Asa's CP Library
a01sa01to's competitive programming library. Requires C++20 or higher with GCC. This documentation is automatically generated by online-judge-tools/verification-helper
tests/math/pollards-rho/libchecker.test.cpp
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- Last update: 2025-06-26 16:44:42+09:00
- Problem: https://judge.yosupo.jp/problem/factorize
Depends on
- FastIO
(library/fastio.hpp)
- ミラー・ラビン素数判定法
(library/math/miller-rabin.hpp)
- ポラード・ロー素因数分解法
(library/math/pollards-rho.hpp)
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 "../../../library/fastio.hpp"
#include "../../../library/math/pollards-rho.hpp"
#define PROBLEM "https://judge.yosupo.jp/problem/factorize"
int main() {
int q;
asalib::FastIO >> q;
while (q--) {
ull a;
asalib::FastIO >> 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);
asalib::FastIO << ans.size();
for (ull x : ans) asalib::FastIO << ' ' << x;
asalib::FastIO << '\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/fastio.hpp"
#line 5 "library/fastio.hpp"
#include <concepts>
#line 11 "library/fastio.hpp"
#include <type_traits>
using namespace std;
// TODO: 何も入力がない場合にも対応する？
namespace asalib {
namespace _internal {
class FastIO {
private:
using uint = unsigned int;
static constexpr uint BUFFER_SIZE = 1 << 20;
static constexpr uint MAX_TOKEN_SIZE = 64;
// ===== Read ===== //
private:
array<char, BUFFER_SIZE> read_buffer;
array<char, BUFFER_SIZE>::iterator read_ptr;
uint read_size = 0;
inline void load() {
// まだ読んでないデータを前に持ってくる
memcpy(read_buffer.begin(), read_ptr, read_size - (read_ptr - read_buffer.begin()));
read_size -= read_ptr - read_buffer.begin();
read_ptr = read_buffer.begin();
// stdin から読み込み
read_size += fread(read_buffer.begin() + read_size, 1, BUFFER_SIZE - read_size, stdin);
}
inline void skip_space() {
// 制御文字 + space
// DEL (127 = 0x7F) がコーナーケースだがまあ使わんやろ
while (*read_ptr <= ' ') ++read_ptr;
}
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _read_uint(T& x) {
x = 0;
while (true) {
uint64_t v;
memcpy(&v, read_ptr, 8);
// '0' -> 0 処理
// こっちを先にやることで制御文字系もはじく
v -= 0x30'30'30'30'30'30'30'30;
// ASCII 範囲外
if (v & 0x80'80'80'80'80'80'80'80) break;
// 桁ごとの数字から数値に
v = (v * 10 + (v >> 8)) & 0x00ff00ff00ff00ff;
v = (v * 100 + (v >> 16)) & 0x0000ffff0000ffff;
v = (v * 10000 + (v >> 32)) & 0x00000000ffffffff;
x = 1'0000'0000 * x + v;
read_ptr += 8;
}
while (true) {
uint32_t v;
memcpy(&v, read_ptr, 4);
v -= 0x30'30'30'30;
if (v & 0x80'80'80'80) break;
v = (v * 10 + (v >> 8)) & 0x00ff00ff;
v = (v * 100 + (v >> 16)) & 0x0000ffff;
x = 1'0000 * x + v;
read_ptr += 4;
}
while (true) {
uint16_t v;
memcpy(&v, read_ptr, 2);
v -= 0x3030;
if (v & 0x8080) break;
v = (v * 10 + (v >> 8)) & 0x00ff;
x = 100 * x + v;
read_ptr += 2;
}
if (*read_ptr > ' ') x = 10 * x + (*read_ptr++ & 0x0f);
}
inline void read_commonop() {
// そろそろ限界なら読み込み
if ((read_ptr - read_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) load();
skip_space();
}
public:
FastIO& operator>>(char& x) {
read_commonop();
x = *read_ptr++;
return *this;
}
FastIO& operator>>(string& x) {
read_commonop();
x.clear();
while (*read_ptr > ' ') {
x += *read_ptr++;
if (read_ptr == read_buffer.end()) load();
}
return *this;
}
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
FastIO& operator>>(T& x) {
read_commonop();
constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
if constexpr (is_signed) {
if (*read_ptr == '-') {
++read_ptr;
_read_uint(x);
x = -x;
return *this;
}
}
_read_uint(x);
return *this;
}
// ===== Write ===== //
private:
array<char, BUFFER_SIZE> write_buffer;
array<char, BUFFER_SIZE>::iterator write_ptr;
static constexpr uint MAX_PRECOMPUTE_NUM = 1'0000;
static constexpr uint MAX_PRECOMPUTE_NUM_DIGIT = 4;
static constexpr array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits = [] {
array<char, MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT> digits {};
for (uint i = 0; i < MAX_PRECOMPUTE_NUM; ++i) {
uint x = i;
for (int j = MAX_PRECOMPUTE_NUM_DIGIT - 1; j >= 0; --j) {
digits[i * MAX_PRECOMPUTE_NUM_DIGIT + j] = '0' + (x % 10);
x /= 10;
}
}
return digits;
}();
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
static constexpr array<T, numeric_limits<T>::digits10 + 1> Pow10 = [] {
array<T, numeric_limits<T>::digits10 + 1> pow10 {};
pow10[0] = 1;
for (uint i = 1; i < pow10.size(); ++i) pow10[i] = pow10[i - 1] * 10;
return pow10;
}();
inline void write_commonop() {
// そろそろ限界なら書き込む
if ((write_ptr - write_buffer.begin()) + MAX_TOKEN_SIZE >= BUFFER_SIZE) flush();
}
inline void putchar(const char& x) { *write_ptr++ = x; }
template<typename T, int NumDig>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _write_uint_top(const T& x) {
// leading-zero を書き込まないようにする
if constexpr (NumDig > 1) {
if (x < Pow10<T>[NumDig - 1]) {
_write_uint_top<T, NumDig - 1>(x);
return;
}
}
copy_n(digits.begin() + (x + 1) * MAX_PRECOMPUTE_NUM_DIGIT - NumDig, NumDig, write_ptr);
write_ptr += NumDig;
}
template<typename T, int NumDig>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _write_uint(const T& x) {
if constexpr (NumDig >= 0) {
if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x / MAX_PRECOMPUTE_NUM);
copy_n(digits.begin() + x % MAX_PRECOMPUTE_NUM * MAX_PRECOMPUTE_NUM_DIGIT, MAX_PRECOMPUTE_NUM_DIGIT, write_ptr);
write_ptr += MAX_PRECOMPUTE_NUM_DIGIT;
}
}
template<typename T, int NumDig>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
inline void _write_uint_root(const T& x) {
if constexpr (is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>) {
// 128bit 除算はおそいので 64bit 除算を使う
if (x < Pow10<T>[16]) {
_write_uint_root<uint64_t, NumDig>(x);
}
else if (x < Pow10<T>[32]) {
_write_uint_root<uint64_t, NumDig>(x / Pow10<T>[16]);
_write_uint<uint64_t, 16>(x % Pow10<T>[16]);
}
else {
_write_uint_root<uint64_t, NumDig>(x / Pow10<T>[32]);
_write_uint<uint64_t, 16>(x % Pow10<T>[32] / Pow10<T>[16]);
_write_uint<uint64_t, 16>(x % Pow10<T>[16]);
}
return;
}
if constexpr (NumDig < numeric_limits<T>::digits10) {
if (x >= Pow10<T>[NumDig]) {
_write_uint_root<T, NumDig + MAX_PRECOMPUTE_NUM_DIGIT>(x);
return;
}
}
_write_uint_top<T, MAX_PRECOMPUTE_NUM_DIGIT>(x / Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
if constexpr (NumDig > MAX_PRECOMPUTE_NUM_DIGIT) _write_uint<T, NumDig - MAX_PRECOMPUTE_NUM_DIGIT>(x % Pow10<T>[NumDig - MAX_PRECOMPUTE_NUM_DIGIT]);
}
public:
inline void flush() {
fwrite(write_buffer.begin(), 1, write_ptr - write_buffer.begin(), stdout);
write_ptr = write_buffer.begin();
}
FastIO& operator<<(const char& x) {
write_commonop();
putchar(x);
return *this;
}
FastIO& operator<<(const string& x) {
write_commonop();
uint idx = 0;
while (idx < x.size()) {
const uint siz = min(BUFFER_SIZE - (uint) (write_ptr - write_buffer.begin()), (uint) x.size() - idx);
copy_n(x.begin() + idx, siz, write_ptr);
write_ptr += siz;
idx += siz;
if (write_ptr == write_buffer.end()) flush();
}
return *this;
}
template<typename T>
requires(integral<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>)
FastIO& operator<<(const T& x) {
write_commonop();
constexpr bool is_signed = is_signed_v<T> || is_same_v<T, __int128_t>;
if constexpr (is_signed) {
if (x < 0) {
putchar('-');
_write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(-x);
return *this;
}
}
_write_uint_root<T, MAX_PRECOMPUTE_NUM_DIGIT>(x);
return *this;
}
// ===== Common ====== //
public:
FastIO() {
read_ptr = read_buffer.begin();
write_ptr = write_buffer.begin();
load();
}
~FastIO() { flush(); }
};
} // namespace _internal
_internal::FastIO FastIO;
} // namespace asalib
#line 2 "library/math/pollards-rho.hpp"
#line 10 "library/math/pollards-rho.hpp"
using namespace std;
#line 2 "library/math/miller-rabin.hpp"
#line 7 "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 13 "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 9 "tests/math/pollards-rho/libchecker.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/factorize"
int main() {
int q;
asalib::FastIO >> q;
while (q--) {
ull a;
asalib::FastIO >> 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);
asalib::FastIO << ans.size();
for (ull x : ans) asalib::FastIO << ' ' << x;
asalib::FastIO << '\n';
}
return 0;
}