Submission #235097

#	Time	Username	Problem	Language	Result	Execution time	Memory
235097		rama_pang	Duathlon (APIO18_duathlon)	C++14	100 / 100	163 ms	42212 KiB

count_triplets

#include <bits/stdc++.h>
using namespace std;

const int MAXN = 300005;

int N, M;
vector<int> G[MAXN];
vector<int> T[MAXN];

// Biconnected Components
int dis[MAXN];
int low[MAXN];

int compsz[MAXN];
vector<vector<int>> comps;

void DfsBcc(int u, int p = 0) {
  static int t = 1;
  dis[u] = low[u] = t++;

  static vector<int> st;
  st.emplace_back(u);

  int child = 0;
  for (auto v : G[u]) if (v != p) {
    if (dis[v]) {
      low[u] = min(low[u], dis[v]);
    } else {
      DfsBcc(v, u);
      low[u] = min(low[u], low[v]);
      child++;
      if ((p == 0 && child > 1) || (p != 0 && low[v] >= dis[u])) {
        comps.emplace_back();
        vector<int> &cur = comps.back();
        cur.emplace_back(u);
        while (cur.back() != v) {
          cur.emplace_back(st.back());
          st.pop_back();
        }
      }
    }
  }

  if (p == 0 && !st.empty()) {
    comps.emplace_back(st);
    st.clear();
  }
}

void InitBcc() {
  for (int i = 1; i <= N; i++) {
    if (!dis[i]) {
      DfsBcc(i);
    }
  }

  for (int i = 0; i < comps.size(); i++) {
    vector<int> &c = comps[i];
    sort(begin(c), end(c));
    c.resize(unique(begin(c), end(c)) - begin(c));
    compsz[i] = c.size();
    for (auto j : c) {
      T[i + N + 1].emplace_back(j);
      T[j].emplace_back(i + N + 1);
    }
  }
}

int vis[MAXN];
int sz[MAXN];

void DfsSize(int u, int p = 0) {
  vis[u] = 1;
  sz[u] = (u <= N);
  for (auto v : T[u]) if (v != p) {
    DfsSize(v, u);
    sz[u] += sz[v];
  }
}

void DfsCount(int u, long long &ans, int p = 0, int r = 0) {
  if (r == 0) {
    r = u;
    ans += 1ll * sz[u] * (sz[u] - 1) * (sz[u] - 2);
  }
  if (u <= N) {
    for (auto v : T[u]) {
      if (v == p) {
        ans -= 1ll * (compsz[v - N - 1] - 1) * sz[u] * (sz[u] - 1);
      } else {
        ans -= 1ll * (compsz[v - N - 1] - 1) * (sz[r] - sz[v]) * (sz[r] - sz[v] - 1);
      }
    }
  }
  for (auto v : T[u]) if (v != p) {
    DfsCount(v, ans, u, r);
  }
}

long long Solve() {
  InitBcc();
  long long res = 0;
  for (int i = 1; i <= N; i++) {
    if (!vis[i]) {
      DfsSize(i);
      DfsCount(i, res);
    }
  }
  return res;
}

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0), cout.tie(0);

  cin >> N >> M;
  for (int i = 0; i < M; i++) {
    int u, v;
    cin >> u >> v;
    G[u].emplace_back(v);
    G[v].emplace_back(u);
  }

  cout << Solve() << "\n";
  return 0;
}

Compilation message (stderr)

count_triplets.cpp: In function 'void InitBcc()':
count_triplets.cpp:57:21: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
   for (int i = 0; i < comps.size(); i++) {
                   ~~^~~~~~~~~~~~~~

• 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