Submission #979156

#	Time	Username	Problem	Language	Result	Execution time	Memory
979156		huutuan	Duathlon (APIO18_duathlon)	C++14	100 / 100	131 ms	71580 KiB

count_triplets

#include<bits/stdc++.h>

using namespace std;

#define int long long

const int N=3e5+10;
int n, m;
vector<int> g[N];
int num[N], low[N], tdfs;
stack<pair<int, int>> stk;
vector<pair<int, int>> bcc[N];
int cnt=0, cc[N], sz[N];
bool joint[N];
vector<int> gg[N];

void dfs_joint(int u, int p){
   num[u]=low[u]=++tdfs;
   int child=0;
   for (int v:g[u]){
      if (v==p) continue;
      if (!num[v]){
         ++child;
         stk.emplace(u, v);
         dfs_joint(v, u);
         low[u]=min(low[u], low[v]);
         if (low[v]>=num[u]){
            joint[u]=1;
            ++cnt;
            pair<int, int> edge={-1, -1};
            do{
               edge=stk.top(); stk.pop();
               bcc[cnt].emplace_back(edge);
            }while (edge!=make_pair(u, v));
         }
      }else low[u]=min(low[u], num[v]);
   }
   if (!p) joint[u]=child>=2;
}

int ans;
int sub_sz[N], sum[N];

void dfs_sz(int u, int p){
   sub_sz[u]=sz[u];
   for (int v:gg[u]) if (v!=p) dfs_sz(v, u), sub_sz[u]+=sub_sz[v];
}

int tot;

void dfs(int u, int p){
   if (u>n){
      for (int v:gg[u]){
         int size=sub_sz[v];
         if (v==p) size=tot-sub_sz[u];
         ans-=size*(size-1)*sz[u];
         sum[u]+=size*(size-1);
      }
   }
   for (int v:gg[u]) if (v!=p) dfs(v, u);
}

void dfs2(int u, int p){
   if (u<=n){
      for (int v:gg[u]){
         ans-=sum[v];
         int size=tot-sub_sz[v];
         if (v==p) size=sub_sz[u];
         ans+=size*(size-1);
      }
   }
   for (int v:gg[u]) if (v!=p) dfs2(v, u);
}

int32_t main(){
   // freopen("duathlon.inp", "r", stdin);
   ios_base::sync_with_stdio(false);
   cin.tie(nullptr);
   cin >> n >> m;
   for (int i=1; i<=m; ++i){
      int u, v; cin >> u >> v;
      g[u].push_back(v);
      g[v].push_back(u);
   }
   for (int i=1; i<=n; ++i) if (!num[i]){
      dfs_joint(i, 0);
   }
   set<pair<int, int>> edge;
   for (int i=1; i<=n; ++i) if (joint[i]) cc[i]=i;
   for (int i=1; i<=cnt; ++i){
      for (auto &j:bcc[i]){
         if (!joint[j.first]) cc[j.first]=n+i;
         else edge.emplace(n+i, j.first);
         if (!joint[j.second]) cc[j.second]=n+i;
         else edge.emplace(n+i, j.second);
      }
   }
   for (int i=1; i<=n; ++i) ++sz[cc[i]];
   for (auto &i:edge){
      gg[i.first].push_back(i.second);
      gg[i.second].push_back(i.first);
   }
   for (int i=1; i<=cnt; ++i){
      if (!sub_sz[n+i]){
         dfs_sz(n+i, 0);
         tot=sub_sz[n+i];
         ans+=tot*(tot-1)*(tot-2);
         dfs(n+i, 0);
         dfs2(n+i, 0);
      }
   }
   cout << ans << '\n';
   return 0;
}

• Subtask 1: 5 / 5
• Subtask 2: 11 / 11
• Subtask 3: 8 / 8
• Subtask 4: 10 / 10
• Subtask 5: 13 / 13
• Subtask 6: 15 / 15
• Subtask 7: 20 / 20
• Subtask 8: 8 / 8
• Subtask 9: 10 / 10