Tifa's CP Library

:heavy_check_mark: bsgs (src/code/nt/bsgs.hpp)

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#ifndef TIFALIBS_MATH_BSGS
#define TIFALIBS_MATH_BSGS

#include "../edh/hash_splitmix64.hpp"
#include "../math/isqrt.hpp"
#include "../math/qpow_mod.hpp"

namespace tifa_libs::math {

// solve a^x=b (mod m)
//! gcd(a, m) == 1 required
inline std::optional<u64> bsgs(u64 a, u64 b, u64 m) {
  a %= m;
  hmap<u64, u64> hmp;
  u64 sqrt_m = isqrt(m), s = mul_mod_u(a, b, m);
  if (sqrt_m * sqrt_m < m) ++sqrt_m;
  for (u64 i = 1; i <= sqrt_m; ++i, s = mul_mod_u(s, a, m)) hmp[s] = i;
  u64 _ = qpow_mod(a, sqrt_m, m);
  s = _;
  for (u64 i = 1; i <= sqrt_m; ++i, s = mul_mod_u(s, _, m))
    if (hmp[s] && i * sqrt_m >= hmp[s]) return i * sqrt_m - hmp[s];
  return {};
}

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/nt/bsgs.hpp"



#line 1 "src/code/edh/hash_splitmix64.hpp"



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

namespace tifa_libs {

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

template <class T>
concept container_c = iterable_c<T> && !std::derived_from<T, std::basic_string<typename T::value_type>>;

template <class T>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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>
constexpr 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 = typename 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 = typename to_uint<T>::type;

}  // namespace tifa_libs


#line 5 "src/code/edh/hash_splitmix64.hpp"

namespace tifa_libs {

class hash_splitmix64 {
  static inline u64 seed = 114514;
  static constexpr u64 splitmix64(u64 x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  static constexpr u64 append(u64 x, u64 y) { return x ^ (y >> 1) ^ ((y & 1) << 63); }

 public:
  explicit hash_splitmix64() { set_seed(); }
  explicit constexpr hash_splitmix64(u64 s) { set_seed(s); }

  static void set_seed() { seed = (u64)std::chrono::steady_clock::now().time_since_epoch().count(); }
  static constexpr void set_seed(u64 s) { seed = s; }
  u64 operator()(u64 x) const { return splitmix64(x + seed); }

  template <class T, class U>
  u64 operator()(std::pair<T, U> const &p) const { return append((*this)(p.first), (*this)(p.second)); }
  template <class... Ts>
  u64 operator()(std::tuple<Ts...> const &tp) const {
    u64 ret = 0;
    std::apply([&](Ts const &...targs) { ((ret = append(ret, (*this)(targs))), ...); }, tp);
    return ret;
  }
  template <iterable_c T>
  u64 operator()(T const &tp) const {
    u64 ret = 0;
    for (auto &&i : tp) ret = append(ret, (*this)(i));
    return ret;
  }
};
template <class T>
using hset = std::unordered_set<T, hash_splitmix64>;
template <class K, class V>
using hmap = std::unordered_map<K, V, hash_splitmix64>;

}  // namespace tifa_libs


#line 1 "src/code/math/isqrt.hpp"



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

namespace tifa_libs::math {

constexpr u32 isqrt(u64 x) {
  if (!x) return 0;
  int c = i32(std::bit_width(x) - 1) / 2, sh = 31 - c;
  u32 u = [](u64 x) {
    constexpr u8 TAB[192] = {128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145, 146, 147, 148, 149, 150, 151, 151, 152, 153, 154, 155, 156, 156, 157, 158, 159, 160, 160, 161, 162, 163, 164, 164, 165, 166, 167, 167, 168, 169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 179, 179, 180, 181, 181, 182, 183, 183, 184, 185, 186, 186, 187, 188, 188, 189, 190, 190, 191, 192, 192, 193, 194, 194, 195, 196, 196, 197, 198, 198, 199, 200, 200, 201, 201, 202, 203, 203, 204, 205, 205, 206, 206, 207, 208, 208, 209, 210, 210, 211, 211, 212, 213, 213, 214, 214, 215, 216, 216, 217, 217, 218, 219, 219, 220, 220, 221, 221, 222, 223, 223, 224, 224, 225, 225, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 255};
    u32 u = TAB[(x >> 56) - 64];
    u = (u << 7) + (u32)(x >> 41) / u;
    return (u << 15) + (u32)((x >> 17) / u);
  }(x << 2 * sh);
  u >>= sh;
  u -= (u64)u * u > x;
  return u;
}

}  // namespace tifa_libs::math


#line 1 "src/code/math/qpow_mod.hpp"



#line 1 "src/code/math/mul_mod_u.hpp"



#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/math/qpow_mod.hpp"

namespace tifa_libs::math {

constexpr u64 qpow_mod(u64 a, u64 b, u64 mod) {
  u64 res(1);
  for (a %= mod; b; b >>= 1, a = mul_mod_u(a, a, mod))
    if (b & 1) res = mul_mod_u(res, a, mod);
  return res;
}

}  // namespace tifa_libs::math


#line 7 "src/code/nt/bsgs.hpp"

namespace tifa_libs::math {

// solve a^x=b (mod m)
//! gcd(a, m) == 1 required
inline std::optional<u64> bsgs(u64 a, u64 b, u64 m) {
  a %= m;
  hmap<u64, u64> hmp;
  u64 sqrt_m = isqrt(m), s = mul_mod_u(a, b, m);
  if (sqrt_m * sqrt_m < m) ++sqrt_m;
  for (u64 i = 1; i <= sqrt_m; ++i, s = mul_mod_u(s, a, m)) hmp[s] = i;
  u64 _ = qpow_mod(a, sqrt_m, m);
  s = _;
  for (u64 i = 1; i <= sqrt_m; ++i, s = mul_mod_u(s, _, m))
    if (hmp[s] && i * sqrt_m >= hmp[s]) return i * sqrt_m - hmp[s];
  return {};
}

}  // namespace tifa_libs::math


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