Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/tetration_mod.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/tetration_mod"

#include "../../code/math/qtetra_mod.hpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  i64 t;
  std::cin >> t;
  while (t--) {
    u64 a, b, m;
    std::cin >> a >> b >> m;
    std::cout << tifa_libs::math::qtetra_mod(a, b, m) << '\n';
  }
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/tetration_mod.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/tetration_mod"

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



#line 1 "src/code/nt/euler_phi_u64.hpp"



#line 1 "src/code/nt/euler_phi_u32.hpp"



#line 1 "src/code/math/isqrt.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/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 5 "src/code/nt/euler_phi_u32.hpp"

namespace tifa_libs::math {

constexpr u32 euler_phi_u32(u32 n) {
  u32 ans = n;
  for (u32 i = 2, ed = isqrt(n); i <= ed; ++i)
    if (!(n % i)) {
      ans = ans / i * (i - 1);
      while (!(n % i)) n /= i;
      ed = isqrt(n);
    }
  if (n > 1) ans = ans / n * (n - 1);
  return ans;
}

}  // namespace tifa_libs::math


#line 1 "src/code/nt/pfactors.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 1 "src/code/rand/gen.hpp"



#line 5 "src/code/rand/gen.hpp"

namespace tifa_libs::rand {

template <class Distri>
class Gen {
  std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::mt19937, std::mt19937_64> re;
  Distri dist;

 public:
  using random_engine = decltype(re);
  using distribution = Distri;
  using result_type = typename Distri::result_type;

  constexpr Gen() : re(std::random_device{}()), dist() {}
  constexpr Gen(result_type a, result_type b) : re(std::random_device{}()), dist(a, b) {}

  constexpr void set_range(result_type a, result_type b) { dist = Distri(a, b); }
  constexpr random_engine& rand_eng() { return re; }
  constexpr Distri& distrib() { return dist; }

  void reset_seed() { re.seed((result_type)std::chrono::duration_cast<std::conditional_t<sizeof(typename Distri::result_type) <= 4, std::chrono::seconds, std::chrono::nanoseconds>>(std::chrono::high_resolution_clock::now().time_since_epoch()).count()); }
  constexpr result_type operator()() { return dist(re); }
  result_type next() { return dist(re); }
};

}  // namespace tifa_libs::rand


#line 1 "src/code/nt/gcd.hpp"



#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<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/nt/gcd.hpp"

namespace tifa_libs::math {

namespace gcd_impl_ {
template <uint_c T, uint_c U>
constexpr std::common_type_t<T, U> gcd__(T u, U v) {
  using W = std::common_type_t<T, U>;
  if (!u || !v) return u ^ v;
  auto k = std::__countr_zero(u | v);
  u >>= k, v >>= k;
  do {
    if (W _ = v >> std::__countr_zero(v); u > _) v = u - _, u = _;
    else v = _ - u;
  } while (v);
  return u << k;
}
}  // namespace gcd_impl_

template <int_c T, int_c U>
constexpr std::common_type_t<T, U> gcd(T a, U b) { return gcd_impl_::gcd__((to_uint_t<T>)abs(a), (to_uint_t<U>)abs(b)); }

}  // namespace tifa_libs::math


#line 1 "src/code/nt/is_prime.hpp"



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



#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 6 "src/code/nt/is_prime.hpp"

namespace tifa_libs::math {

constexpr bool is_prime(u64 n) {
  if (n <= 2) return n == 2;
  if (~n & 1) return false;
  if (n < 8 || n == 61) return true;

  auto f = [n, d = (n - 1) >> std::countr_zero(n - 1)](auto const& bases) -> bool {
    for (u64 i : bases) {
      if (!(i % n)) continue;
      u64 t = d, y = qpow_mod(i, t, n);
      while (t != n - 1 && y != 1 && y != n - 1) {
        y = mul_mod_u(y, y, n);
        t *= 2;
      }
      if (y != n - 1 && (~t & 1)) return false;
    }
    return true;
  };

  if (n < (1 << 30)) {
    constexpr u64 bases[3] = {2, 7, 61};
    return f(bases);
  }
  constexpr u64 bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
  return f(bases);
}

}  // namespace tifa_libs::math


#line 8 "src/code/nt/pfactors.hpp"

namespace tifa_libs::math {
namespace pfactors_impl_ {
class PollardRho {
  rand::Gen<std::uniform_int_distribution<u64>> e;

  constexpr u64 rho(u64 n) {
    e.set_range(2, n - 1);
    auto f = [n, r = e()](u64 x) { return (mul_mod_u(x, x, n) + r) % n; };
    u64 g = 1, x = 0, y = e(), yy = 0;
    const u32 LIM = 128;
    for (u64 r = 1, q = 1; g == 1; r *= 2) {
      x = y;
      for (u64 i = 0; i < r; ++i) y = f(y);
      for (u64 k = 0; g == 1 && k < r; k += LIM) {
        yy = y;
        for (u64 i = 0; i < LIM && i < r - k; ++i) q = mul_mod_u(q, (x + (n - (y = f(y)))) % n, n);
        g = gcd(q, n);
      }
    }
    if (g == n) do {
        g = gcd((x + (n - (yy = f(yy)))) % n, n);
      } while (g == 1);
    return g == n ? rho(n) : g;
  }

 public:
  explicit constexpr PollardRho() : e() {}

  constexpr void operator()(u64 n, std::map<u64, u32> &ans) {
    if (n < 2) return;
    if (is_prime(n)) {
      ++ans[n];
      return;
    }
    auto g = rho(n);
    (*this)(n / g, ans);
    (*this)(g, ans);
  }
};
}  // namespace pfactors_impl_

inline std::map<u64, u32> pfactors(u64 n) {
  std::map<u64, u32> ans;
  if (n < 2) return ans;
  if (~n & 1) n >>= (ans[2] = (u32)std::countr_zero(n));
  pfactors_impl_::PollardRho()(n, ans);
  return ans;
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/euler_phi_u64.hpp"

namespace tifa_libs::math {

inline u64 euler_phi_u64(u64 n) {
  if (n <= (u64)-1_u32) return euler_phi_u32((u32)n);
  auto pf = pfactors(n);
  for (auto [p, k] : pf) n = n / p * (p - 1);
  return n;
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {
namespace qtetra_mod_impl_ {
constexpr u64 mpow(u64 a, u64 b, u64 m, u64 &f) {
  if (a == 1 || b == 0) return 1;
  u64 v = 1, x = a, z = m;
  f |= x >= z;
  x %= m;
  while (true) {
    if (b & 1) v *= x;
    if (v >= z) {
      f = 1;
      v %= m;
    }
    if (!(b >>= 1)) break;
    if ((x *= x) >= z) {
      f = 1;
      x %= m;
    }
  }
  return v;
}

constexpr u64 qtetra(u64 a, u64 b, u64 m, u64 &f) {
  if (a == 0) return ~b & 1;
  if (m == 1) return f = 1;
  if (a == 1 || b == 0) return 1;
  if (b == 1) {
    f |= a >= m;
    return a % m + f * m;
  }
  u64 z = qtetra(a, b - 1, euler_phi_u64(m), f), r = mpow(a, z, m, f);
  return r + f * m;
}
}  // namespace qtetra_mod_impl_

constexpr u64 qtetra_mod(u64 a, u64 b, u64 m) {
  u64 f = 0;
  return qtetra_mod_impl_::qtetra(a, b, m, f) % m;
}

}  // namespace tifa_libs::math


#line 4 "src/test_cpverifier/library-checker/tetration_mod.test.cpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  i64 t;
  std::cin >> t;
  while (t--) {
    u64 a, b, m;
    std::cin >> a >> b >> m;
    std::cout << tifa_libs::math::qtetra_mod(a, b, m) << '\n';
  }
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 2_3_32_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 example_00 :heavy_check_mark: AC 7 ms 4 MB
g++-12 example_01 :heavy_check_mark: AC 7 ms 4 MB
g++-12 max_00 :heavy_check_mark: AC 18 ms 4 MB
g++-12 max_01 :heavy_check_mark: AC 18 ms 4 MB
g++-12 max_02 :heavy_check_mark: AC 18 ms 4 MB
g++-12 max_1000000000_00 :heavy_check_mark: AC 11 ms 4 MB
g++-12 max_1000000000_01 :heavy_check_mark: AC 11 ms 4 MB
g++-12 max_1000000000_02 :heavy_check_mark: AC 11 ms 4 MB
g++-12 max_998244353_00 :heavy_check_mark: AC 70 ms 4 MB
g++-12 max_998244353_01 :heavy_check_mark: AC 70 ms 4 MB
g++-12 max_998244353_02 :heavy_check_mark: AC 71 ms 4 MB
g++-12 random_00 :heavy_check_mark: AC 15 ms 4 MB
g++-12 random_01 :heavy_check_mark: AC 9 ms 4 MB
g++-12 random_02 :heavy_check_mark: AC 8 ms 4 MB
g++-12 random_03 :heavy_check_mark: AC 9 ms 4 MB
g++-12 random_04 :heavy_check_mark: AC 13 ms 4 MB
g++-12 small_00 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_ab_00 :heavy_check_mark: AC 13 ms 4 MB
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