cp-includes

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:heavy_check_mark: tests/yosupo/biconnected-components.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components"

#include "graphs/BlockCut.cpp"
#include "Template.cpp"

using namespace lib;

int32_t main() {
  iopt;

  int n, m; cin >> n >> m;

  graph::Graph<int> g(n);

  for(int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    g.add_2edge(a, b);
  }

  auto bct = graph::make_block_cut(g);

  cout << bct.n_components() << endl;
  for(int i = 0; i < bct.n_components(); i++) {
    const auto comp = bct.component(i);
    cout << comp.size() << " ";
    for(const auto v : comp) cout << v << " ";
    cout << endl;
  }
}
#line 1 "tests/yosupo/biconnected-components.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components"

#line 1 "graphs/BlockCut.cpp"


#include <bits/stdc++.h>
#line 1 "Graph.cpp"


#line 1 "Traits.cpp"


#line 4 "Traits.cpp"

namespace lib {
using namespace std;
namespace traits {

template <typename...> struct make_void { using type = void; };

template <typename... T> using void_t = typename make_void<T...>::type;

/// keep caide
template <typename Iterator>
using IteratorCategory = typename iterator_traits<Iterator>::iterator_category;

/// keep caide
template <typename Container>
using IteratorCategoryOf = IteratorCategory<typename Container::iterator>;

/// keep caide
template <typename Iterator>
using IteratorValue = typename iterator_traits<Iterator>::value_type;

/// keep caide
template <typename Container>
using IteratorValueOf = IteratorValue<typename Container::iterator>;

/// keep caide
template <typename Iterator>
using IsRandomIterator =
    is_base_of<random_access_iterator_tag, IteratorCategory<Iterator>>;

/// keep caide
template <typename Iterator>
using IsInputIterator =
    is_base_of<input_iterator_tag, IteratorCategory<Iterator>>;

/// keep caide
template <typename Iterator>
using IsBidirectionalIterator =
    is_base_of<bidirectional_iterator_tag, IteratorCategory<Iterator>>;

/// keep caide
template <typename Container>
using HasRandomIterator =
    is_base_of<random_access_iterator_tag, IteratorCategoryOf<Container>>;

/// keep caide
template <typename Container>
using HasInputIterator =
    is_base_of<input_iterator_tag, IteratorCategoryOf<Container>>;

/// keep caide
template <typename Container>
using HasBidirectionalIterator =
    is_base_of<bidirectional_iterator_tag, IteratorCategoryOf<Container>>;
} // namespace traits
} // namespace lib


#line 1 "utils/Wrappers.cpp"


#line 4 "utils/Wrappers.cpp"

namespace lib {
using namespace std;
namespace graph {
template <typename T> struct Edge {
  const int from, to;
  T data;
};

template <> struct Edge<void> { const int from, to; };

template <typename T> struct VertexWrapper { T data; };

template <> struct VertexWrapper<void> {};
} // namespace graph
} // namespace lib


#line 6 "Graph.cpp"

namespace lib {
using namespace std;
namespace graph {
template <typename V = void, typename E = void, bool Directed = false>
struct GraphImpl {
  typedef GraphImpl<V, E> self_type;
  typedef vector<vector<int>> adj_list;
  typedef Edge<E> edge_type;
  typedef VertexWrapper<V> vertex_type;

  const static bool directed = Directed;

  vector<edge_type> edges;
  adj_list adj;

  vector<vertex_type> vertices;

  class iterator {
  public:
    typedef iterator self_type;
    typedef edge_type value_type;
    typedef edge_type &reference;
    typedef edge_type *pointer;
    typedef std::forward_iterator_tag iterator_category;
    typedef int difference_type;
    iterator(vector<int> *adj, vector<edge_type> *edges, int ptr = 0)
        : adj_(adj), edges_(edges), ptr_(ptr) {}
    self_type operator++() {
      ptr_++;
      return *this;
    }
    self_type operator++(int junk) {
      self_type i = *this;
      ptr_++;
      return i;
    }
    reference operator*() { return (*edges_)[(*adj_)[ptr_]]; }
    pointer operator->() { return &(*edges_)[(*adj_)[ptr_]]; }
    bool operator==(const self_type &rhs) const {
      return adj_ == rhs.adj_ && ptr_ == rhs.ptr_;
    }
    bool operator!=(const self_type &rhs) const { return !(*this == rhs); }

  private:
    vector<int> *adj_;
    vector<edge_type> *edges_;
    int ptr_;
  };

  class const_iterator {
  public:
    typedef const_iterator self_type;
    typedef edge_type value_type;
    typedef edge_type &reference;
    typedef edge_type *pointer;
    typedef std::forward_iterator_tag iterator_category;
    typedef int difference_type;
    const_iterator(vector<int> *adj, vector<edge_type> *edges, int ptr = 0)
        : adj_(adj), edges_(edges), ptr_(ptr) {}
    self_type operator++() {
      ptr_++;
      return *this;
    }
    self_type operator++(int junk) {
      self_type i = *this;
      ptr_++;
      return i;
    }
    const value_type &operator*() { return (*edges_)[(*adj_)[ptr_]]; }
    const value_type *operator->() { return &(*edges_)[(*adj_)[ptr_]]; }
    bool operator==(const self_type &rhs) const {
      return adj_ == rhs.adj_ && ptr_ == rhs.ptr_;
    }
    bool operator!=(const self_type &rhs) const { return !(*this == rhs); }

  private:
    vector<int> *adj_;
    vector<edge_type> *edges_;
    int ptr_;
  };

  struct iterable {
    vector<int> *adj_;
    vector<edge_type> *edges_;

    iterable(vector<int> *adj, vector<edge_type> *edges)
        : adj_(adj), edges_(edges) {}

    inline iterator begin() { return iterator(adj_, edges_); }
    inline iterator end() { return iterator(adj_, edges_, adj_->size()); }

    inline const_iterator cbegin() const {
      return const_iterator(adj_, edges_);
    }
    inline const_iterator cend() const {
      return const_iterator(adj_, edges_, adj_->size());
    }

    inline const_iterator begin() const { return cbegin(); }
    inline const_iterator end() const { return cend(); }

    inline edge_type &operator[](int i) { return (*edges_)[(*adj_)[i]]; }
    inline const edge_type &operator[](int i) const {
      return (*edges_)[(*adj_)[i]];
    }

    inline int index(int i) const { return (*adj_)[i]; }
    inline int size() const { return adj_->size(); }
  };

  GraphImpl() {}

  template <typename S = V,
            typename enable_if<is_void<S>::value>::type * = nullptr>
  GraphImpl(size_t n) : adj(n) {}

  template <typename S = V,
            typename enable_if<!is_void<S>::value>::type * = nullptr>
  GraphImpl(size_t n) : adj(n), vertices(n) {}

  inline iterable n_edges(int i) { return iterable(&adj[i], &edges); }
  inline const iterable n_edges(int i) const {
    return iterable(const_cast<vector<int> *>(&adj[i]),
                    const_cast<vector<edge_type> *>(&edges));
  }
  inline int degree(int i) const { return adj[i].size(); }

  inline int size() const { return adj.size(); }
  inline int edge_size() const { return edges.size(); }
  inline edge_type &edge(int i) { return edges[i]; }
  inline edge_type edge(int i) const { return edges[i]; }

  inline vector<edge_type> all_edges() const { return edges; }

  template <typename S = V,
            typename enable_if<!is_void<S>::value>::type * = nullptr>
  inline S &vertex(int i) {
    return vertices[i];
  }

  template <typename S = V,
            typename enable_if<!is_void<S>::value>::type * = nullptr>
  inline V vertex(int i) const {
    return vertices[i];
  }

  template <typename S = V,
            typename enable_if<is_void<S>::value>::type * = nullptr>
  inline void add_vertex() {
    adj.emplace_back();
  }

  template <typename S = V,
            typename enable_if<!is_void<S>::value>::type * = nullptr>
  inline S &add_vertex() {
    adj.emplace_back();
    return vertices.emplace_back().data;
  }

  template <typename S = E,
            typename enable_if<is_void<S>::value>::type * = nullptr>
  inline void add_edge_(int u, int v) {
    adj[u].push_back(edges.size());
    edges.push_back({u, v});
  }

  template <typename S = E,
            typename enable_if<!is_void<S>::value>::type * = nullptr>
  inline S &add_edge_(int u, int v) {
    adj[u].push_back(edges.size());
    edges.push_back({u, v});
    return edges.back().data;
  }

  void add_2edge(int u, int v) {
    add_edge_(u, v);
    add_edge_(v, u);
  }

  template <typename S = E,
            typename enable_if<!is_void<S>::value>::type * = nullptr>
  inline void add_2edge(int u, int v, const S &data) {
    add_edge_(u, v) = data;
    add_edge_(v, u) = data;
  }

  template <typename S = E,
            typename enable_if<is_void<S>::value && Directed>::type * = nullptr>
  inline void add_edge(int u, int v) {
    adj[u].push_back(edges.size());
    edges.push_back({u, v});
  }

  template <typename S = E,
            typename enable_if<!is_void<S>::value && Directed>::type * = nullptr>
  inline S &add_edge(int u, int v) {
    adj[u].push_back(edges.size());
    edges.push_back({u, v});
    return edges.back().data;
  }
};

template<typename V = void, typename E = void>
using Graph = GraphImpl<V, E, false>;

template<typename V = void, typename E = void>
using DirectedGraph = GraphImpl<V, E, true>;

template <typename V = void, typename E = void>
struct RootedForest : public DirectedGraph<V, E> {
  typedef RootedForest<V, E> self_type;
  using typename DirectedGraph<V, E>::adj_list;
  using typename DirectedGraph<V, E>::edge_type;
  using DirectedGraph<V, E>::DirectedGraph;
  using DirectedGraph<V, E>::adj;
  using DirectedGraph<V, E>::edge;
  vector<int> p, pe;

  void build_parents() {
    if ((int)p.size() == this->size())
      return;

    int n = this->size();
    stack<int> st;
    vector<bool> vis(n);
    p.assign(n, -1), pe.assign(n, -1);
    for (int i = 0; i < n; i++) {
      if (!vis[i]) {
        st.push(i);
        vis[i] = true;
        while (!st.empty()) {
          int u = st.top();
          st.pop();

          for (int k : adj[u]) {
            int v = edge(k).to;
            vis[v] = true;
            st.push(v), pe[v] = k, p[v] = u;
          }
        }
      }
    }
  }

  inline int parent(int i) const {
    const_cast<self_type *>(this)->build_parents();
    return p[i];
  }

  inline bool is_root(int i) const { return parent(i) != -1; }

  inline edge_type &parent_edge(int i) {
    build_parents();
    return edge(pe[i]);
  }
  inline edge_type &parent_edge(int i) const {
    const_cast<self_type *>(this)->build_parents();
    return edge(pe[i]);
  }

  vector<int> roots() const {
    vector<int> res;
    const_cast<self_type *>(this)->build_parents();
    int n = this->size();

    for (int i = 0; i < n; i++)
      if (p[i] == -1)
        res.push_back(i);
    return res;
  }
};

template <typename V = void, typename E = void>
struct RootedTree : public RootedForest<V, E> {
  using typename RootedForest<V, E>::adj_list;
  int root;

  RootedTree(int n, int root) : RootedForest<V, E>(n) {
    assert(n > 0);
    assert(root < n);
    this->root = root;
  }

  RootedTree(const adj_list &adj, int root) : RootedForest<V, E>(adj) {
    assert(adj.size() > 0);
    assert(root < adj.size());
    this->root = root;
  }
};

namespace builders {
namespace {
template <typename F, typename G>
void dfs_rooted_forest(F &forest, const G &graph, int u, vector<bool> &vis) {
  vis[u] = true;
  for (const auto &ed : graph.n_edges(u)) {
    int v = ed.to;
    if (!vis[v]) {
      forest.add_edge(u, v);
      dfs_rooted_forest(forest, graph, v, vis);
    }
  }
}
} // namespace

template <typename A, typename B>
RootedForest<A, B> make_rooted_forest(const Graph<A, B> &graph,
                                      const vector<int> &roots) {
  RootedForest<A, B> res(graph.size());
  vector<bool> vis(graph.size());
  for (int i : roots)
    if (!vis[i])
      dfs_rooted_forest(res, graph, i, vis);
  for (int i = 0; i < graph.size(); i++)
    if (!vis[i])
      dfs_rooted_forest(res, graph, i, vis);
  return res;
}
} // namespace builders
} // namespace graph
} // namespace lib


#line 1 "utils/LazyArray.cpp"


#line 4 "utils/LazyArray.cpp"

namespace lib {
  using namespace std;
template<typename T>
struct LazyArray {
  vector<T> v;
  vector<int> lz;
  T lz_v;
  int tempo = 1;

  LazyArray() {}
  LazyArray(int n, T lz_v) : v(n), lz(n), lz_v(lz_v) {}

  int size() const { return v.size(); }
  void fill(T vv) { lz_v = vv, tempo++; }
  void clear() {
    fill(T());
  }
  T get(int i) const {
    return tempo == lz[i] ? v[i] : lz_v;
  }
  T operator[](int i) const {
    return get(i);
  }
  T& operator[](int i) {
    if(lz[i] != tempo) {
      lz[i] = tempo;
      v[i] = lz_v;
    }
    return v[i];
  }
};
} // namespace lib


#line 6 "graphs/BlockCut.cpp"

namespace lib {
  using namespace std;
namespace graph {
template<typename V, typename E>
struct BlockCut {
  int n, m;
  Graph<V, E> g;
  int tempo = 0;
  vector<int> vis, low, seen;
  vector<int> st;
  LazyArray<char> seen_v;

  Graph<V, E> g2;
  int n2 = 0;

  BlockCut(const Graph<V, E>& g) : g(g) {
    n = g.size();
    m = g.edge_size();
    vis = low = vector<int>(n);
    seen = vector<int>(m);
    st.reserve(m);
    seen_v = LazyArray<char>(n, 0);

    g2 = Graph<V, E>(n);

    for(int i = 0; i < n; i++) {
      if(!vis[i]) {
        tarjan(i, -1);
        if (g.degree(i) == 0) {
          // Vertex is isolated, process separately.
          g2.add_vertex();
          g2.add_2edge(n + n2, i);
          n2++;
        }
      }
    }
  }
  Graph<V, E> graph() const { return g2; }

  int n_components() const { return n2; }
  vector<int> component(int i) const {
    vector<int> res;
    for(const auto& v : g2.n_edges(n + i))
      if (v.to < n)
        res.push_back(v.to);
    return res;
  }

  vector<int> get_vertices_(const vector<int>& e) {
    seen_v.clear();
    vector<int> comp;
    for(int kk : e) {
      auto ed = g.edge(kk);
      if(!seen_v.get(ed.from)) comp.push_back(ed.from), seen_v[ed.from] = true;
      if(!seen_v.get(ed.to)) comp.push_back(ed.to), seen_v[ed.to] = true;
    }
    return comp;
  }
  void process_component_(int k) {
    vector<int> e;
    int cur;
    do {
      cur = st.back(); st.pop_back();
      e.push_back(cur);
    } while(cur != k);
    auto comp = get_vertices_(e);
    g2.add_vertex();
    for(int w : comp) {
      g2.add_2edge(n + n2, w);
    }
    n2++;
  }
  void tarjan(int u, int p) {
    vis[u] = low[u] = ++tempo;
    auto nei = g.n_edges(u);
    for(int i = 0; i < nei.size(); i++) {
      int k = nei.index(i);
      int v = g.edge(k).to;

      if(!seen[k]) {
        seen[k] = seen[k^1] = 1;
        st.push_back(k);
      }

      if(!vis[v]) {
        tarjan(v, u);
        low[u] = min(low[u], low[v]);

        if(low[v] >= vis[u]) {
          process_component_(k);
        }
      } else {
        low[u] = min(low[u], vis[v]);
      }
    }
  }
};

template<typename V, typename E>
BlockCut<V, E> make_block_cut(const Graph<V, E>& g) {
  return BlockCut<V, E>(g);
}
} // namespace graph
} // namespace lib


#line 2 "Template.cpp"
#define int long long
using namespace std;
 
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define ms(v, x) memset((v), (x), sizeof(v))
#define all(v) (v).begin(), (v).end()
#define ff first
#define ss second
#define iopt ios::sync_with_stdio(false); cin.tie(0)
#define untie(p, a, b) decltype(p.first) a = p.first, decltype(p.second) b = p.second
#define TESTCASE(tn) cout << "Case #" << tn << ": "
 
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a%b); }

int floor2(int x, int y);
int ceil2(int x, int y) {
  if(y < 0) return ceil2(-x, -y);
  return x < 0 ? -floor2(-x, y) : (x + y - 1) / y;
}
int floor2(int x, int y) {
  if(y < 0) return floor2(-x, -y);
  return x < 0 ? -ceil2(-x, y) : x / y;
}
 
typedef pair<int, int> ii;
typedef long double LD;
typedef vector<int> vi;

#define TC_MAIN int32_t main() { iopt; int T; cin >> T; for(int i = 1; i <= T; i++) solve(i); }
#line 5 "tests/yosupo/biconnected-components.test.cpp"

using namespace lib;

int32_t main() {
  iopt;

  int n, m; cin >> n >> m;

  graph::Graph<int> g(n);

  for(int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    g.add_2edge(a, b);
  }

  auto bct = graph::make_block_cut(g);

  cout << bct.n_components() << endl;
  for(int i = 0; i < bct.n_components(); i++) {
    const auto comp = bct.component(i);
    cout << comp.size() << " ";
    for(const auto v : comp) cout << v << " ";
    cout << endl;
  }
}
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