Tifa's CP Library

:heavy_check_mark: src/test_cpverifier/library-checker/gcd_convolution.ss.test.cpp

Depends on

Code

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

#include "../../code/conv/conv_gcd.hpp"

constexpr u32 MOD = 998244353;

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

using mint = tifa_libs::math::mint_ss<MOD>;

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n;
  std::cin >> n;
  vec<mint> a(n + 1), b(n + 1);
  for (u32 i = 1; i <= n; ++i) std::cin >> a[i];
  for (u32 i = 1; i <= n; ++i) std::cin >> b[i];
  auto c = tifa_libs::math::conv_gcd(a, b);
  for (u32 i = 1; i < c.size(); ++i) std::cout << c[i] << " \n"[i + 1 == c.size()];
  return 0;
}
#line 1 "src/test_cpverifier/library-checker/gcd_convolution.ss.test.cpp"
#define AUTO_GENERATED
#define PROBLEM "https://judge.yosupo.jp/problem/gcd_convolution"

#line 1 "src/code/conv/conv_gcd.hpp"



#line 1 "src/code/conv/zmt_multiple.hpp"



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

namespace tifa_libs::math {

constexpr vecu prime_seq(u32 n) {
  vecb sieve(n / 3 + 1, 1);
  for (u32 p = 5, d = 4, i = 1, sqn = isqrt(n); p <= sqn; p += d = 6 - d, ++i) {
    if (!sieve[i]) continue;
    for (u64 q = p * p / 3, r = d * p / 3 + (d * p % 3 == 2), s = 2 * p, qe = sieve.size(); q < qe; q += r = s - r) sieve[q] = 0;
  }
  vecu ret{2, 3};
  for (u32 p = 5, d = 4, i = 1; p <= n; p += d = 6 - d, ++i)
    if (sieve[i]) ret.push_back(p);
  while (!ret.empty() && ret.back() > n) ret.pop_back();
  return ret;
}

}  // namespace tifa_libs::math


#line 5 "src/code/conv/zmt_multiple.hpp"

namespace tifa_libs::math {

template <class T>
constexpr void zt_multiple(vec<T>& a, vecu const& pf) {
  for (u32 p : pf)
    for (u64 k = (a.size() - 1) / p; k; --k) a[k] += a[k * p];
}
template <class T>
constexpr void zt_multiple(vec<T>& a) { zt_multiple(a, prime_seq(a.size() - 1)); }
template <class T>
constexpr void mt_multiple(vec<T>& a, vecu const& pf) {
  for (u32 p : pf)
    for (u64 k = 1; k * p < a.size(); ++k) a[k] -= a[k * p];
}
template <class T>
constexpr void mt_multiple(vec<T>& a) { mt_multiple(a, prime_seq(a.size() - 1)); }

}  // namespace tifa_libs::math


#line 5 "src/code/conv/conv_gcd.hpp"

namespace tifa_libs::math {

template <class T>
constexpr vec<T> conv_gcd(vec<T> l, vec<T> r) {
  assert(l.size() == r.size());
  auto pf = prime_seq((u32)l.size() - 1);
  zt_multiple(l, pf);
  zt_multiple(r, pf);
  for (u32 i = 0; i < l.size(); ++i) l[i] *= r[i];
  mt_multiple(l, pf);
  return l;
}

}  // namespace tifa_libs::math


#line 5 "src/test_cpverifier/library-checker/gcd_convolution.ss.test.cpp"

constexpr u32 MOD = 998244353;

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



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



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



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



#line 1 "src/code/math/safe_mod.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/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/exgcd.hpp"



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

namespace tifa_libs::math {

// Binary exgcd
template <uint_c U, bool only_x = false>
constexpr auto exgcd_b(U a, U b) {
  using T = to_sint_t<U>;
  if constexpr (only_x) {
    if (!a) return std::make_tuple(b, (T)0);
    if (!b) return std::make_tuple(a, (T)1);
  } else {
    if (!a) return std::make_tuple(b, (T)0, (T) !!b);
    if (!b) return std::make_tuple(a, (T)1, (T)0);
  }
  auto r = std::__countr_zero(a | b);
  a >>= r, b >>= r;
  T x = (T)a, y = (T)b;
  T s = 1, t = 0, u = 0, v = 1;
  while (x) {
    while (!(x & 1)) {
      x /= 2;
      if (!((s | t) & 1)) s /= 2, t /= 2;
      else s = (s + (T)b) / 2, t = (t - (T)a) / 2;
    }
    while (!(y & 1)) {
      y /= 2;
      if (!((u | v) & 1)) u /= 2, v /= 2;
      else u = (u + (T)b) / 2, v = (v - (T)a) / 2;
    }
    if (x >= y) x -= y, s -= u, t -= v;
    else y -= x, u -= s, v -= t;
  }
  if (y > 1) a /= (U)y, b /= (U)y;
  if (a && (U)abs(v) >= a) {
    T _ = v / (T)a;
    v -= _ * (T)a, u += _ * (T)b;
  }
  if (b && (U)abs(u) >= b) {
    T _ = u / (T)b;
    u -= _ * (T)b, v += _ * (T)a;
  }
  if (T u_ = u + (T)b, v_ = v - (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if (T u_ = u - (T)b, v_ = v + (T)a; abs(u_) + abs(v_) <= abs(u) + abs(v)) u = u_, v = v_;
  if constexpr (only_x) return std::make_tuple(U(y << r), u);
  else return std::make_tuple(U(y << r), u, v);
}
// @return then 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, bool only_x = false>
constexpr auto exgcd(T a, T b) {
  using U = to_uint_t<T>;
  if (auto [x, y] = std::minmax(a, b); x >= 0 && y <= T(U(-1) >> sizeof(U))) return exgcd_b<U, only_x>((U)a, (U)b);
  if constexpr (only_x) {
    T s = 1, u = 0;
    while (b) {
      T c = a / b;
      std::tie(s, u, a, b) = std::make_tuple(u, s - u * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s);
  } else {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
      T c = a / b;
      std::tie(s, t, u, v, a, b) = std::make_tuple(u, v, s - u * c, t - v * c, b, a - b * c);
    }
    return std::make_tuple((U)a, s, t);
  }
}

}  // 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] = exgcd<U, true>(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/math/mint.hpp"

namespace tifa_libs::math {

template <class D, uint_c Rt>
class mint {
  constexpr D const &d() const { return static_cast<D const &>(*this); }
  constexpr D &d() { return static_cast<D &>(*this); }

 protected:
  Rt v_{};

 public:
  constexpr mint() {}
  template <int_c T>
  constexpr mint(T v) : v_(D::mod_(v)) {}
  constexpr operator D() { return d(); }

  using raw_type = Rt;
  using sraw_type = to_sint_t<Rt>;
  static constexpr raw_type mod() { return D::mod_(); }
  static constexpr sraw_type smod() { return (sraw_type)D::mod_(); }
  constexpr raw_type val() const { return d().val_(); }
  constexpr sraw_type sval() const { return (sraw_type)d().val_(); }
  constexpr raw_type &data() { return d().data_(); }

  template <int_c T>
  explicit constexpr operator T() const { return (T)val(); }
  constexpr mint &operator+=(mint const &r) { return d().adde_(r.d()); }
  constexpr mint &operator-=(mint const &r) { return d().sube_(r.d()); }
  constexpr mint &operator*=(mint const &r) { return d().mule_(r.d()); }
  constexpr mint &operator/=(mint const &r) { return *this = *this * r.inv(); }
  constexpr mint const &operator+() const { return *this; }
  constexpr mint operator-() const { return d().neg_(); }
  constexpr mint inv() const { return inverse(val(), mod()); }
  friend constexpr mint operator+(mint l, mint const &r) { return l += r; }
  friend constexpr mint operator-(mint l, mint const &r) { return l -= r; }
  friend constexpr mint operator*(mint l, mint const &r) { return l *= r; }
  friend constexpr mint operator/(mint l, mint const &r) { return l /= r; }
  friend constexpr bool operator==(mint const &l, mint const &r) { return l.val() == r.val(); }
  friend constexpr auto operator<=>(mint const &l, mint const &r) { return l.sval() - r.sval(); }
  friend std::istream &operator>>(std::istream &is, mint &x) {
    i64 _;
    is >> _;
    x = mint(_);
    return is;
  }
  friend std::ostream &operator<<(std::ostream &os, mint const &x) { return os << x.val(); }
  friend constexpr mint abs(mint const &x) { return x.val(); }
};

}  // namespace tifa_libs::math


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

namespace tifa_libs::math {

template <u32 MOD>
class mint_ss : public mint<mint_ss<MOD>, u32> {
  using base = mint<mint_ss<MOD>, u32>;
  friend base;
  static_assert(MOD >= 1);

 public:
  static constexpr bool FIXED_MOD = true;
  constexpr mint_ss() {}
  template <int_c T>
  constexpr mint_ss(T v) { this->v_ = mod_(v); }

 private:
  using raw_t = typename base::raw_type;
  using sraw_t = typename base::sraw_type;
  template <sint_c T>
  static constexpr raw_t mod_(T v) {
    i64 x = i64(v % (i64)mod_());
    return raw_t(x + (x < 0 ? mod_() : 0));
  }
  template <uint_c T>
  static constexpr raw_t mod_(T v) { return raw_t(v % mod_()); }
  static constexpr raw_t mod_() { return MOD; }
  constexpr raw_t val_() const { return this->v_; }
  constexpr raw_t &data_() { return this->v_; }

  constexpr mint_ss neg_() const { return -(sraw_t)val_(); }
  constexpr mint_ss &adde_(mint_ss const &r) {
    data_() += r.val_();
    if (val_() >= mod_()) data_() -= mod_();
    return *this;
  }
  constexpr mint_ss &sube_(mint_ss const &r) {
    data_() -= r.val_();
    if (val_() >= mod_()) data_() += mod_();
    return *this;
  }
  constexpr mint_ss &mule_(mint_ss const &r) {
    data_() = u32((u64)val_() * r.val_() % mod_());
    return *this;
  }
};

}  // namespace tifa_libs::math


#line 9 "src/test_cpverifier/library-checker/gcd_convolution.ss.test.cpp"

using mint = tifa_libs::math::mint_ss<MOD>;

int main() {
  std::ios::sync_with_stdio(false);
  std::cin.tie(nullptr);
  u32 n;
  std::cin >> n;
  vec<mint> a(n + 1), b(n + 1);
  for (u32 i = 1; i <= n; ++i) std::cin >> a[i];
  for (u32 i = 1; i <= n; ++i) std::cin >> b[i];
  auto c = tifa_libs::math::conv_gcd(a, b);
  for (u32 i = 1; i < c.size(); ++i) std::cout << c[i] << " \n"[i + 1 == c.size()];
  return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-12 all_zero_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 example_00 :heavy_check_mark: AC 7 ms 4 MB
g++-12 max_random_00 :heavy_check_mark: AC 198 ms 20 MB
g++-12 max_random_01 :heavy_check_mark: AC 202 ms 20 MB
g++-12 near_prime_00 :heavy_check_mark: AC 195 ms 20 MB
g++-12 near_prime_01 :heavy_check_mark: AC 196 ms 20 MB
g++-12 near_prime_02 :heavy_check_mark: AC 209 ms 20 MB
g++-12 near_prime_squared_00 :heavy_check_mark: AC 193 ms 19 MB
g++-12 near_prime_squared_01 :heavy_check_mark: AC 196 ms 19 MB
g++-12 near_prime_squared_02 :heavy_check_mark: AC 194 ms 19 MB
g++-12 random_00 :heavy_check_mark: AC 84 ms 10 MB
g++-12 random_01 :heavy_check_mark: AC 100 ms 11 MB
g++-12 random_02 :heavy_check_mark: AC 117 ms 13 MB
g++-12 small_00 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_01 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_02 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_03 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_04 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_05 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_06 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_07 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_08 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_09 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_10 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_11 :heavy_check_mark: AC 7 ms 4 MB
g++-12 small_12 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_13 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_14 :heavy_check_mark: AC 8 ms 4 MB
g++-12 small_15 :heavy_check_mark: AC 8 ms 4 MB
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