test/verify/yosupo-primality-test.test.cpp

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Last update: 2024-07-28 19:56:12+09:00
Problem: https://judge.yosupo.jp/problem/primality_test

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/primality_test

#include "../../template/template.hpp"

#include "../../math/number-theory/fast-prime-factorization.hpp"

int main() {
  int Q;
  cin >> Q;
  while(Q--) {
    int64 N;
    cin >> N;
    cout << (FastPrimeFactorization::is_prime(N) ? "Yes" : "No") << "\n";
  }
}

#line 1 "test/verify/yosupo-primality-test.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/primality_test

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-primality-test.test.cpp"

#line 1 "math/number-theory/fast-prime-factorization.hpp"
namespace FastPrimeFactorization {

template <typename word, typename dword, typename sword>
struct UnsafeMod {
  UnsafeMod() : x(0) {}

  UnsafeMod(word _x) : x(init(_x)) {}

  bool operator==(const UnsafeMod &rhs) const { return x == rhs.x; }

  bool operator!=(const UnsafeMod &rhs) const { return x != rhs.x; }

  UnsafeMod &operator+=(const UnsafeMod &rhs) {
    if ((x += rhs.x) >= mod) x -= mod;
    return *this;
  }

  UnsafeMod &operator-=(const UnsafeMod &rhs) {
    if (sword(x -= rhs.x) < 0) x += mod;
    return *this;
  }

  UnsafeMod &operator*=(const UnsafeMod &rhs) {
    x = reduce(dword(x) * rhs.x);
    return *this;
  }

  UnsafeMod operator+(const UnsafeMod &rhs) const {
    return UnsafeMod(*this) += rhs;
  }

  UnsafeMod operator-(const UnsafeMod &rhs) const {
    return UnsafeMod(*this) -= rhs;
  }

  UnsafeMod operator*(const UnsafeMod &rhs) const {
    return UnsafeMod(*this) *= rhs;
  }

  UnsafeMod pow(uint64_t e) const {
    UnsafeMod ret(1);
    for (UnsafeMod base = *this; e; e >>= 1, base *= base) {
      if (e & 1) ret *= base;
    }
    return ret;
  }

  word get() const { return reduce(x); }

  static constexpr int word_bits = sizeof(word) * 8;

  static word modulus() { return mod; }

  static word init(word w) { return reduce(dword(w) * r2); }

  static void set_mod(word m) {
    mod = m;
    inv = mul_inv(mod);
    r2 = -dword(mod) % mod;
  }

  static word reduce(dword x) {
    word y =
        word(x >> word_bits) - word((dword(word(x) * inv) * mod) >> word_bits);
    return sword(y) < 0 ? y + mod : y;
  }

  static word mul_inv(word n, int e = 6, word x = 1) {
    return !e ? x : mul_inv(n, e - 1, x * (2 - x * n));
  }

  static word mod, inv, r2;

  word x;
};

using uint128_t = __uint128_t;

using Mod64 = UnsafeMod<uint64_t, uint128_t, int64_t>;
template <>
uint64_t Mod64::mod = 0;
template <>
uint64_t Mod64::inv = 0;
template <>
uint64_t Mod64::r2 = 0;

using Mod32 = UnsafeMod<uint32_t, uint64_t, int32_t>;
template <>
uint32_t Mod32::mod = 0;
template <>
uint32_t Mod32::inv = 0;
template <>
uint32_t Mod32::r2 = 0;

bool miller_rabin_primality_test_uint64(uint64_t n) {
  Mod64::set_mod(n);
  uint64_t d = n - 1;
  while (d % 2 == 0) d /= 2;
  Mod64 e{1}, rev{n - 1};
  // http://miller-rabin.appspot.com/  < 2^64
  for (uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
    if (n <= a) break;
    uint64_t t = d;
    Mod64 y = Mod64(a).pow(t);
    while (t != n - 1 && y != e && y != rev) {
      y *= y;
      t *= 2;
    }
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool miller_rabin_primality_test_uint32(uint32_t n) {
  Mod32::set_mod(n);
  uint32_t d = n - 1;
  while (d % 2 == 0) d /= 2;
  Mod32 e{1}, rev{n - 1};
  for (uint32_t a : {2, 7, 61}) {
    if (n <= a) break;
    uint32_t t = d;
    Mod32 y = Mod32(a).pow(t);
    while (t != n - 1 && y != e && y != rev) {
      y *= y;
      t *= 2;
    }
    if (y != rev && t % 2 == 0) return false;
  }
  return true;
}

bool is_prime(uint64_t n) {
  if (n == 2) return true;
  if (n == 1 || n % 2 == 0) return false;
  if (n < uint64_t(1) << 31) return miller_rabin_primality_test_uint32(n);
  return miller_rabin_primality_test_uint64(n);
}

uint64_t pollard_rho(uint64_t n) {
  if (is_prime(n)) return n;
  if (n % 2 == 0) return 2;
  Mod64::set_mod(n);
  uint64_t d;
  Mod64 one{1};
  for (Mod64 c{one};; c += one) {
    Mod64 x{2}, y{2};
    do {
      x = x * x + c;
      y = y * y + c;
      y = y * y + c;
      d = __gcd((x - y).get(), n);
    } while (d == 1);
    if (d < n) return d;
  }
  assert(0);
}

vector<uint64_t> prime_factor(uint64_t n) {
  if (n <= 1) return {};
  uint64_t p = pollard_rho(n);
  if (p == n) return {p};
  auto l = prime_factor(p);
  auto r = prime_factor(n / p);
  copy(begin(r), end(r), back_inserter(l));
  return l;
}
};  // namespace FastPrimeFactorization
#line 6 "test/verify/yosupo-primality-test.test.cpp"

int main() {
  int Q;
  cin >> Q;
  while(Q--) {
    int64 N;
    cin >> N;
    cout << (FastPrimeFactorization::is_prime(N) ? "Yes" : "No") << "\n";
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	all_prime_00	AC	197 ms	3 MB
g++	carmichael_00	AC	5 ms	3 MB
g++	example_00	AC	5 ms	3 MB
g++	hack_issue996_00	AC	5 ms	3 MB
g++	less_1000000000_00	AC	22 ms	3 MB
g++	prod_two_prime_00	AC	44 ms	3 MB
g++	random_00	AC	35 ms	3 MB
g++	random_01	AC	34 ms	3 MB
g++	random_02	AC	34 ms	3 MB
g++	small_00	AC	19 ms	3 MB
clang++	all_prime_00	AC	229 ms	3 MB
clang++	carmichael_00	AC	5 ms	3 MB
clang++	example_00	AC	4 ms	3 MB
clang++	hack_issue996_00	AC	4 ms	3 MB
clang++	less_1000000000_00	AC	23 ms	3 MB
clang++	prod_two_prime_00	AC	48 ms	3 MB
clang++	random_00	AC	38 ms	3 MB
clang++	random_01	AC	38 ms	3 MB
clang++	random_02	AC	37 ms	3 MB
clang++	small_00	AC	19 ms	3 MB