This documentation is automatically generated by online-judge-tools/verification-helper
View the Project on GitHub kmyk/competitive-programming-library
#include "number/primes.hpp"
#pragma once
#include <algorithm>
#include <cassert>
#include <cstdint>
#include <vector>
#include "../utils/macros.hpp"
struct prepared_primes {
int size;
std::vector<int> sieve;
std::vector<int> primes;
/**
* @note O(size)
*/
prepared_primes(int size_)
: size(size_) {
sieve.resize(size);
REP3 (p, 2, size) if (sieve[p] == 0) {
primes.push_back(p);
for (int k = p; k < size; k += p) {
if (sieve[k] == 0) {
sieve[k] = p;
}
}
}
}
/**
* @note let k be the length of the result, O(k) if n < size; O(\sqrt{n} + k) if size <= n < size^2
*/
std::vector<int64_t> list_prime_factors(int64_t n) const {
assert (1 <= n and n < (int64_t)size * size);
std::vector<int64_t> result;
// trial division for large part
for (int p : primes) {
if (n < size or n < (int64_t)p * p) {
break;
}
while (n % p == 0) {
n /= p;
result.push_back(p);
}
}
// small part
if (n == 1) {
// nop
} else if (n < size) {
while (n != 1) {
result.push_back(sieve[n]);
n /= sieve[n];
}
} else {
result.push_back(n);
}
assert (std::is_sorted(ALL(result)));
return result;
}
std::vector<int64_t> list_all_factors(int64_t n) const {
auto p = list_prime_factors(n);
std::vector<int64_t> d;
d.push_back(1);
for (int l = 0; l < p.size(); ) {
int r = l + 1;
while (r < p.size() and p[r] == p[l]) ++ r;
int n = d.size();
REP (k1, r - l) {
REP (k2, n) {
d.push_back(d[d.size() - n] * p[l]);
}
}
l = r;
}
return d;
}
/**
* @note O(1) if n < size; O(sqrt n) if size <= n < size^2
*/
bool is_prime(int64_t n) const {
assert (1 <= n and n < (int64_t)size * size);
if (n < size) {
return sieve[n] == n;
}
for (int p : primes) {
if (n < (int64_t)p * p) {
break;
}
if (n % p == 0) {
return false;
}
}
return true;
}
};
#line 2 "number/primes.hpp"
#include <algorithm>
#include <cassert>
#include <cstdint>
#include <vector>
#line 2 "utils/macros.hpp"
#define REP(i, n) for (int i = 0; (i) < (int)(n); ++ (i))
#define REP3(i, m, n) for (int i = (m); (i) < (int)(n); ++ (i))
#define REP_R(i, n) for (int i = (int)(n) - 1; (i) >= 0; -- (i))
#define REP3R(i, m, n) for (int i = (int)(n) - 1; (i) >= (int)(m); -- (i))
#define ALL(x) std::begin(x), std::end(x)
#line 7 "number/primes.hpp"
struct prepared_primes {
int size;
std::vector<int> sieve;
std::vector<int> primes;
/**
* @note O(size)
*/
prepared_primes(int size_)
: size(size_) {
sieve.resize(size);
REP3 (p, 2, size) if (sieve[p] == 0) {
primes.push_back(p);
for (int k = p; k < size; k += p) {
if (sieve[k] == 0) {
sieve[k] = p;
}
}
}
}
/**
* @note let k be the length of the result, O(k) if n < size; O(\sqrt{n} + k) if size <= n < size^2
*/
std::vector<int64_t> list_prime_factors(int64_t n) const {
assert (1 <= n and n < (int64_t)size * size);
std::vector<int64_t> result;
// trial division for large part
for (int p : primes) {
if (n < size or n < (int64_t)p * p) {
break;
}
while (n % p == 0) {
n /= p;
result.push_back(p);
}
}
// small part
if (n == 1) {
// nop
} else if (n < size) {
while (n != 1) {
result.push_back(sieve[n]);
n /= sieve[n];
}
} else {
result.push_back(n);
}
assert (std::is_sorted(ALL(result)));
return result;
}
std::vector<int64_t> list_all_factors(int64_t n) const {
auto p = list_prime_factors(n);
std::vector<int64_t> d;
d.push_back(1);
for (int l = 0; l < p.size(); ) {
int r = l + 1;
while (r < p.size() and p[r] == p[l]) ++ r;
int n = d.size();
REP (k1, r - l) {
REP (k2, n) {
d.push_back(d[d.size() - n] * p[l]);
}
}
l = r;
}
return d;
}
/**
* @note O(1) if n < size; O(sqrt n) if size <= n < size^2
*/
bool is_prime(int64_t n) const {
assert (1 <= n and n < (int64_t)size * size);
if (n < size) {
return sieve[n] == n;
}
for (int p : primes) {
if (n < (int64_t)p * p) {
break;
}
if (n % p == 0) {
return false;
}
}
return true;
}
};