test/verify/yosupo-factorize.test.cpp

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• Last update: 2026-08-10 11:04:56+00:00
• Problem: https://judge.yosupo.jp/problem/factorize

Depends on

• math/number-theory/fast-prime-factorization.hpp

Code

// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/factorize
// clang-format on

#include <algorithm>
#include <iostream>

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

using namespace std;

int main() {
  int Q;
  cin >> Q;
  while (Q--) {
    long long X;
    cin >> X;
    auto ret = FastPrimeFactorization::prime_factor(X);
    sort(ret.begin(), ret.end());
    cout << ret.size();
    for (auto factor : ret) cout << " " << factor;
    cout << "\n";
  }
}

#line 1 "test/verify/yosupo-factorize.test.cpp"
// clang-format off
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/factorize
// clang-format on

#include <algorithm>
#include <iostream>

#line 2 "math/number-theory/fast-prime-factorization.hpp"

#line 4 "math/number-theory/fast-prime-factorization.hpp"
#include <cassert>
#include <cstdint>
#include <iterator>
#include <numeric>
#include <vector>

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(std::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<std::uint64_t, uint128_t, std::int64_t>;
template <>
std::uint64_t Mod64::mod = 0;
template <>
std::uint64_t Mod64::inv = 0;
template <>
std::uint64_t Mod64::r2 = 0;

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

bool miller_rabin_primality_test_uint64(std::uint64_t n) {
  Mod64::set_mod(n);
  std::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 (std::uint64_t a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) {
    if (n <= a) break;
    std::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(std::uint32_t n) {
  Mod32::set_mod(n);
  std::uint32_t d = n - 1;
  while (d % 2 == 0) d /= 2;
  Mod32 e{1}, rev{n - 1};
  for (std::uint32_t a : {2, 7, 61}) {
    if (n <= a) break;
    std::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(std::uint64_t n) {
  if (n == 2) return true;
  if (n == 1 || n % 2 == 0) return false;
  if (n < std::uint64_t(1) << 31) return miller_rabin_primality_test_uint32(n);
  return miller_rabin_primality_test_uint64(n);
}

std::uint64_t pollard_rho(std::uint64_t n) {
  if (is_prime(n)) return n;
  if (n % 2 == 0) return 2;
  Mod64::set_mod(n);
  std::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 = std::gcd((x - y).get(), n);
    } while (d == 1);
    if (d < n) return d;
  }
  assert(0);
}

std::vector<std::uint64_t> prime_factor(std::uint64_t n) {
  if (n <= 1) return {};
  std::uint64_t p = pollard_rho(n);
  if (p == n) return {p};
  auto l = prime_factor(p);
  auto r = prime_factor(n / p);
  std::copy(r.begin(), r.end(), std::back_inserter(l));
  return l;
}
};  // namespace FastPrimeFactorization
#line 9 "test/verify/yosupo-factorize.test.cpp"

using namespace std;

int main() {
  int Q;
  cin >> Q;
  while (Q--) {
    long long X;
    cin >> X;
    auto ret = FastPrimeFactorization::prime_factor(X);
    sort(ret.begin(), ret.end());
    cout << ret.size();
    for (auto factor : ret) cout << " " << factor;
    cout << "\n";
  }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	4295098369_00	AC	4 ms	4 MB
g++	999381247093216751_00	AC	1251 ms	4 MB
g++	big2_00	AC	326 ms	4 MB
g++	big2_01	AC	324 ms	4 MB
g++	big2_02	AC	338 ms	4 MB
g++	big2_worse_00	AC	795 ms	4 MB
g++	big_semiprime_gen_00	AC	322 ms	4 MB
g++	big_semiprime_gen_01	AC	317 ms	4 MB
g++	big_semiprime_random_00	AC	250 ms	4 MB
g++	big_semiprime_random_01	AC	273 ms	4 MB
g++	carmichael_00	AC	22 ms	4 MB
g++	example_00	AC	2 ms	4 MB
g++	fixed_RNG_buster_00	AC	2 ms	4 MB
g++	hack00_00	AC	2 ms	4 MB
g++	max_00	AC	19 ms	4 MB
g++	pow2_00	AC	23 ms	4 MB
g++	pow2_01	AC	25 ms	4 MB
g++	pow2_02	AC	44 ms	4 MB
g++	prime_test_special_00	AC	4 ms	4 MB
g++	prime_test_special_01	AC	7 ms	4 MB
g++	prime_test_special_02	AC	17 ms	4 MB
g++	prime_test_special_03	AC	4 ms	4 MB
g++	prime_test_special_bug_00	AC	2 ms	4 MB
g++	prime_test_special_bug_01	AC	2 ms	4 MB
g++	prime_test_special_bug_02	AC	2 ms	4 MB
g++	random_00	AC	5 ms	4 MB
g++	random_01	AC	6 ms	4 MB
g++	random_02	AC	8 ms	4 MB
g++	small_00	AC	2 ms	4 MB
g++	small_01	AC	2 ms	4 MB
g++	small_02	AC	2 ms	4 MB
clang++	4295098369_00	AC	5 ms	4 MB
clang++	999381247093216751_00	AC	654 ms	4 MB
clang++	big2_00	AC	172 ms	4 MB
clang++	big2_01	AC	172 ms	4 MB
clang++	big2_02	AC	179 ms	4 MB
clang++	big2_worse_00	AC	414 ms	4 MB
clang++	big_semiprime_gen_00	AC	169 ms	4 MB
clang++	big_semiprime_gen_01	AC	168 ms	4 MB
clang++	big_semiprime_random_00	AC	134 ms	4 MB
clang++	big_semiprime_random_01	AC	145 ms	4 MB
clang++	carmichael_00	AC	14 ms	4 MB
clang++	example_00	AC	2 ms	4 MB
clang++	fixed_RNG_buster_00	AC	2 ms	4 MB
clang++	hack00_00	AC	2 ms	4 MB
clang++	max_00	AC	11 ms	4 MB
clang++	pow2_00	AC	13 ms	4 MB
clang++	pow2_01	AC	14 ms	4 MB
clang++	pow2_02	AC	25 ms	4 MB
clang++	prime_test_special_00	AC	3 ms	4 MB
clang++	prime_test_special_01	AC	5 ms	4 MB
clang++	prime_test_special_02	AC	8 ms	4 MB
clang++	prime_test_special_03	AC	3 ms	4 MB
clang++	prime_test_special_bug_00	AC	2 ms	4 MB
clang++	prime_test_special_bug_01	AC	2 ms	4 MB
clang++	prime_test_special_bug_02	AC	2 ms	4 MB
clang++	random_00	AC	4 ms	4 MB
clang++	random_01	AC	5 ms	4 MB
clang++	random_02	AC	6 ms	4 MB
clang++	small_00	AC	2 ms	4 MB
clang++	small_01	AC	2 ms	4 MB
clang++	small_02	AC	2 ms	4 MB

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