Prime Number Aizu - 0009线性筛素数

Write a program which reads an integer n and prints the number of prime numbers which are less than or equal to n. A prime number is a natural number which has exactly two distinct natural number divisors: 1 and itself. For example, the first four prime numbers are: 2, 3, 5 and 7.

Input

Input consists of several datasets. Each dataset has an integer n (1 ≤ n ≤ 999,999) in a line.

The number of datasets is less than or equal to 30.

Output

For each dataset, prints the number of prime numbers.

Sample Input

10
3
11

Output for the Sample Input

4
2
5

#include <cstdio>
#include <vector>

using namespace std;

class Factor {
public:
    vector<bool> is_prime;//pi : min prime factor
    vector<int> prime, pi;
    int sieve(int sz) {
        int cnt = 0;

        is_prime.resize(sz + 1, false);
        pi.resize(sz + 1, 0);
        for (int i = 1; i <= sz; i++) {
            pi[i] = i;
        }
        for (int i = 2; i <= sz; i++) {
            if (pi[i] == i) {
                prime.push_back(i);
                is_prime[i] = true;
                ++cnt;
            }
            for (int j = 0; j < cnt && 1LL * prime[j] * i <= sz; j++) {
                pi[prime[j] * i] = prime[j];
                if (i % prime[j] == 0) {
                    break;
                }
            }
        }
        return cnt;
    }
};

const int MAXN = 1e6 + 10;

int ans[MAXN];

int main() {
    Factor fa;
    int n = 1000000;
    fa.sieve(n);
    for (int i = 1; i <= n; i++) {
        ans[i] = ans[i - 1] + fa.is_prime[i];
    }
    int x;
    while (~scanf("%d", &x)) {
        printf("%d\n", ans[x]);
    }

    return 0;
}