Tifa's CP Library

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

Depends on

Verified with

Code

#ifndef TIFALIBS_GRAPH_EULER_TRAIL
#define TIFALIBS_GRAPH_EULER_TRAIL

#include "alist.hpp"

namespace tifa_libs::graph {
namespace euler_trail_impl_ {
template <bool cyc>
CEXP std::optional<vecptu> run_(u32 n, u32 m, cT_(vvecptu) g, u32 s) {
  vec<vecptu::const_iterator> its(n);
  flt_ (u32, i, 0, n) its[i] = g[i].begin();
  veci f(n);
  if CEXP (!cyc) ++f[s];
  vecb vis(m);
  vecptu ret, stk = {{s, -1_u32}};
  while (!stk.empty()) {
    auto [i, p] = stk.back();
    auto &it = its[i];
    if (it == g[i].end()) {
      ret.emplace_back(i, p), stk.pop_back();
      continue;
    }
    if (auto [j, e] = *(it++); !vis[e]) --f[i], ++f[j], stk.emplace_back(j, e), vis[e] = true;
  }
  if (ret.size() != m + 1) return {};
  for (i32 i : f)
    if (i < 0) return {};
  return std::ranges::reverse(ret), ret;
}
}  // namespace euler_trail_impl_

// @return vector of {v, eid} of Eulerian trail if found
// edges[eid[i]] = v[i-1] -> v[i], eid[0] = -1
template <bool directed, bool cycle = false>
CEXP std::optional<vecptu> euler_trail(u32 n, cT_(vecptu) edges) {
  vvecptu g(n);
  vecu deg_in(0);
  if CEXP (directed) deg_in.resize(n);
  u32 e = 0;
  for (auto [u, v] : edges) {
    g[u].emplace_back(v, e);
    if CEXP (directed) ++deg_in[v];
    else g[v].emplace_back(u, e);
    ++e;
  }
  u32 s = 0;
  flt_ (u32, i, 1, (u32)g.size())
    if (!g[i].empty()) s = i;
  flt_ (u32, i, 0, (u32)g.size())
    if CEXP (directed) {
      if (deg_in[i] < g[i].size()) s = i;
    } else if (g[i].size() & 1) s = i;
  return euler_trail_impl_::run_<cycle>(n, (u32)edges.size(), g, s);
}
template <class G>
CEXP bool is_eulerian(G CR g) {
  const u32 n = (u32)g.g.size();
  assert(n == g.deg_in.size());
  vecb vis(n);
  u32 cnt = 0;
  auto f = [&](auto &&f, u32 x) -> void {
    for (auto v : g.g[x]) {
      ++cnt;
      if CEXP (is_alist<G>) {
        if (!vis[v]) vis[v] = 1, f(f, v);
      } else if (!vis[v.first]) vis[v.first] = 1, f(f, v.first);
    }
  };
  vis[0] = 1, f(f, 0);
  if (g.cnt_arc != cnt) return 0;
  flt_ (u32, i, 0, n)
    if (g.deg_in[i] != g.deg_out[i]) return 0;
  return 1;
}

}  // namespace tifa_libs::graph

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



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



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



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

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

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

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
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 T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
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, 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>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


#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, deg_out;

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

  CEXP void add_arc(u32 u, u32 v) {
    g[u].push_back(v), ++cnt_arc;
    if CEXP (with_deg) ++deg_in[v], ++deg_out[u];
  }
};
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 5 "src/code/graph/euler_trail.hpp"

namespace tifa_libs::graph {
namespace euler_trail_impl_ {
template <bool cyc>
CEXP std::optional<vecptu> run_(u32 n, u32 m, cT_(vvecptu) g, u32 s) {
  vec<vecptu::const_iterator> its(n);
  flt_ (u32, i, 0, n) its[i] = g[i].begin();
  veci f(n);
  if CEXP (!cyc) ++f[s];
  vecb vis(m);
  vecptu ret, stk = {{s, -1_u32}};
  while (!stk.empty()) {
    auto [i, p] = stk.back();
    auto &it = its[i];
    if (it == g[i].end()) {
      ret.emplace_back(i, p), stk.pop_back();
      continue;
    }
    if (auto [j, e] = *(it++); !vis[e]) --f[i], ++f[j], stk.emplace_back(j, e), vis[e] = true;
  }
  if (ret.size() != m + 1) return {};
  for (i32 i : f)
    if (i < 0) return {};
  return std::ranges::reverse(ret), ret;
}
}  // namespace euler_trail_impl_

// @return vector of {v, eid} of Eulerian trail if found
// edges[eid[i]] = v[i-1] -> v[i], eid[0] = -1
template <bool directed, bool cycle = false>
CEXP std::optional<vecptu> euler_trail(u32 n, cT_(vecptu) edges) {
  vvecptu g(n);
  vecu deg_in(0);
  if CEXP (directed) deg_in.resize(n);
  u32 e = 0;
  for (auto [u, v] : edges) {
    g[u].emplace_back(v, e);
    if CEXP (directed) ++deg_in[v];
    else g[v].emplace_back(u, e);
    ++e;
  }
  u32 s = 0;
  flt_ (u32, i, 1, (u32)g.size())
    if (!g[i].empty()) s = i;
  flt_ (u32, i, 0, (u32)g.size())
    if CEXP (directed) {
      if (deg_in[i] < g[i].size()) s = i;
    } else if (g[i].size() & 1) s = i;
  return euler_trail_impl_::run_<cycle>(n, (u32)edges.size(), g, s);
}
template <class G>
CEXP bool is_eulerian(G CR g) {
  const u32 n = (u32)g.g.size();
  assert(n == g.deg_in.size());
  vecb vis(n);
  u32 cnt = 0;
  auto f = [&](auto &&f, u32 x) -> void {
    for (auto v : g.g[x]) {
      ++cnt;
      if CEXP (is_alist<G>) {
        if (!vis[v]) vis[v] = 1, f(f, v);
      } else if (!vis[v.first]) vis[v.first] = 1, f(f, v.first);
    }
  };
  vis[0] = 1, f(f, 0);
  if (g.cnt_arc != cnt) return 0;
  flt_ (u32, i, 0, n)
    if (g.deg_in[i] != g.deg_out[i]) return 0;
  return 1;
}

}  // namespace tifa_libs::graph


Back to top page