Tifa's CP Library

:heavy_check_mark: cantor_seq2val (src/code/edh/cantor_seq2val.hpp)

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#ifndef TIFALIBS_EDH_CANTOR_SEQ2VAL
#define TIFALIBS_EDH_CANTOR_SEQ2VAL

#include "../comb/gen_fact.hpp"

namespace tifa_libs {

constexpr u64 cantor_seq2val(vecu const &s, vecu64 const &fact, u64 mod = -1_u64) {
  u32 n = (u32)s.size();
  u64 ret = 1;
  for (u32 i = 0; i < n; ++i) (ret += math::mul_mod_u(s[i], fact[n - i - 1], mod)) %= mod;
  return ret;
}
constexpr u64 cantor_seq2val(vecu const &s, u64 mod = -1_u64) { return cantor_seq2val(s, math::gen_fact((u32)s.size(), mod), mod); }

}  // namespace tifa_libs

#endif
#line 1 "src/code/edh/cantor_seq2val.hpp"



#line 1 "src/code/comb/gen_fact.hpp"



#line 1 "src/code/math/mul_mod_u.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&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };


#line 5 "src/code/math/mul_mod_u.hpp"

namespace tifa_libs::math {

constexpr u64 mul_mod_u(u64 a, u64 b, u64 mod) {
  if (std::bit_width(a) + std::bit_width(b) <= 64) return a * b % mod;
  else return (u64)((u128)a * b % mod);
}

}  // namespace tifa_libs::math


#line 5 "src/code/comb/gen_fact.hpp"

namespace tifa_libs::math {

// i! from i=0..n-1
constexpr vecu64 gen_fact(u32 n, u64 mod) {
  if (n == 0) return {};
  if (n == 1) return {1};
  vecu64 ans(n);
  ans[0] = ans[1] = 1;
  for (u32 i = 2; i < n; ++i) ans[i] = mul_mod_u(ans[i - 1], i, mod);
  return ans;
}
// i! from i=0..n-1
template <class mint>
constexpr vec<mint> gen_fact(u32 n) {
  vec<mint> ans(n);
  auto _ = gen_fact(n, mint::mod());
  for (u32 i = 0; i < n; ++i) ans[i] = _[i];
  return ans;
}

}  // namespace tifa_libs::math


#line 5 "src/code/edh/cantor_seq2val.hpp"

namespace tifa_libs {

constexpr u64 cantor_seq2val(vecu const &s, vecu64 const &fact, u64 mod = -1_u64) {
  u32 n = (u32)s.size();
  u64 ret = 1;
  for (u32 i = 0; i < n; ++i) (ret += math::mul_mod_u(s[i], fact[n - i - 1], mod)) %= mod;
  return ret;
}
constexpr u64 cantor_seq2val(vecu const &s, u64 mod = -1_u64) { return cantor_seq2val(s, math::gen_fact((u32)s.size(), mod), mod); }

}  // namespace tifa_libs


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