Some sieve method

reference

OI-wiki

Prime 筛

Erichsen screen

This is well understood that, considering each of the small to large number, this number will be a multiple of the number of engagement can be labeled, but this would be a lot number of repeating sieve screen, complexity is \ (O (n \ log \ logn) \) , so you can use Euler screen.

int Eratosthenes(int n) {
    int cnt = 0;
    memset(is_prime, 1, sizeof(is_prime));
    is_prime[0] = is_prime[1] = 0;
    for (int i = 2; i <= n; ++i)
        if (is_prime[i]) {
            prime[++cnt] = i;
            for (int j = i * 2; j <= n; j += i) is_prime[j] = 0;
        }
    return cnt;
}

Euler screen

That linear sieve, sieve equivalent optimized version of the Eppendorf, so that each screen is a composite number only once.

Complexity: \ (O (n-) \)

void Euler(int n) {
    int cnt = 0;
    memset(vis, 0, sizeof(vis));
    for (int i = 2; i <= n; ++i) {
        if (!vis[i]) prime[++cnt] = i;
        for (int j = 1; j <= cnt && i * prime[j] <= n; ++j) {
            vis[i*prime[j]] = 1;
            if (i % prime[j] == 0) break;
        }
    }
}

Euler function

Linear sieve.

void phi_table(int n) {
    memset(phi, 0, sizeof(phi));
    phi[1] = 1;
    for (int i = 2; i <= n; ++i)
        if (!phi[i]) {
            for (int j = i; j <= n; j += i) {
                if (!phi[j]) phi[j] = j;
                phi[j] = phi[j] / i * (i - 1);
            }
        }
}