Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/yukicoder/0448.test.cpp

Depends on

Code

#define PROBLEM "https://yukicoder.me/problems/448"

#include "../../code/nt/crt_mod.hpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n;
  std::cin >> n;
  vec<i32> r(n);
  vecu m(n);
  for (u32 i = 0; i < n; ++i) std::cin >> r[i] >> m[i];
  auto res = tifa_libs::math::crt_mod(r, m, 1'000'000'007);
  if (!res) {
    std::cout << "-1\n";
    return 0;
  }
  std::cout << ((usz)std::ranges::count(r, 0) == n ? res->second : res->first) << '\n';
  return 0;
}
#line 1 "src/test_cpverifier/yukicoder/0448.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/448"

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



#line 1 "src/code/math/safe_mod.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&&...) {};


#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/math/safe_mod.hpp"

namespace tifa_libs::math {

template <sint_c T>
constexpr T safe_mod(T x, to_uint_t<T> mod) { return ((x %= (T)mod) < 0 ? x + (T)mod : x); }

}  // namespace tifa_libs::math


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



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



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



#line 5 "src/code/nt/exgcd.hpp"

namespace tifa_libs::math {

// @return tuple(g, x, y) s.t. g = gcd(a, b), xa + yb = g, |x| + |y| is the minimal (primary) and x <= y (secondarily)
template <sint_c T>
constexpr auto exgcd(T a, T b) {
  T x1 = 1, x2 = 0, x3 = 0, x4 = 1;
  while (b) {
    T c = a / b;
    std::tie(x1, x2, x3, x4, a, b) = std::make_tuple(x3, x4, x1 - x3 * c, x2 - x4 * c, b, a - b * c);
  }
  return std::make_tuple(to_uint_t<T>(a), x1, x2);
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <uint_c T>
constexpr ptt<T> inv_gcd(T n, T mod) {
  using U = to_sint_t<T>;
  auto [g, x, y] = exgcd(U(n % mod), (U)mod);
  return {g, safe_mod(x, mod)};
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/inverse.hpp"

namespace tifa_libs::math {

template <uint_c T, uint_c U>
constexpr U inverse(T n, U mod) {
  auto [g, x] = inv_gcd(U(n % mod), mod);
  assert(g == 1);
  return x;
}

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

constexpr std::optional<ptt<u32>> crt_mod(vec<i32> const &a, vecu const &m, u32 const mod) {
  if (a.size() != m.size()) return {};
  vecu m_cpy(m);
  u32 n = (u32)a.size();
  for (u32 i = 0; i < n; ++i) {
    u32 &mi = m_cpy[i];
    for (u32 j = 0; j < i; ++j) {
      u32 &mj = m_cpy[j], d = std::gcd(mi, mj);
      if (d == 1) continue;
      if (safe_mod(a[i], d) != safe_mod(a[j], d)) return {};
      mi /= d;
      mj /= d;
      if (u32 k = std::gcd(mi, d); k != 1)
        while (d % k == 0) {
          mi *= k;
          d /= k;
        }
      mj *= d;
    }
  }
  m_cpy.push_back(mod);
  vec<i32> pp(n + 1, 1), res(n + 1);
  for (u32 i = 0; i < n; ++i) {
    i64 u = safe_mod((safe_mod(a[i], m_cpy[i]) - res[i]) * (i64)inverse((u64)pp[i], m_cpy[i]), m_cpy[i]);
    for (u32 j = i + 1; j <= n; ++j) {
      res[j] = (i32)((res[j] + u * pp[j]) % m_cpy[j]);
      pp[j] = (i32)((i64)pp[j] * m_cpy[i] % m_cpy[j]);
    }
  }
  return std::make_pair(res.back(), pp.back());
}

}  // namespace tifa_libs::math


#line 4 "src/test_cpverifier/yukicoder/0448.test.cpp"

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n;
  std::cin >> n;
  vec<i32> r(n);
  vecu m(n);
  for (u32 i = 0; i < n; ++i) std::cin >> r[i] >> m[i];
  auto res = tifa_libs::math::crt_mod(r, m, 1'000'000'007);
  if (!res) {
    std::cout << "-1\n";
    return 0;
  }
  std::cout << ((usz)std::ranges::count(r, 0) == n ? res->second : res->first) << '\n';
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 0.in :heavy_check_mark: AC 11 ms 4 MB
g++-12 1.in :heavy_check_mark: AC 11 ms 4 MB
g++-12 2.in :heavy_check_mark: AC 47 ms 4 MB
g++-12 3.in :heavy_check_mark: AC 46 ms 4 MB
g++-12 4.in :heavy_check_mark: AC 56 ms 4 MB
g++-12 5.in :heavy_check_mark: AC 56 ms 4 MB
g++-12 6.in :heavy_check_mark: AC 56 ms 4 MB
g++-12 7.in :heavy_check_mark: AC 56 ms 4 MB
g++-12 8.in :heavy_check_mark: AC 39 ms 4 MB
g++-12 9.in :heavy_check_mark: AC 38 ms 4 MB
g++-12 A.in :heavy_check_mark: AC 38 ms 4 MB
g++-12 B.in :heavy_check_mark: AC 55 ms 4 MB
g++-12 C.in :heavy_check_mark: AC 56 ms 4 MB
g++-12 D.in :heavy_check_mark: AC 14 ms 4 MB
g++-12 E.in :heavy_check_mark: AC 14 ms 4 MB
g++-12 F.in :heavy_check_mark: AC 45 ms 4 MB
g++-12 G.in :heavy_check_mark: AC 47 ms 4 MB
g++-12 H.in :heavy_check_mark: AC 10 ms 4 MB
g++-12 I.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 J.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 K.in :heavy_check_mark: AC 44 ms 4 MB
g++-12 L.in :heavy_check_mark: AC 10 ms 4 MB
g++-12 M.in :heavy_check_mark: AC 55 ms 4 MB
g++-12 N.in :heavy_check_mark: AC 9 ms 4 MB
g++-12 system_test1.txt :heavy_check_mark: AC 9 ms 4 MB
Back to top page