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math/primefactor_ll2.cpp
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- Last update: 2021-06-21 15:24:20+09:00
Code
#include <random>
using ull = unsigned long long;
using u128 = __uint128_t;
template< class T>
T pow_ (T x, ull n, ull M){
T u = 1;
if(n > 0){
u = pow_(x, n/2, M);
if (n % 2 == 0) u = (u*u) % M;
else u = (((u * u)% M) * x) % M;
}
return u;
};
bool suspect(__uint128_t a, ull s, ull d, ull n){
__uint128_t x = pow_(a, d, n);
if (x == 1) return true;
for (int r = 0; r < s; ++r) {
if(x == n-1) return true;
x = x * x % n;
}
return false;
}
template<class T>
bool miller_rabin(T m){
ull n = m;
if (n <= 1 || (n > 2 && n % 2 == 0)) return false;
ull d = n - 1, s = 0;
while (!(d&1)) {++s; d >>= 1;}
vector<ull> v = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
if(n <= 4759123141LL) v = {2, 7, 61};
for (auto &&p : v) {
if(p >= n) break;
if(!suspect(p, s, d, n)) return false;
}
return true;
}
template<typename T>
struct ExactDiv {
T t, i, val;
ExactDiv() {}
ExactDiv(T n) : t(T(-1) / n), i(mul_inv(n)) , val(n) {};
T mul_inv(T n) {
T x = n;
for (int i = 0; i < 5; ++i) x *= 2 - n * x;
return x;
}
bool divide(T n) const {
if(val == 2) return !(n & 1);
return n * this->i <= this->t;
}
};
vector<ExactDiv<ull>> get_prime(int n){
if(n <= 1) return vector<ExactDiv<ull>>();
vector<bool> is_prime(n+1, true);
vector<ExactDiv<ull>> prime;
is_prime[0] = is_prime[1] = false;
for (int i = 2; i <= n; ++i) {
if(is_prime[i]) prime.emplace_back(i);
for (auto &&j : prime){
if(i*j.val > n) break;
is_prime[i*j.val] = false;
if(j.divide(i)) break;
}
}
return prime;
}
const auto primes = get_prime(50000);
random_device rng;
struct mod64 {
ull n;
static ull mod, inv, r2;
mod64() : n(0) {}
mod64(ull x) : n(init(x)) {}
static ull init(ull w) { return reduce(u128(w) * r2); }
static void set_mod(ull m) {
mod = inv = m;
for (int i = 0; i < 5; ++i) inv *= 2 - inv * m;
r2 = -u128(m) % m;
}
static ull reduce(u128 x) {
ull y = ull(x >> 64) - ull((u128(ull(x) * inv) * mod) >> 64);
return ll(y) < 0 ? y + mod : y;
};
mod64& operator+=(mod64 x) { n += x.n - mod; if(ll(n) < 0) n += mod; return *this; }
mod64 operator+(mod64 x) const { return mod64(*this) += x; }
mod64& operator*=(mod64 x) { n = reduce(u128(n) * x.n); return *this; }
mod64 operator*(mod64 x) const { return mod64(*this) *= x; }
ull val() const { return reduce(n); }
};
ull mod64::mod, mod64::inv, mod64::r2;
template<class T>
T pollard_rho2(T n) {
uniform_int_distribution<T> ra(1, n-1);
mod64::set_mod(n);
while(true){
ull c_ = ra(rng), g = 1, r = 1, m = 500;
while(c_ == n-2) c_ = ra(rng);
mod64 y(ra(rng)), xx(0), c(c_), ys(0), q(1);
while(g == 1){
xx.n = y.n;
for (int i = 1; i <= r; ++i) {
y *= y; y += c;
}
T k = 0; g = 1;
while(k < r && g == 1){
for (int i = 1; i <= (m > (r-k) ? (r-k) : m); ++i) {
ys.n = y.n;
y *= y; y += c;
ull xxx = xx.val(), yyy = y.val();
q *= mod64(xxx > yyy ? xxx - yyy : yyy - xxx);
}
g = __gcd<ll>(q.val(), n);
k += m;
}
r *= 2;
}
if(g == n) g = 1;
while (g == 1){
ys *= ys; ys += c;
ull xxx = xx.val(), yyy = ys.val();
g = __gcd<ll>(xxx > yyy ? xxx - yyy : yyy - xxx, n);
}
if (g != n && miller_rabin(g)) return g;
}
}
template<class T>
vector<T> prime_factor(T n, int d = 0){
vector<T> a, res;
if(!d) for (auto &&i : primes) {
while (i.divide(n)){
res.emplace_back(i.val);
n /= i.val;
}
}
while(n != 1){
if(miller_rabin(n)){
a.emplace_back(n);
break;
}
T x = pollard_rho2(n);
n /= x;
a.emplace_back(x);
}
for (auto &&i : a) {
if (miller_rabin(i)) {
res.emplace_back(i);
} else {
vector<T> b = prime_factor(i, d + 1);
for (auto &&j : b) res.emplace_back(j);
}
}
sort(res.begin(),res.end());
return res;
}#line 1 "math/primefactor_ll2.cpp"
#include <random>
using ull = unsigned long long;
using u128 = __uint128_t;
template< class T>
T pow_ (T x, ull n, ull M){
T u = 1;
if(n > 0){
u = pow_(x, n/2, M);
if (n % 2 == 0) u = (u*u) % M;
else u = (((u * u)% M) * x) % M;
}
return u;
};
bool suspect(__uint128_t a, ull s, ull d, ull n){
__uint128_t x = pow_(a, d, n);
if (x == 1) return true;
for (int r = 0; r < s; ++r) {
if(x == n-1) return true;
x = x * x % n;
}
return false;
}
template<class T>
bool miller_rabin(T m){
ull n = m;
if (n <= 1 || (n > 2 && n % 2 == 0)) return false;
ull d = n - 1, s = 0;
while (!(d&1)) {++s; d >>= 1;}
vector<ull> v = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
if(n <= 4759123141LL) v = {2, 7, 61};
for (auto &&p : v) {
if(p >= n) break;
if(!suspect(p, s, d, n)) return false;
}
return true;
}
template<typename T>
struct ExactDiv {
T t, i, val;
ExactDiv() {}
ExactDiv(T n) : t(T(-1) / n), i(mul_inv(n)) , val(n) {};
T mul_inv(T n) {
T x = n;
for (int i = 0; i < 5; ++i) x *= 2 - n * x;
return x;
}
bool divide(T n) const {
if(val == 2) return !(n & 1);
return n * this->i <= this->t;
}
};
vector<ExactDiv<ull>> get_prime(int n){
if(n <= 1) return vector<ExactDiv<ull>>();
vector<bool> is_prime(n+1, true);
vector<ExactDiv<ull>> prime;
is_prime[0] = is_prime[1] = false;
for (int i = 2; i <= n; ++i) {
if(is_prime[i]) prime.emplace_back(i);
for (auto &&j : prime){
if(i*j.val > n) break;
is_prime[i*j.val] = false;
if(j.divide(i)) break;
}
}
return prime;
}
const auto primes = get_prime(50000);
random_device rng;
struct mod64 {
ull n;
static ull mod, inv, r2;
mod64() : n(0) {}
mod64(ull x) : n(init(x)) {}
static ull init(ull w) { return reduce(u128(w) * r2); }
static void set_mod(ull m) {
mod = inv = m;
for (int i = 0; i < 5; ++i) inv *= 2 - inv * m;
r2 = -u128(m) % m;
}
static ull reduce(u128 x) {
ull y = ull(x >> 64) - ull((u128(ull(x) * inv) * mod) >> 64);
return ll(y) < 0 ? y + mod : y;
};
mod64& operator+=(mod64 x) { n += x.n - mod; if(ll(n) < 0) n += mod; return *this; }
mod64 operator+(mod64 x) const { return mod64(*this) += x; }
mod64& operator*=(mod64 x) { n = reduce(u128(n) * x.n); return *this; }
mod64 operator*(mod64 x) const { return mod64(*this) *= x; }
ull val() const { return reduce(n); }
};
ull mod64::mod, mod64::inv, mod64::r2;
template<class T>
T pollard_rho2(T n) {
uniform_int_distribution<T> ra(1, n-1);
mod64::set_mod(n);
while(true){
ull c_ = ra(rng), g = 1, r = 1, m = 500;
while(c_ == n-2) c_ = ra(rng);
mod64 y(ra(rng)), xx(0), c(c_), ys(0), q(1);
while(g == 1){
xx.n = y.n;
for (int i = 1; i <= r; ++i) {
y *= y; y += c;
}
T k = 0; g = 1;
while(k < r && g == 1){
for (int i = 1; i <= (m > (r-k) ? (r-k) : m); ++i) {
ys.n = y.n;
y *= y; y += c;
ull xxx = xx.val(), yyy = y.val();
q *= mod64(xxx > yyy ? xxx - yyy : yyy - xxx);
}
g = __gcd<ll>(q.val(), n);
k += m;
}
r *= 2;
}
if(g == n) g = 1;
while (g == 1){
ys *= ys; ys += c;
ull xxx = xx.val(), yyy = ys.val();
g = __gcd<ll>(xxx > yyy ? xxx - yyy : yyy - xxx, n);
}
if (g != n && miller_rabin(g)) return g;
}
}
template<class T>
vector<T> prime_factor(T n, int d = 0){
vector<T> a, res;
if(!d) for (auto &&i : primes) {
while (i.divide(n)){
res.emplace_back(i.val);
n /= i.val;
}
}
while(n != 1){
if(miller_rabin(n)){
a.emplace_back(n);
break;
}
T x = pollard_rho2(n);
n /= x;
a.emplace_back(x);
}
for (auto &&i : a) {
if (miller_rabin(i)) {
res.emplace_back(i);
} else {
vector<T> b = prime_factor(i, d + 1);
for (auto &&j : b) res.emplace_back(j);
}
}
sort(res.begin(),res.end());
return res;
}