Tifa's CP Library

:heavy_check_mark: kosaraju (src/code/graph/kosaraju.hpp)

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#ifndef TIFALIBS_GRAPH_KOSARAJU
#define TIFALIBS_GRAPH_KOSARAJU

#include "alist.hpp"
#include "alistr.hpp"

namespace tifa_libs::graph {

template <bool with_deg = false>
class kosaraju {
  const alist<with_deg>::value_type &g, &rev_g;

 public:
  alist<with_deg> dag;
  vecu scc_id;
  vvecu belongs;

  explicit constexpr kosaraju(alist<with_deg> const &g) : kosaraju(g, alistr(g)) {}
  constexpr kosaraju(alist<with_deg> const &g, alist<with_deg> const &rev_g) : g(g.g), rev_g(rev_g.g) { build(); }

 private:
  constexpr void build() {
    vecb vis(g.size());
    vecu ord;
    auto dfs = [&, this](auto &&dfs, u32 idx) {
      if (vis[idx]) return;
      vis[idx] = true;
      for (auto to : g[idx]) dfs(dfs, to);
      ord.push_back(idx);
    };
    auto rdfs = [this](auto &&rdfs, u32 idx, u32 cnt) {
      if (~scc_id[idx]) return;
      scc_id[idx] = cnt;
      for (auto to : rev_g[idx]) rdfs(rdfs, to, cnt);
    };
    for (u32 i = 0; i < g.size(); ++i) dfs(dfs, i);
    std::ranges::reverse(ord);
    scc_id.resize(g.size(), -1_u32);
    u32 cnt = 0;
    for (u32 i : ord)
      if (!~scc_id[i]) rdfs(rdfs, i, cnt++);
    dag.g.resize(cnt);
    belongs.resize(cnt);
    for (u32 i = 0; i < g.size(); ++i) {
      belongs[scc_id[i]].push_back(i);
      for (auto to : g[i])
        if (u32 x = scc_id[i], y = scc_id[to]; x != y) dag.add_arc(x, y);
    }
  }
};

}  // namespace tifa_libs::graph

#endif
#line 1 "src/code/graph/kosaraju.hpp"



#line 1 "src/code/graph/alist.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;

using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;

using f32 = float;
using f64 = double;
using f128 = long double;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
template <class T>
using vec = std::vector<T>;
template <class T>
using vvec = vec<vec<T>>;
template <class T>
using v3ec = vec<vvec<T>>;
template <class U, class T>
using vecp = vec<std::pair<U, T>>;
template <class U, class T>
using vvecp = vvec<std::pair<U, T>>;
template <class T>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<T>>;

template <class T, class C = std::less<T>>
using pq = std::priority_queue<T, vec<T>, C>;
template <class T>
using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

inline const auto fn_0 = [](auto&&...) {};


#line 5 "src/code/graph/alist.hpp"

namespace tifa_libs::graph {

template <bool with_deg = false>
struct alist {
  using weight_type = u32;
  using value_type = vvecu;
  value_type g;
  u32 cnt_arc;
  vecu deg_in;

  //! vertex ID: [0, n)
  explicit constexpr alist(u32 n = 0) : g(n), cnt_arc(0), deg_in(0) {
    if constexpr (with_deg) deg_in.resize(n);
  }

  constexpr void add_arc(u32 u, u32 v) {
    g[u].push_back(v), ++cnt_arc;
    if constexpr (with_deg) ++deg_in[v];
  }
};
template <class G>
concept is_alist = (std::is_base_of_v<alist<true>, G> || std::is_base_of_v<alist<false>, G>);

}  // namespace tifa_libs::graph


#line 1 "src/code/graph/alistr.hpp"



#line 5 "src/code/graph/alistr.hpp"

namespace tifa_libs::graph {

template <bool with_deg>
constexpr alist<with_deg> alistr(alist<with_deg> const& ag) {
  alist ret((u32)ag.g.size());
  for (u32 u = 0; u < ag.g.size(); ++u)
    for (u32 v : ag.g[u]) ret.add_arc(v, u);
  return ret;
}

}  // namespace tifa_libs::graph


#line 6 "src/code/graph/kosaraju.hpp"

namespace tifa_libs::graph {

template <bool with_deg = false>
class kosaraju {
  const alist<with_deg>::value_type &g, &rev_g;

 public:
  alist<with_deg> dag;
  vecu scc_id;
  vvecu belongs;

  explicit constexpr kosaraju(alist<with_deg> const &g) : kosaraju(g, alistr(g)) {}
  constexpr kosaraju(alist<with_deg> const &g, alist<with_deg> const &rev_g) : g(g.g), rev_g(rev_g.g) { build(); }

 private:
  constexpr void build() {
    vecb vis(g.size());
    vecu ord;
    auto dfs = [&, this](auto &&dfs, u32 idx) {
      if (vis[idx]) return;
      vis[idx] = true;
      for (auto to : g[idx]) dfs(dfs, to);
      ord.push_back(idx);
    };
    auto rdfs = [this](auto &&rdfs, u32 idx, u32 cnt) {
      if (~scc_id[idx]) return;
      scc_id[idx] = cnt;
      for (auto to : rev_g[idx]) rdfs(rdfs, to, cnt);
    };
    for (u32 i = 0; i < g.size(); ++i) dfs(dfs, i);
    std::ranges::reverse(ord);
    scc_id.resize(g.size(), -1_u32);
    u32 cnt = 0;
    for (u32 i : ord)
      if (!~scc_id[i]) rdfs(rdfs, i, cnt++);
    dag.g.resize(cnt);
    belongs.resize(cnt);
    for (u32 i = 0; i < g.size(); ++i) {
      belongs[scc_id[i]].push_back(i);
      for (auto to : g[i])
        if (u32 x = scc_id[i], y = scc_id[to]; x != y) dag.add_arc(x, y);
    }
  }
};

}  // namespace tifa_libs::graph


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