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#define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components" #include <iostream> #include <vector> #include "../../graph/base.hpp" #include "../../tree/block_cut_tree.hpp" int main() { int n, m; std::cin >> n >> m; ebi::Graph<int> g(n); g.read_graph(m, 0); ebi::block_cut_tree bct(g); auto bc = bct.bcc(); int k = bc.size(); std::cout << k << '\n'; for (auto vs : bc) { std::cout << vs.size(); for (auto v : vs) { std::cout << " " << v; } std::cout << '\n'; } }
#line 1 "test/graph/Biconnected_Components.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/biconnected_components" #include <iostream> #include <vector> #line 2 "graph/base.hpp" #include <cassert> #line 5 "graph/base.hpp" #include <ranges> #line 7 "graph/base.hpp" #line 2 "data_structure/simple_csr.hpp" #line 4 "data_structure/simple_csr.hpp" #include <utility> #line 6 "data_structure/simple_csr.hpp" namespace ebi { template <class E> struct simple_csr { simple_csr() = default; simple_csr(int n, const std::vector<std::pair<int, E>>& elements) : start(n + 1, 0), elist(elements.size()) { for (auto e : elements) { start[e.first + 1]++; } for (auto i : std::views::iota(0, n)) { start[i + 1] += start[i]; } auto counter = start; for (auto [i, e] : elements) { elist[counter[i]++] = e; } } simple_csr(const std::vector<std::vector<E>>& es) : start(es.size() + 1, 0) { int n = es.size(); for (auto i : std::views::iota(0, n)) { start[i + 1] = (int)es[i].size() + start[i]; } elist.resize(start.back()); for (auto i : std::views::iota(0, n)) { std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]); } } int size() const { return (int)start.size() - 1; } const auto operator[](int i) const { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } auto operator[](int i) { return std::ranges::subrange(elist.begin() + start[i], elist.begin() + start[i + 1]); } const auto operator()(int i, int l, int r) const { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } auto operator()(int i, int l, int r) { return std::ranges::subrange(elist.begin() + start[i] + l, elist.begin() + start[i + 1] + r); } private: std::vector<int> start; std::vector<E> elist; }; } // namespace ebi #line 9 "graph/base.hpp" namespace ebi { template <class T> struct Edge { int from, to; T cost; int id; }; template <class E> struct Graph { using cost_type = E; using edge_type = Edge<cost_type>; Graph(int n_) : n(n_) {} Graph() = default; void add_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); edges.emplace_back(edge_type{u, v, c, m++}); } void add_undirected_edge(int u, int v, cost_type c) { buff.emplace_back(u, edge_type{u, v, c, m}); buff.emplace_back(v, edge_type{v, u, c, m}); edges.emplace_back(edge_type{u, v, c, m}); m++; } void read_tree(int offset = 1, bool is_weighted = false) { read_graph(n - 1, offset, false, is_weighted); } void read_parents(int offset = 1) { for (auto i : std::views::iota(1, n)) { int p; std::cin >> p; p -= offset; add_undirected_edge(p, i, 1); } build(); } void read_graph(int e, int offset = 1, bool is_directed = false, bool is_weighted = false) { for (int i = 0; i < e; i++) { int u, v; std::cin >> u >> v; u -= offset; v -= offset; if (is_weighted) { cost_type c; std::cin >> c; if (is_directed) { add_edge(u, v, c); } else { add_undirected_edge(u, v, c); } } else { if (is_directed) { add_edge(u, v, 1); } else { add_undirected_edge(u, v, 1); } } } build(); } void build() { assert(!prepared); csr = simple_csr<edge_type>(n, buff); buff.clear(); prepared = true; } int size() const { return n; } int node_number() const { return n; } int edge_number() const { return m; } edge_type get_edge(int i) const { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { return csr[i]; } private: int n, m = 0; std::vector<std::pair<int,edge_type>> buff; std::vector<edge_type> edges; simple_csr<edge_type> csr; bool prepared = false; }; } // namespace ebi #line 2 "tree/block_cut_tree.hpp" #line 4 "tree/block_cut_tree.hpp" #line 2 "graph/biconnected_components.hpp" #line 2 "graph/low_link.hpp" #include <algorithm> #line 6 "graph/low_link.hpp" #line 8 "graph/low_link.hpp" namespace ebi { template <class T> struct low_link { private: void dfs(int v, int par = -1) { static int k = 0; low[v] = ord[v] = k++; int cnt = 0; bool is_arti = false, is_second = false; for (auto e : g[v]) { int nv = e.to; if (ord[nv] == -1) { cnt++; dfs(nv, v); low[v] = std::min(low[v], low[nv]); is_arti |= (par != -1) && (low[nv] >= ord[v]); if (ord[v] < low[nv]) { _bridge.emplace_back(std::minmax(v, nv)); } } else if (nv != par || is_second) { low[v] = std::min(low[v], ord[nv]); } else { is_second = true; } } is_arti |= par == -1 && cnt > 1; if (is_arti) _articulation.emplace_back(v); } public: low_link(const Graph<T> &g) : n(g.size()), g(g), ord(n, -1), low(n) { for (int i = 0; i < n; i++) { if (ord[i] == -1) dfs(i); } } std::vector<int> articulation() const { return _articulation; } std::vector<std::pair<int, int>> bridge() const { return _bridge; } protected: int n; Graph<T> g; std::vector<int> ord, low, _articulation; std::vector<std::pair<int, int>> _bridge; }; } // namespace ebi #line 4 "graph/biconnected_components.hpp" namespace ebi { template <class T> struct biconnected_components : low_link<T> { private: void dfs(int v, int par = -1) { used[v] = true; for (auto e : this->g[v]) { int nv = e.to; if (nv == par) continue; if (!used[nv] || this->ord[nv] < this->ord[v]) { tmp.emplace_back(std::minmax(v, nv)); } if (!used[nv]) { dfs(nv, v); if (this->low[nv] >= this->ord[v]) { bc.emplace_back(); while (true) { auto e = tmp.back(); bc.back().emplace_back(e); tmp.pop_back(); if (e.first == std::min(v, nv) && e.second == std::max(v, nv)) { break; } } } } } } public: biconnected_components(const Graph<T> &g) : low_link<T>(g), used(this->n, false) { for (int i = 0; i < this->n; i++) { if (!used[i]) dfs(i); } } protected: std::vector<bool> used; std::vector<std::vector<std::pair<int, int>>> bc; std::vector<std::pair<int, int>> tmp; }; } // namespace ebi #line 6 "tree/block_cut_tree.hpp" namespace ebi { template <class T> struct block_cut_tree : biconnected_components<T> { public: block_cut_tree(const Graph<T> &g) : biconnected_components<T>(g), rev(this->n, -1) { int cnt = 0; for (auto v : this->_articulation) { rev[v] = cnt++; } int sz = cnt + this->bc.size(); tree.resize(sz); std::vector<int> last(this->n, -1); for (int i = cnt; i < sz; i++) { for (auto e : this->bc[i - cnt]) { for (auto v : {e.first, e.second}) { if (rev[v] != -1 && rev[v] < cnt) { if (std::exchange(last[v], i) != i) { tree[i].emplace_back(rev[v]); tree[rev[v]].emplace_back(i); } } else { rev[v] = i; } } } } groups.resize(sz); for (int i = 0; i < this->n; i++) { if (rev[i] < 0) { rev[i] = sz++; groups.emplace_back(); tree.emplace_back(); } groups[rev[i]].emplace_back(i); } } std::vector<std::vector<int>> bcc() { int cnt = this->_articulation.size(); int sz = groups.size() - cnt; std::vector _bcc(sz, std::vector<int>()); for (int i = 0; i < sz; i++) { _bcc[i] = groups[cnt + i]; for (auto nv : tree[cnt + i]) { assert(0 <= nv && nv < cnt); assert(groups[nv].size() == 1); _bcc[i].emplace_back(groups[nv][0]); } } return _bcc; } private: std::vector<int> rev; std::vector<std::vector<int>> tree; std::vector<std::vector<int>> groups; }; } // namespace ebi #line 8 "test/graph/Biconnected_Components.test.cpp" int main() { int n, m; std::cin >> n >> m; ebi::Graph<int> g(n); g.read_graph(m, 0); ebi::block_cut_tree bct(g); auto bc = bct.bcc(); int k = bc.size(); std::cout << k << '\n'; for (auto vs : bc) { std::cout << vs.size(); for (auto v : vs) { std::cout << " " << v; } std::cout << '\n'; } }