제출 #1225291

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1225291		mychecksedad	Duathlon (APIO18_duathlon)	C++20	0 / 100	175 ms	50876 KiB

count_triplets

/* Author : Mychecksdead  */
#include<bits/stdc++.h>
using namespace std;
#define ll long long int
#define MOD (1000000000+7)
#define MOD1 (998244353)
#define pb push_back
#define all(x) x.begin(), x.end()
#define en cout << '\n'
#define ff first
#define ss second
#define pii pair<int,int>
#define vi vector<int>
const int N = 1e6+100, M = 1e5+10, K = 52, MX = 30;
const ll INF = 1e18;

ll n, m, ans = 0, SZ[N];
vector<int> g[N];
bitset<N> vis, cut;
vi st;
vector<vi> C;
int root;
int tin[N], timer = 0, low[N];
void dfs(int v, int p){
  vis[v] = 1;
  st.pb(v);
  tin[v] = low[v] = timer++;
  int ch = 1;
  for(int u: g[v]){
    if(u == p) continue;
    if(vis[u]){
      low[v] = min(low[v], tin[u]);
    }else{
      dfs(u, v);
      low[v] = min(low[v], low[u]);
      if(low[u] >= tin[v]){
        cut[v] = v != root || ch > 1;
        C.pb(vi{v});
        while(C.back().back() != u){
          C.back().pb(st.back());
          st.pop_back();
        }
      }
    }
    ++ch;
  }
  // cerr << v << ' ' << cut[v] << '\n';
}
int cu =0 ;
ll nn;
ll sz[N], SZ2[N];
vi ID(N);
vector<vi> T; // graph
void dfs2(int v, int p){
  sz[v] = SZ[v];
  vis[v] = 1;
  for(int u: T[v]){
    if(u != p){
      dfs2(u, v);
      sz[v] += sz[u];
    }
  }
  // cerr << v << ' ' << SZ[v] << ' ' << sz[v] << '\n';
    // cerr << v << '\n';
  if(v < cu){
    ll sum = 0;
    for(int u: T[v]){
      if(u != p){
        ans -= sum * (sz[u] + 1) * (sz[u]);
        ans -= sum * (sum + 1) * sz[u];
        sum += sz[u];
      }
    }
    ans -= sum * (nn - sz[v] + 1) * (nn - sz[v]);
    ans -= sum * (sum + 1) * (nn - sz[v]);
  }
}
int sz2[N];
void pre(int v, int p){
  sz2[v] = SZ[v];
  for(int u: T[v]){
    if(u != p){
      pre(u, v);
      sz2[v] += sz2[u];
    }
  }
}

void solve(){
  cin >> n >> m;
  for(int i = 1; i <= m; ++i){
    int u, v, w; cin >> u >> v;
    g[u].pb(v);
    g[v].pb(u);
  } 
  if(n < 3){
    cout << 0;
    return;
  }
  for(int i = 1; i <= n; ++i){
    if(!vis[i]){
      root = i;
      dfs(root, root);
    }
  }

  int id = 0;
  for(int i = 1; i <= n; ++i){
    if(cut[i]){
      ID[i] = id++;
      SZ[ID[i]] = 1;
      T.pb({});
      ++cu;
    }
  }

  for(auto c: C){
    int node = id++;
    SZ2[node] = c.size();
    T.pb({});
    SZ[node] = 0;
    for(int x: c){
      if(!cut[x]){
        ID[x] = node;
        SZ[node]++;
      }else{
        T[ID[x]].pb(node);
        T[node].pb(ID[x]);
      }
    }
  }

  vis = 0;

  for(int i = 0; i < id; ++i){
    if(!vis[i]){
      pre(i, i);
      nn = sz2[i];
      dfs2(i, i);
      ans += sz[i] * (sz[i] - 1) * (sz[i] - 2);
    }
  }

  cout << ans;
}


int main(){
  cin.tie(0); ios::sync_with_stdio(0);
  int tt = 1, aa;
  // freopen("in.txt", "r", stdin);
  // freopen("out.txt", "w", stdout);
  while(tt--){
    solve();
    en;
  }
  cerr<<"time taken : "<<(float)clock()/CLOCKS_PER_SEC<<" seconds\n";
  return 0;
} 

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