強連結成分分解 (src/Graph/StronglyConnectedComponents.hpp)

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Last update: 2024-02-19 15:31:52+09:00
Include: #include "src/Graph/StronglyConnectedComponents.hpp"

強連結成分はトポロジカルソートされている

メンバ関数

メンバ関数	概要
`StronglyConnectedComponents(g)`	コンストラクタ. 引数は `Graph` クラス
`size()`	強連結成分の個数を返す
`block(k)`	k 番目の強連結成分の頂点集合を返す
`operator()(i)`	頂点 i が属する強連結成分が何番目かを返す
`dag()`	強連結成分を一つの頂点に潰したDAGを返す

Depends on

Required by

2-SAT (src/Misc/TwoSatisfiability.hpp)

Verified with

Code

#pragma once
#include <algorithm>
#include "src/Graph/Graph.hpp"
class StronglyConnectedComponents {
 std::vector<int> m, q, b;
public:
 StronglyConnectedComponents(const Graph &g) {
  const int n= g.vertex_size();
  m.assign(n, -2), b.resize(n);
  {
   auto adj= g.adjacency_vertex(1);
   std::vector<int> c(adj.p.begin(), adj.p.begin() + n);
   for (int s= 0, k= n, p; s < n; ++s)
    if (m[s] == -2)
     for (m[p= s]= -1; p >= 0;) {
      if (c[p] == adj.p[p + 1]) b[--k]= p, p= m[p];
      else if (int w= adj.dat[c[p]++]; m[w] == -2) m[w]= p, p= w;
     }
  }
  auto adj= g.adjacency_vertex(-1);
  std::vector<char> z(n);
  int k= 0, p= 0;
  q= {0};
  for (int s: b)
   if (!z[s]) {
    for (z[m[k++]= s]= 1; p < k; ++p)
     for (int u: adj[m[p]])
      if (!z[u]) z[m[k++]= u]= 1;
    q.push_back(k);
   }
  for (int i= q.size() - 1; i--;)
   while (k > q[i]) b[m[--k]]= i;
 }
 size_t size() const { return q.size() - 1; }
 ConstListRange<int> block(int k) const { return {m.cbegin() + q[k], m.cbegin() + q[k + 1]}; }
 int operator()(int i) const { return b[i]; }
 Graph dag(const Graph &g) const {
  Graph ret(size());
  for (auto [s, d]: g)
   if (b[s] != b[d]) ret.add_edge(b[s], b[d]);
  return std::sort(ret.begin(), ret.end()), ret.erase(std::unique(ret.begin(), ret.end()), ret.end()), ret;
 }
};

#line 2 "src/Graph/StronglyConnectedComponents.hpp"
#include <algorithm>
#line 2 "src/Internal/ListRange.hpp"
#include <vector>
#include <iostream>
#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 4 "src/Graph/StronglyConnectedComponents.hpp"
class StronglyConnectedComponents {
 std::vector<int> m, q, b;
public:
 StronglyConnectedComponents(const Graph &g) {
  const int n= g.vertex_size();
  m.assign(n, -2), b.resize(n);
  {
   auto adj= g.adjacency_vertex(1);
   std::vector<int> c(adj.p.begin(), adj.p.begin() + n);
   for (int s= 0, k= n, p; s < n; ++s)
    if (m[s] == -2)
     for (m[p= s]= -1; p >= 0;) {
      if (c[p] == adj.p[p + 1]) b[--k]= p, p= m[p];
      else if (int w= adj.dat[c[p]++]; m[w] == -2) m[w]= p, p= w;
     }
  }
  auto adj= g.adjacency_vertex(-1);
  std::vector<char> z(n);
  int k= 0, p= 0;
  q= {0};
  for (int s: b)
   if (!z[s]) {
    for (z[m[k++]= s]= 1; p < k; ++p)
     for (int u: adj[m[p]])
      if (!z[u]) z[m[k++]= u]= 1;
    q.push_back(k);
   }
  for (int i= q.size() - 1; i--;)
   while (k > q[i]) b[m[--k]]= i;
 }
 size_t size() const { return q.size() - 1; }
 ConstListRange<int> block(int k) const { return {m.cbegin() + q[k], m.cbegin() + q[k + 1]}; }
 int operator()(int i) const { return b[i]; }
 Graph dag(const Graph &g) const {
  Graph ret(size());
  for (auto [s, d]: g)
   if (b[s] != b[d]) ret.add_edge(b[s], b[d]);
  return std::sort(ret.begin(), ret.end()), ret.erase(std::unique(ret.begin(), ret.end()), ret.end()), ret;
 }
};