tests/math/pollards-rho/libchecker.test.cpp

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Last update: 2025-03-03 00:33:48+09:00
Problem: https://judge.yosupo.jp/problem/factorize

Depends on

Code

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#include "../../../cpp/library/math/pollards-rho.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/factorize"

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int q;
  cin >> q;
  while (q--) {
    ull a;
    cin >> a;
    vector<pair<ull, ull>> res = asalib::math::pollards_rho(a);
    vector<ull> ans(0);
    for (auto [p, e] : res) rep(_, e) ans.push_back(p);
    cout << ans.size();
    for (ull x : ans) cout << ' ' << x;
    cout << '\n';
  }
  return 0;
}

#line 1 "tests/math/pollards-rho/libchecker.test.cpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); ++i)
using ll = long long;
using ull = unsigned long long;

#line 2 "library/math/pollards-rho.hpp"

#include <concepts>
#line 5 "library/math/pollards-rho.hpp"
using namespace std;

#line 2 "library/math/miller-rabin.hpp"

#line 6 "library/math/miller-rabin.hpp"
using namespace std;

namespace asalib {
  namespace math {
    template<integral T>
    constexpr bool miller_rabin_test(T n) {
      if (n < 2) [[unlikely]]
        return false;
      if (n % 2 == 0) return n == 2;
      T d = n - 1, s = 0;
      while (d % 2 == 0) d >>= 1, ++s;
      assert(d % 2 == 1);

      static_assert(sizeof(T) == 4 || sizeof(T) == 8, "T must be 32-bit or 64-bit integer type");
      constexpr bool is_64bit = sizeof(T) == 8;

      function<T(T, T, T)> modpow = [&](T a, T n, T mod) {
        T res = 1;
        while (n) {
          if constexpr (is_64bit) {
            if (n & 1) res = (__uint128_t) res * a % mod;
            a = (__uint128_t) a * a % mod;
          }
          else {
            if (n & 1) res = (unsigned long long) res * a % mod;
            a = (unsigned long long) a * a % mod;
          }
          n >>= 1;
        }
        return res;
      };

      function<bool(T)> test = [&](T a) {
        T x = modpow(a, d, n);
        if (x == 0) [[unlikely]]
          return false;
        if (x == 1) [[unlikely]]
          return true;
        for (T _ = 0; _ < s; ++_) {
          T y;
          if constexpr (is_64bit)
            y = (__uint128_t) x * x % n;
          else
            y = (unsigned long long) x * x % n;
          if (y == 1 && x != 1 && x != n - 1) return false;
          x = y;
        }
        return x == 1;
      };

      function<bool(vector<T>)> tests = [&](vector<T> basis) {
        for (T a : basis)
          if (!test(a)) return false;
        return true;
      };

      if (n < 2'047) return test(2);
      if (n < 1'373'653) return tests({ 2, 3 });
      if (n < 9'080'191) return tests({ 31, 73 });
      if (n < 25'326'001) return tests({ 2, 3, 5 });
      if (n < 3'215'031'751) return tests({ 2, 3, 5, 7 });
      if (n < 4'759'123'141) return tests({ 2, 7, 61 });
      if (n < 1'122'004'669'633) return tests({ 2, 13, 23, 1662803 });
      if (n < 2'152'302'898'747) return tests({ 2, 3, 5, 7, 11 });
      if (n < 3'474'749'660'383) return tests({ 2, 3, 5, 7, 11, 13 });
      if (n < 341'550'071'728'321) return tests({ 2, 3, 5, 7, 11, 13, 17 });
      if (n < 3'825'123'056'546'413'051) return tests({ 2, 3, 5, 7, 11, 13, 17, 19, 23 });
      if (ull(n) <= 18'446'744'073'709'551'615ULL) return tests({ 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 });
      // 18'446'744'073'709'551'616 は 2^64 であり、これ以上の数は 64 ビット整数型では表現できない
      // TODO: 多倍長整数を使う場合は if を追加する
      // TODO: C++23 以降なら __builtin_unreachable() -> std::unreachable() に変更可能
      __builtin_unreachable();
    }
  }  // namespace math
}  // namespace asalib
#line 8 "library/math/pollards-rho.hpp"

namespace asalib {
  namespace math {
    template<integral T>
    constexpr vector<pair<T, T>> pollards_rho(T n) {
      if (n < 2) [[unlikely]]
        return {};

      vector<pair<T, T>> res(0);
      // ある程度小さい素因数については前もって素因数分解しておく
      for (T i = 2; i * i <= min((T) 10000, n); ++i) {
        if (n % i == 0) {
          T e = 0;
          while (n % i == 0) n /= i, ++e;
          res.push_back({ i, e });
        }
      }
      if (n == 1) [[unlikely]]
        return res;

      // ここからメイン
      static_assert(sizeof(T) == 4 || sizeof(T) == 8, "T must be 32-bit or 64-bit integer type");
      constexpr bool is_64bit = sizeof(T) == 8;
      auto f = [&](T x, T s) -> T {
        if constexpr (is_64bit) return ((__uint128_t) x * x + s) % n;
        else
          return ((unsigned long long) x * x + s) % n;
      };
      function<void(T&, T)> rho = [&](T& n, T cnt) {
        if (n == 1) [[unlikely]]
          return;
        if (miller_rabin_test(n)) {
          res.push_back({ n, cnt });
          n = 1;
          return;
        }
        T s = 0;
        while (true) {
          T x = ++s, y = f(x, s);
          while (true) {
            T p = gcd(y - x + n, n);
            if (p == 0 || p == n) break;  // 失敗、 seed 変えてやり直し
            if (p != 1) {
              assert(n % p == 0);
              T e = 0;
              while (n % p == 0) n /= p, ++e;
              rho(p, cnt * e);
              if (n > 1) rho(n, cnt);
              return;
            }
            x = f(x, s), y = f(f(y, s), s);
          }
        }
      };
      while (n > 1) rho(n, 1);

      sort(res.begin(), res.end());
      return res;
    }
  }  // namespace math
}  // namespace asalib
#line 8 "tests/math/pollards-rho/libchecker.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/factorize"

int main() {
  cin.tie(nullptr)->sync_with_stdio(false);
  int q;
  cin >> q;
  while (q--) {
    ull a;
    cin >> a;
    vector<pair<ull, ull>> res = asalib::math::pollards_rho(a);
    vector<ull> ans(0);
    for (auto [p, e] : res) rep(_, e) ans.push_back(p);
    cout << ans.size();
    for (ull x : ans) cout << ' ' << x;
    cout << '\n';
  }
  return 0;
}