Luzhiled's Library

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View the Project on GitHub ei1333/library

:heavy_check_mark: test/verify/yosupo-three-edge-connected-components.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/three_edge_connected_components

#include "../../template/template.hpp"

#include "../../graph/connected-components/three-edge-connected-components.hpp"

int main() {
  int N, M;
  cin >> N >> M;
  ThreeEdgeConnectedComponents<> g(N);
  g.read(M, 0);
  g.build();
  cout << g.group.size() << "\n";
  for(auto &p : g.group) {
    cout << p.size() << " " << p << "\n";
  }
}

#line 1 "test/verify/yosupo-three-edge-connected-components.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/three_edge_connected_components

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{forward<F>(f)};
}
#line 4 "test/verify/yosupo-three-edge-connected-components.test.cpp"

#line 2 "graph/connected-components/three-edge-connected-components.hpp"

#line 2 "graph/graph-template.hpp"

/**
 * @brief Graph Template(グラフテンプレート)
 */
template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  vector<vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

  inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 2 "graph/connected-components/incremental-bridge-connectivity.hpp"

#line 2 "structure/union-find/union-find.hpp"

struct UnionFind {
  vector<int> data;

  UnionFind() = default;

  explicit UnionFind(size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) { return -data[find(k)]; }

  bool same(int x, int y) { return find(x) == find(y); }

  vector<vector<int> > groups() {
    int n = (int)data.size();
    vector<vector<int> > ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(remove_if(begin(ret), end(ret),
                        [&](const vector<int> &v) { return v.empty(); }),
              end(ret));
    return ret;
  }
};
#line 4 "graph/connected-components/incremental-bridge-connectivity.hpp"

struct IncrementalBridgeConnectivity {
 private:
  UnionFind cc, bcc;
  vector<int> bbf;
  size_t bridge;

  int size() { return bbf.size(); }

  int par(int x) { return bbf[x] == size() ? size() : bcc.find(bbf[x]); }

  int lca(int x, int y) {
    unordered_set<int> used;
    for (;;) {
      if (x != size()) {
        if (!used.insert(x).second) return x;
        x = par(x);
      }
      swap(x, y);
    }
  }

  void compress(int x, int y) {
    while (bcc.find(x) != bcc.find(y)) {
      int nxt = par(x);
      bbf[x] = bbf[y];
      bcc.unite(x, y);
      x = nxt;
      --bridge;
    }
  }

  void link(int x, int y) {
    int v = x, pre = y;
    while (v != size()) {
      int nxt = par(v);
      bbf[v] = pre;
      pre = v;
      v = nxt;
    }
  }

 public:
  IncrementalBridgeConnectivity() = default;

  explicit IncrementalBridgeConnectivity(int sz)
      : cc(sz), bcc(sz), bbf(sz, sz), bridge(0) {}

  int find(int k) { return bcc.find(k); }

  size_t bridge_size() const { return bridge; }

  void add_edge(int x, int y) {
    x = bcc.find(x);
    y = bcc.find(y);
    if (cc.find(x) == cc.find(y)) {
      int w = lca(x, y);
      compress(x, w);
      compress(y, w);
    } else {
      if (cc.size(x) > cc.size(y)) swap(x, y);
      link(x, y);
      cc.unite(x, y);
      ++bridge;
    }
  }
};
#line 5 "graph/connected-components/three-edge-connected-components.hpp"

template <typename T = int>
struct ThreeEdgeConnectedComponents : Graph<T> {
 public:
  using Graph<T>::Graph;
  using Graph<T>::g;
  vector<vector<int> > group;

  void build() {
    uf = UnionFind(g.size());
    bcc = IncrementalBridgeConnectivity(g.size());
    used.assign(g.size(), 0);
    in.assign(g.size(), 0);
    out.assign(g.size(), 0);
    deg.assign(g.size(), 0);
    low.assign(g.size(), g.size());
    for (size_t from = 0; from < g.size(); from++) {
      for (auto &to : g[from]) {
        if ((T)from < to) bcc.add_edge(from, to);
      }
    }
    int cnt = 0;
    for (size_t i = 0; i < g.size(); i++) {
      if (used[i]) continue;
      vector<int> tmp;
      dfs(i, -1, tmp, cnt);
      cnt++;
    }
    vector<int> id(g.size(), -1);
    cnt = 0;
    for (size_t i = 0; i < g.size(); i++) {
      if (id[uf.find(i)] == -1) id[uf.find(i)] = cnt++;
    }
    group.resize(cnt);
    for (size_t i = 0; i < g.size(); i++) {
      group[id[uf.find(i)]].emplace_back(i);
    }
  }

  int operator[](const int &k) { return uf.find(k); }

 private:
  vector<int> used;
  vector<int> in, out, low, deg;
  IncrementalBridgeConnectivity bcc;
  UnionFind uf;

  void absorb(vector<int> &path, int v, int w = -1) {
    while (!path.empty()) {
      int x = path.back();
      if (w != -1 && (in[x] > in[w] or in[w] >= out[x])) break;
      path.pop_back();
      uf.unite(v, x);
      deg[v] += deg[x] - 2;
    }
  }

  void dfs(int idx, int p, vector<int> &path, int &k) {
    used[idx] = 1;
    in[idx] = low[idx] = k++;
    for (auto &to : g[idx]) {
      if (idx == to || bcc.find(idx) != bcc.find(to)) continue;
      deg[idx]++;
      if (to == p) {
        p = -1;
        continue;
      }
      if (used[to]) {
        if (in[idx] > in[to]) {
          if (in[to] < low[idx]) {
            low[idx] = in[to];
            absorb(path, idx);
          }
        } else {
          deg[idx] -= 2;
          absorb(path, idx, to);
        }
      } else {
        vector<int> ps;
        dfs(to, idx, ps, k);
        if (deg[to] == 2) ps.pop_back();
        if (low[to] < low[idx]) {
          low[idx] = low[to];
          absorb(path, idx);
          path = ps;
        } else {
          absorb(ps, idx);
        }
      }
    }
    out[idx] = k;
    path.push_back(idx);
  }
};
#line 6 "test/verify/yosupo-three-edge-connected-components.test.cpp"

int main() {
  int N, M;
  cin >> N >> M;
  ThreeEdgeConnectedComponents<> g(N);
  g.read(M, 0);
  g.build();
  cout << g.group.size() << "\n";
  for(auto &p : g.group) {
    cout << p.size() << " " << p << "\n";
  }
}

Test cases

Env Name Status Elapsed Memory
g++ example_00 :heavy_check_mark: AC 6 ms 4 MB
g++ example_01 :heavy_check_mark: AC 6 ms 4 MB
g++ large_cycle_00 :heavy_check_mark: AC 111 ms 48 MB
g++ max_random_00 :heavy_check_mark: AC 172 ms 46 MB
g++ max_random_01 :heavy_check_mark: AC 172 ms 46 MB
g++ max_random_02 :heavy_check_mark: AC 168 ms 46 MB
g++ random_1_00 :heavy_check_mark: AC 112 ms 33 MB
g++ random_1_01 :heavy_check_mark: AC 114 ms 35 MB
g++ random_1_02 :heavy_check_mark: AC 75 ms 21 MB
g++ random_2_00 :heavy_check_mark: AC 32 ms 9 MB
g++ random_2_01 :heavy_check_mark: AC 13 ms 5 MB
g++ random_2_02 :heavy_check_mark: AC 46 ms 12 MB
g++ random_2_03 :heavy_check_mark: AC 61 ms 14 MB
g++ random_2_04 :heavy_check_mark: AC 28 ms 8 MB
g++ small_random_1_00 :heavy_check_mark: AC 7 ms 4 MB
g++ small_random_1_01 :heavy_check_mark: AC 6 ms 4 MB
g++ small_random_1_02 :heavy_check_mark: AC 6 ms 4 MB
g++ small_random_2_00 :heavy_check_mark: AC 7 ms 4 MB
g++ small_random_2_01 :heavy_check_mark: AC 7 ms 4 MB
g++ small_random_2_02 :heavy_check_mark: AC 7 ms 4 MB
clang++ example_00 :heavy_check_mark: AC 6 ms 4 MB
clang++ example_01 :heavy_check_mark: AC 6 ms 4 MB
clang++ large_cycle_00 :heavy_check_mark: AC 109 ms 39 MB
clang++ max_random_00 :heavy_check_mark: AC 172 ms 42 MB
clang++ max_random_01 :heavy_check_mark: AC 177 ms 42 MB
clang++ max_random_02 :heavy_check_mark: AC 173 ms 42 MB
clang++ random_1_00 :heavy_check_mark: AC 117 ms 30 MB
clang++ random_1_01 :heavy_check_mark: AC 120 ms 32 MB
clang++ random_1_02 :heavy_check_mark: AC 69 ms 18 MB
clang++ random_2_00 :heavy_check_mark: AC 35 ms 9 MB
clang++ random_2_01 :heavy_check_mark: AC 13 ms 5 MB
clang++ random_2_02 :heavy_check_mark: AC 51 ms 11 MB
clang++ random_2_03 :heavy_check_mark: AC 71 ms 14 MB
clang++ random_2_04 :heavy_check_mark: AC 31 ms 8 MB
clang++ small_random_1_00 :heavy_check_mark: AC 7 ms 4 MB
clang++ small_random_1_01 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_random_1_02 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_random_2_00 :heavy_check_mark: AC 7 ms 4 MB
clang++ small_random_2_01 :heavy_check_mark: AC 6 ms 4 MB
clang++ small_random_2_02 :heavy_check_mark: AC 7 ms 4 MB
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