pa]-siz[to[x][i]]);
        s2[x]-=(siz[pa]-siz[to[x][i]])*(siz[pa]-siz[to[x][i]]);
      }
      if (x!=pa) {
        s1[x]-=siz[x];
        s2[x]-=siz[x]*siz[x];
      }
      ans+=(s1[x]*s1[x]-s2[x])/2;
    }
  }
} T;

struct graph {
  vector<int> to[N];
  int clo,top;
  int dfn[N],low[N];
  int S[N];
  void add_edge(int u,int v) {
    to[u].push_back(v);
    to[v].push_back(u);
  }
  void tarjan(int x) {
    dfn[x]=low[x]=++clo; S[++top]=x;
    for (ri i=0;i<to[x].size();i++) {
      int y=to[x][i];
      if (dfn[y]) {
        low[x]=min(low[x],dfn[y]);
      }
      else {
        tarjan(y);
        low[x]=min(low[x],low[y]);
        if (low[y]>=dfn[x]) {
          ++n;
          T.add_edge(x,n);
          int t;
          do {
            t=S[top--];
            T.add_edge(t,n);
          }
          while (t!=y);
        }
      }
    }
  }
} G;

int main(){
  tn=n=read(); m=read();
  for (ri i=1;i<=m;i++) {
    int u=read(),v=read();
    G.add_edge(u,v);
  }
  for (ri i=1;i<=tn;i++) if (!G.dfn[i]) {
    G.tarjan(i);
    int tot=0;
    T.tonji(i,i,tot);
    T.dp(i,i,i,tot);
    T.getans(i,i,i);
  }
  printf("%lld
",ans*2);
}