朴素筛法 O(n)
#include<bits/stdc++.h>
using namespace std;
const int N = 1e6 + 10;
int primes[N], cnt;
bool st[N];
void get_primes(int n) {
for (int i = 2; i <= n; i ++ ) {
if (st[i]) continue;
primes[cnt ++ ] = i;
for (int j = i + i; j <= n; j += i) {
st[j] =true;
}
}
}
int main() {
int n;
cin >> n;
get_primes(n);
cout << cnt << endl;
return 0;
}
线性筛法(比朴素筛法快)
#include<bits/stdc++.h>
using namespace std;
const int N = 1e6 + 10;
int primes[N], cnt;
bool st[N];
void get_primes(int n) {
for (int i = 2; i <= n;i ++ ) {
if (!st[i]) primes[cnt ++ ] = i;
for (int j = 0; primes[j] <= n / i; j ++ ) {
st[primes[j] * i] = true;
if (i % primes[j] == 0) break; //primes[j] 一定是i的最小质因子
}
}
}
int main() {
int n;
cin >> n;
get_primes(n);
cout << cnt << endl;
return 0;
}