首先要了解什么式埃式筛法之前，需要知道一个定理。
就是素数的整数倍一定不是素数。
了解了这个就基本大概懂了埃式筛法。
Code
#include <iostream>
#include <vector>
#include <ctime>
using namespace std;
vector <int> sieve_of_eratosthenes(int n) {
vector <int> primes;
vector <bool> is_prime(n + 1, true);
is_prime[0] = is_prime[1] = false;
for (int i = 2; i <= n; i++) {
if (is_prime[i]) {
primes.push_back(i);
}
for (int j = 2; i * j <= n; j++) {
is_prime[i * j] = false;
}
}
return primes;
}
int main() {
clock_t start, end;
start = clock();
int n;
cout << "Please Enter n: ";
cin >> n;
vector <int> primes = sieve_of_eratosthenes(n);
cout << "Primes: ";
for (int prime : primes) {
cout << prime << " ";
}
cout << "\n素数个数为" << primes.size() << "个\n";
end = clock();
cout << "The run time is: " << (double)(end - start) / CLOCKS_PER_SEC << "s" << endl;
return 0;
}
运行结果
Code
#include <iostream>
#include <vector>
#include <ctime>
using namespace std;
// 埃式筛法求解素数
bool sieve_of_eratosthenes(int n) {
vector <bool> is_prime(n + 1, true);
is_prime[0] = is_prime[1] = false;
for (int i = 2; i <= n; i++) {
if (is_prime[i] && i == n) {
return true;
}
for (int j = 2; i * j <= n; j++) {
is_prime[i * j] = false;
if (i * j == n) {
return false;
}
}
}
}
int main() {
clock_t start, end;
start = clock();
int n;
cout << "Please Enter n: ";
cin >> n;
if (sieve_of_eratosthenes(n)) {
cout << n << "是素数!!!";
}
else {
cout << n << "不是素数...";
}
end = clock();
cout << "The run time is: " << (double)(end - start) / CLOCKS_PER_SEC << "s" << endl;
return 0;
}
运行结果
