test/yosupo/biconnected_components.test.cpp

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• Last update: 2024-09-01 12:11:12+09:00
• Problem: https://judge.yosupo.jp/problem/biconnected_components

Depends on

• 二点連結成分分解 (block-cut-tree (拡張)) (src/Graph/block_cut_tree.hpp)
• グラフ (src/Graph/Graph.hpp)
• CSR 表現を用いた二次元配列 他 (src/Internal/ListRange.hpp)

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/biconnected_components
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include "src/Graph/Graph.hpp"
#include "src/Graph/block_cut_tree.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 Graph g(N, M);
 for (int i= 0; i < M; ++i) cin >> g[i];
 auto bct= block_cut_tree(g).adjacency_vertex(0);
 int K= bct.size();
 cout << K - N << '\n';
 for (int i= N; i < K; ++i) {
  cout << bct[i].size();
  for (int v: bct[i]) cout << " " << v;
  cout << '\n';
 }
 return 0;
}

#line 1 "test/yosupo/biconnected_components.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/biconnected_components
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#line 2 "src/Internal/ListRange.hpp"
#include <vector>
#line 4 "src/Internal/ListRange.hpp"
#include <iterator>
#include <type_traits>
#define _LR(name, IT, CT) \
 template <class T> struct name { \
  using Iterator= typename std::vector<T>::IT; \
  Iterator bg, ed; \
  Iterator begin() const { return bg; } \
  Iterator end() const { return ed; } \
  size_t size() const { return std::distance(bg, ed); } \
  CT &operator[](int i) const { return bg[i]; } \
 }
_LR(ListRange, iterator, T);
_LR(ConstListRange, const_iterator, const T);
#undef _LR
template <class T> struct CSRArray {
 std::vector<T> dat;
 std::vector<int> p;
 size_t size() const { return p.size() - 1; }
 ListRange<T> operator[](int i) { return {dat.begin() + p[i], dat.begin() + p[i + 1]}; }
 ConstListRange<T> operator[](int i) const { return {dat.cbegin() + p[i], dat.cbegin() + p[i + 1]}; }
};
template <template <class> class F, class T> std::enable_if_t<std::disjunction_v<std::is_same<F<T>, ListRange<T>>, std::is_same<F<T>, ConstListRange<T>>, std::is_same<F<T>, CSRArray<T>>>, std::ostream &> operator<<(std::ostream &os, const F<T> &r) {
 os << '[';
 for (int _= 0, __= r.size(); _ < __; ++_) os << (_ ? ", " : "") << r[_];
 return os << ']';
}
#line 3 "src/Graph/Graph.hpp"
struct Edge: std::pair<int, int> {
 using std::pair<int, int>::pair;
 Edge &operator--() { return --first, --second, *this; }
 int to(int v) const { return first ^ second ^ v; }
 friend std::istream &operator>>(std::istream &is, Edge &e) { return is >> e.first >> e.second, is; }
};
struct Graph: std::vector<Edge> {
 size_t n;
 Graph(size_t n= 0, size_t m= 0): vector(m), n(n) {}
 size_t vertex_size() const { return n; }
 size_t edge_size() const { return size(); }
 size_t add_vertex() { return n++; }
 size_t add_edge(int s, int d) { return emplace_back(s, d), size() - 1; }
 size_t add_edge(Edge e) { return emplace_back(e), size() - 1; }
#define _ADJ_FOR(a, b) \
 for (auto [u, v]: *this) a; \
 for (size_t i= 0; i < n; ++i) p[i + 1]+= p[i]; \
 for (int i= size(); i--;) { \
  auto [u, v]= (*this)[i]; \
  b; \
 }
#define _ADJ(a, b) \
 vector<int> p(n + 1), c(size() << !dir); \
 if (!dir) { \
  _ADJ_FOR((++p[u], ++p[v]), (c[--p[u]]= a, c[--p[v]]= b)) \
 } else if (dir > 0) { \
  _ADJ_FOR(++p[u], c[--p[u]]= a) \
 } else { \
  _ADJ_FOR(++p[v], c[--p[v]]= b) \
 } \
 return {c, p}
 CSRArray<int> adjacency_vertex(int dir) const { _ADJ(v, u); }
 CSRArray<int> adjacency_edge(int dir) const { _ADJ(i, i); }
#undef _ADJ
#undef _ADJ_FOR
};
#line 3 "src/Graph/block_cut_tree.hpp"
// [0,n) : vertex
// [n,n+b) : block
// deg(v) > 1 -> articulation point
Graph block_cut_tree(const CSRArray<int> &adj) {
 const int n= adj.size();
 std::vector<int> ord(n), par(n, -2), dat(adj.p.begin(), adj.p.begin() + n);
 int k= 0;
 for (int s= n, p; s--;)
  if (par[s] == -2)
   for (par[p= s]= -1; p >= 0;) {
    if (dat[p] == adj.p[p]) ord[k++]= p;
    if (dat[p] == adj.p[p + 1]) p= par[p];
    else if (int q= adj.dat[dat[p]++]; par[q] == -2) par[q]= p, p= q;
   }
 for (int i= n; i--;) dat[ord[i]]= i;
 auto low= dat;
 for (int v= n; v--;)
  for (int u: adj[v]) low[v]= std::min(low[v], dat[u]);
 for (int i= n; i--;)
  if (int p= ord[i], pp= par[p]; pp >= 0) low[pp]= std::min(low[pp], low[p]);
 Graph ret(k);
 for (int p: ord)
  if (par[p] >= 0) {
   if (int pp= par[p]; low[p] < dat[pp]) ret.add_edge(low[p]= low[pp], p);
   else ret.add_vertex(), ret.add_edge(k, pp), ret.add_edge(k, p), low[p]= k++;
  }
 for (int s= 0; s < n; ++s)
  if (!adj[s].size()) ret.add_edge(ret.add_vertex(), s);
 return ret;
}
Graph block_cut_tree(const Graph &g) { return block_cut_tree(g.adjacency_vertex(0)); }
#line 7 "test/yosupo/biconnected_components.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N, M;
 cin >> N >> M;
 Graph g(N, M);
 for (int i= 0; i < M; ++i) cin >> g[i];
 auto bct= block_cut_tree(g).adjacency_vertex(0);
 int K= bct.size();
 cout << K - N << '\n';
 for (int i= N; i < K; ++i) {
  cout << bct[i].size();
  for (int v: bct[i]) cout << " " << v;
  cout << '\n';
 }
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	example_00	AC	6 ms	4 MB
g++-13	example_01	AC	5 ms	4 MB
g++-13	example_02	AC	5 ms	4 MB
g++-13	large_cycle_00	AC	148 ms	34 MB
g++-13	max_line_clique_00	AC	134 ms	24 MB
g++-13	max_random_00	AC	159 ms	35 MB
g++-13	max_random_2_00	AC	191 ms	35 MB
g++-13	max_random_2_01	AC	170 ms	35 MB
g++-13	max_random_2_02	AC	180 ms	35 MB
g++-13	max_star_00	AC	172 ms	42 MB
g++-13	max_tree_00	AC	181 ms	43 MB
g++-13	min_00	AC	6 ms	4 MB
g++-13	min_01	AC	5 ms	4 MB
g++-13	min_02	AC	5 ms	4 MB
g++-13	random_1_00	AC	139 ms	25 MB
g++-13	random_2_00	AC	144 ms	27 MB
g++-13	random_2_01	AC	110 ms	27 MB
g++-13	random_2_02	AC	72 ms	14 MB
g++-13	small_random_1_00	AC	6 ms	4 MB
g++-13	small_random_2_00	AC	5 ms	4 MB
g++-13	small_random_2_01	AC	5 ms	4 MB
g++-13	small_random_2_02	AC	5 ms	4 MB
clang++-18	example_00	AC	6 ms	4 MB
clang++-18	example_01	AC	6 ms	4 MB
clang++-18	example_02	AC	6 ms	4 MB
clang++-18	large_cycle_00	AC	171 ms	35 MB
clang++-18	max_line_clique_00	AC	127 ms	24 MB
clang++-18	max_random_00	AC	176 ms	35 MB
clang++-18	max_random_2_00	AC	167 ms	35 MB
clang++-18	max_random_2_01	AC	163 ms	35 MB
clang++-18	max_random_2_02	AC	177 ms	35 MB
clang++-18	max_star_00	AC	184 ms	43 MB
clang++-18	max_tree_00	AC	198 ms	43 MB
clang++-18	min_00	AC	6 ms	4 MB
clang++-18	min_01	AC	6 ms	4 MB
clang++-18	min_02	AC	6 ms	4 MB
clang++-18	random_1_00	AC	132 ms	26 MB
clang++-18	random_2_00	AC	139 ms	27 MB
clang++-18	random_2_01	AC	105 ms	27 MB
clang++-18	random_2_02	AC	71 ms	14 MB
clang++-18	small_random_1_00	AC	6 ms	4 MB
clang++-18	small_random_2_00	AC	5 ms	4 MB
clang++-18	small_random_2_01	AC	5 ms	4 MB
clang++-18	small_random_2_02	AC	5 ms	4 MB

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