Submission #1043458

#	Time	Username	Problem	Language	Result	Execution time	Memory
1043458		vjudge1	Duathlon (APIO18_duathlon)	C++17	23 / 100	739 ms	1048576 KiB

count_triplets

#include<bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 100'000 + 10;
int n, m;
vector<int> G[N], T[N];
bool seen[N];
ll cnt[N][3];
int h[N], minh[N], par[N], sz[N];
bool bridge[N];
vector<pair<int,int> > edges;

int root(int x)
{
  if(par[x] == x) return x;
  return par[x] = root(par[x]);
}

void merge(int a, int b)
{
  a = root(a), b = root(b);
  if(a == b) return;
  if(sz[a] > sz[b]) swap(a, b);
  par[a] = b;
  sz[b] += sz[a];
}

void dfs(int v, int p = 0)
{
  minh[v] = h[v] = h[p] + 1;
  seen[v] = true;
  for(int u : G[v])
    {
      if(u > v)
	edges.push_back({u, v});
      if(u == p) continue;
      if(seen[u])
	{
	  minh[v] = min(h[u], minh[v]);
	}
      else
	{
	  dfs(u, v);
	  if(minh[u] > h[v])
	    bridge[u] = bridge[v] = true;
	  minh[v] = min(minh[u], minh[v]);
	}
    }
}

void compute(int v, int p = 0)
{
  cnt[v][0] = sz[v];
  cnt[v][1] = (sz[v] * (sz[v] - 1));
  cnt[v][2] = (sz[v] * (sz[v] - 1) * (sz[v] - 2));
  for(int u : T[v])
    {
      if(u == p) continue;
      compute(u, v);

      cnt[v][2] += 2 *(cnt[v][1] * cnt[u][0] + cnt[v][0] * cnt[u][1]) + cnt[u][2];
      cnt[v][1] += cnt[u][1] + cnt[u][0];
      cnt[v][0] += cnt[u][0];
    }
  // cerr << v << ' ' << cnt[v][0] << ' ' << cnt[v][1] << ' ' << cnt[v][2] << ' ' << sz[v] << endl;
}

ll solve(int v)
{
  dfs(v);
  vector<pair<int,int> > tree;
  for(auto [x, y] : edges)
    {
      if(!bridge[x] && !bridge[y])
	merge(x, y);
      else
	tree.push_back({x, y});
    }
  
  edges.clear();
  for(auto& [x, y] : tree)
    {
      x = root(x);
      y = root(y);
      if(x > y) swap(x, y);
      edges.push_back({x, y});
    }
  sort(edges.begin(), edges.end());
  edges.resize(unique(edges.begin(), edges.end()) - edges.begin());
  for(auto [x, y] : edges)
    {
      T[x].push_back(y);
      T[y].push_back(x);
      // cerr << x << ' ' << y << endl;
    }
  edges.clear();
  compute(root(v));
  return cnt[root(v)][2];
}

int main()
{
  cin >> n >> m;
  for(int i = 0; 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 ++)
    par[i] = i, sz[i] = 1;
  
  ll ways = 0;
  for(int i = 1; i < n; i ++)
    {
      if(seen[i]) continue;
      ways += solve(i);
    }
  cout << ways << endl;
  
  return 0;
}

• Subtask 1: 0 / 5
• Subtask 2: 0 / 11
• Subtask 3: 0 / 8
• Subtask 4: 10 / 10
• Subtask 5: 13 / 13
• Subtask 6: 0 / 15
• Subtask 7: 0 / 20
• Subtask 8: 0 / 8
• Subtask 9: 0 / 10