Tifa's CP Library

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

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#ifndef TIFALIBS_GRAPH_DIJKSTRA
#define TIFALIBS_GRAPH_DIJKSTRA

#include "../ds/radix_heap.hpp"
#include "../util/traits.hpp"
#include "alistw.hpp"

namespace tifa_libs::graph {

// relax(now, to)
template <class T, class F, bool with_deg>
requires(!sint_c<T>) && requires(F relex, u32 now, u32 to) { relex(now, to); }
CEXP vec<T> dijkstra(alistw<T, with_deg> CR fg, u32 s, F &&relax, T INF = std::numeric_limits<T>::max() / 2 - 1) {
  auto &&g = fg.g;
  vec<T> dis(g.size(), INF);
  vecb vis(g.size());
  ds::rheap<T, u32> q;
  q.emplace(dis[s] = 0, s);
  while (!q.empty()) {
    auto [dis_now, u] = q.top();
    if (dis_now > INF) dis_now = INF;
    if (q.pop(); vis[u]) continue;
    for (vis[u] = true; auto [v, w] : g[u])
      if (dis[u] + w < dis[v])
        if (relax(u, v), dis[v] = dis[u] + w; !vis[v]) q.emplace(dis[v], v);
  }
  return dis;
}

}  // namespace tifa_libs::graph

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



#line 1 "src/code/ds/radix_heap.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/ds/radix_heap.hpp"

namespace tifa_libs::ds {

template <std::unsigned_integral K, class V, class C = std::less<K>>
class radix_heap {
  static CEXP u32 B = sizeof(K) * 8;
  static CEXP C comp{};
  arr<vecp<K, V>, B + 1> vs;
  arr<K, B + 1> ms;
  u32 s;
  K last;

 public:
  CEXPE radix_heap() : s(0), last(0) { std::ranges::fill(ms, K(-1)); }

  CEXP u32 size() const { return s; }
  CEXP bool empty() const { return !s; }
  CEXP void emplace(K key, cT_(V) val) {
    const K b = (K)std::bit_width(key ^ last);
    ++s, vs[b].emplace_back(key, val), ms[b] = min(key, ms[b], comp);
  }
  CEXP std::pair<K, V> top() {
    if (!~ms[0]) {
      const u32 idx = u32(std::ranges::find_if(ms, [](auto x) { return !!~x; }) - ms.begin());
      for (last = ms[idx]; auto &p : vs[idx]) {
        const K b = (K)std::bit_width(p.first ^ last);
        vs[b].emplace_back(p), ms[b] = min(p.first, ms[b], comp);
      }
      vs[idx].clear(), ms[idx] = K(-1);
    }
    return vs[0].back();
  }

  CEXP void pop() {
    if (top(), --s, vs[0].pop_back(); vs[0].empty()) ms[0] = K(-1);
  }
};

template <class K, class V>
using rheap = std::conditional_t<std::unsigned_integral<K>, ds::radix_heap<K, V>, pqg<std::pair<K, V>>>;
template <class K, class V>
using rheapg = std::conditional_t<std::unsigned_integral<K>, ds::radix_heap<K, V, std::greater<K>>, pq<std::pair<K, V>>>;

}  // namespace tifa_libs::ds


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



#line 5 "src/code/util/traits.hpp"

namespace tifa_libs {

template <class T>
concept iterable_c = requires(T v) {
  { v.begin() } -> std::same_as<TPN T::iterator>;
  { v.end() } -> std::same_as<TPN T::iterator>;
};

template <class T>
concept container_c = iterable_c<T> && !std::same_as<std::remove_cvref_t<T>, strn> && !std::same_as<std::remove_cvref_t<T>, strnv>;

template <class T>
CEXP bool is_char_v = std::is_same_v<T, char> || std::is_same_v<T, signed char> || std::is_same_v<T, unsigned char>;
template <class T>
concept char_c = is_char_v<T>;

template <class T>
CEXP bool is_s128_v = std::is_same_v<T, __int128_t> || std::is_same_v<T, __int128>;
template <class T>
concept s128_c = is_s128_v<T>;

template <class T>
CEXP bool is_u128_v = std::is_same_v<T, __uint128_t> || std::is_same_v<T, unsigned __int128>;
template <class T>
concept u128_c = is_u128_v<T>;

template <class T>
CEXP bool is_i128_v = is_s128_v<T> || is_u128_v<T>;
template <class T>
concept i128_c = is_u128_v<T>;

template <class T>
CEXP bool is_int_v = std::is_integral_v<T> || is_i128_v<T>;
template <class T>
concept int_c = is_int_v<T>;

template <class T>
CEXP bool is_sint_v = is_s128_v<T> || (is_int_v<T> && std::is_signed_v<T>);
template <class T>
concept sint_c = is_sint_v<T>;

template <class T>
CEXP bool is_uint_v = is_u128_v<T> || (is_int_v<T> && std::is_unsigned_v<T>);
template <class T>
concept uint_c = is_uint_v<T>;

template <class T>
concept mint_c = requires(T x) {
  { x.mod() } -> uint_c;
  { x.val() } -> uint_c;
};

template <class T>
concept dft_c = requires(T x, vec<TPN T::data_t> v, u32 n) {
  { x.size() } -> std::same_as<u32>;
  x.bzr(n);
  x.dif(v, n);
  x.dit(v, n);
};

template <class T>
concept ntt_c = dft_c<T> && requires(T x) {
  T::max_size;
  T::G;
};

template <class T>
CEXP bool is_arithm_v = std::is_arithmetic_v<T> || is_int_v<T>;
template <class T>
concept arithm_c = is_arithm_v<T>;

template <class T>
struct to_sint : std::make_signed<T> {};
template <>
struct to_sint<u128> {
  using type = u128;
};
template <>
struct to_sint<i128> {
  using type = u128;
};
template <class T>
using to_sint_t = TPN to_sint<T>::type;

template <class T>
struct to_uint : std::make_unsigned<T> {};
template <>
struct to_uint<u128> {
  using type = u128;
};
template <>
struct to_uint<i128> {
  using type = u128;
};
template <class T>
using to_uint_t = TPN to_uint<T>::type;

}  // namespace tifa_libs


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



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

namespace tifa_libs::graph {

template <class T, bool with_deg = false>
struct alistw {
  using weight_type = T;
  using value_type = vvecp<u32, T>;
  value_type g;
  u32 cnt_arc;
  vecu deg_in, deg_out;

  //! vertex ID: [0, n)
  CEXPE alistw(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, cT_(T) w) {
    g[u].emplace_back(v, w), ++cnt_arc;
    if CEXP (with_deg) ++deg_in[v], ++deg_out[u];
  }
};

}  // namespace tifa_libs::graph


#line 7 "src/code/graph/dijkstra.hpp"

namespace tifa_libs::graph {

// relax(now, to)
template <class T, class F, bool with_deg>
requires(!sint_c<T>) && requires(F relex, u32 now, u32 to) { relex(now, to); }
CEXP vec<T> dijkstra(alistw<T, with_deg> CR fg, u32 s, F &&relax, T INF = std::numeric_limits<T>::max() / 2 - 1) {
  auto &&g = fg.g;
  vec<T> dis(g.size(), INF);
  vecb vis(g.size());
  ds::rheap<T, u32> q;
  q.emplace(dis[s] = 0, s);
  while (!q.empty()) {
    auto [dis_now, u] = q.top();
    if (dis_now > INF) dis_now = INF;
    if (q.pop(); vis[u]) continue;
    for (vis[u] = true; auto [v, w] : g[u])
      if (dis[u] + w < dis[v])
        if (relax(u, v), dis[v] = dis[u] + w; !vis[v]) q.emplace(dis[v], v);
  }
  return dis;
}

}  // namespace tifa_libs::graph


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