Enumerate Primes(素数列挙) (math/number-theory/enumerate-primes.hpp)

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• Last update: 2024-04-24 02:34:04+09:00
• Include: #include "math/number-theory/enumerate-primes.hpp"

エラトステネスの篩を用いて素数を列挙します。

enumerate_primes

vector< int > enumerate_primes(int n)

$n$ 以下の素数を昇順に返します。

制約

• $0 \le n$

計算量

• $O(n \log \log n)$

Depends on

• Prime Table(素数テーブル) (math/number-theory/prime-table.hpp)

Verified with

• test/verify/yosupo-enumerate-primes.test.cpp

Code

#include "prime-table.hpp"

vector< int > enumerate_primes(int n) {
  if(n <= 1) return {};
  auto d = prime_table(n);
  vector< int > primes;
  primes.reserve(count(begin(d), end(d), true));
  for(int i = 0; i < d.size(); i++) {
    if(d[i]) primes.push_back(i);
  }
  return primes;
}

#line 1 "math/number-theory/prime-table.hpp"
/**
 * @brief Prime Table(素数テーブル)
 * 
 */
vector< bool > prime_table(int n) {
  vector< bool > prime(n + 1, true);
  if(n >= 0) prime[0] = false;
  if(n >= 1) prime[1] = false;
  for(int i = 2; i * i <= n; i++) {
    if(!prime[i]) continue;
    for(int j = i * i; j <= n; j += i) {
      prime[j] = false;
    }
  }
  return prime;
}
#line 2 "math/number-theory/enumerate-primes.hpp"

vector< int > enumerate_primes(int n) {
  if(n <= 1) return {};
  auto d = prime_table(n);
  vector< int > primes;
  primes.reserve(count(begin(d), end(d), true));
  for(int i = 0; i < d.size(); i++) {
    if(d[i]) primes.push_back(i);
  }
  return primes;
}

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