筛素数

筛素数

1.暴力筛

#include <cstdio>
#include <iostream>
using namespace std;

int n, q;

bool check (int);

int main () {
    scanf ("%d %d", &n, &q);
    for (int i = 1; i <= q; i++) {
        int x; scanf ("%d", &x);
        if (check (x)) {
            printf ("Yes\n");
        }
        else {
            printf ("No\n");
        }
    }
    return 0;
}

bool check (int x) {
    if (x == 1) return 0;
    for (int i = 2; i <= x / i; i++) {
        if (x % i == 0) return 0;
    }
    return 1;
}

2.埃筛

#include <cstdio>
#include <iostream>
using namespace std;

const int MAXN = 100000005;

int n, q, len;
int prime[MAXN];

bool vis[MAXN];

void Make ();

int main () {
    scanf ("%d %d", &n, &q);
    Make ();
    for (int i = 1; i <= q; i++) {
        int x; scanf ("%d", &x);
        if (vis[x] == 0) {
            printf ("Yes\n");
        }
        else {
            printf ("No\n");
        }
    }
    return 0;
}

void Make () {
    vis[1] = 1;
    for (int i = 2; i <= n; i++) {
        if (vis[i] == 0) {
            prime[++len] = i;
            for (int j = i; j <= n / i; j++) {
                vis[i * j] = 1;
            }
        }
    }
}

3.线性筛(欧拉筛)

#include <cstdio>
#include <iostream>
using namespace std;

const int MAXN = 100000005;
int n, m, num;
int prime[MAXN];

bool vis[MAXN];

void oulasai();

int main() {
    cin >> n >> m;
    oulasai();
    for (int i = 1; i <= m; i++) {
        int tem;
        scanf("%d", &tem);
        if (vis[tem] == 0)
            printf("Yes\n");
        else
            printf("No\n");
    }
    return 0;
}

void oulasai() {
    vis[1] = 1;
    for (int i = 2; i <= n; i++) {
        if (vis[i] == 0) {  //如果是质数
            prime[++num] = i;
        }
        for (int j = 1; j <= num; j++) {
            if (prime[j] > n / i)
                break;
            vis[i * prime[j]] = 1;
            if (i % prime[j] == 0)
                break;
        }
    }
}