(数论)判断素数(朴素,根号,埃氏筛,欧拉筛线性筛)

// 最基本求一个素数(on),(osqrt(n))
#include<bits/stdc++.h>
using namespace std;
int main()
{
    int n;
    cin>>n;
    for(int i=2;i<n;i++)//o(n)
        if(n%i==0){
            cout<<"no";
            return 0;
        }
    for(int i=2;i<=n/i;i++)//o(sqrt(n))
        if(n%i==0){
            cout<<"no";
            return 0;
        }    
    cout<<"yes";
    return 0;
}

//埃氏筛,一次性求n之前所有素数(on)
#include<bits/stdc++.h>
using namespace std;
const int N=1e5+10;
int n,f[N],a[N],res,maxx=-1;
map<int,int>mp;
bool vis[N];
int main()
{
    cin>>n;
    for(int i=0;i<n;i++) cin>>a[i],maxx=max(maxx,a[i]);
    for(int i=2;i<=maxx;i++){
        if(!vis[i]){
            mp[i]=1;
            for(int j=i;j<=maxx;j+=i) vis[j]=true;
        }
    }
    for(int i=0;i<=n;i++) if(mp.count(a[i])) cout<<a[i]<<" ";
    return 0;
}

//欧拉筛(线性筛)(时间复杂度最快):https://www.luogu.com.cn/problem/P3383
//https://www.bilibili.com/video/BV1hR4y1u7e1/?spm_id_from=333.337.search-card.all.click&vd_source=b44efb267aea765a23ee5e2d900d1d5a
#include<bits/stdc++.h>
using namespace std;
const int N=1e8+10;
int n,res,k,prime[N],num;
bool vis[N];
int main()
{
    scanf("%d%d",&n,&k);
    for(int i=2;i<=n;i++){
        if(!vis[i]) prime[++res]=i;
        for(int j=1;prime[j]<=n/i;j++){
            vis[prime[j]*i]=true;
            if(!(i%prime[j])) break;
        }
    }
    while(k--){
        scanf("%d",&num);
        printf("%d\n",prime[num]);
    }
    return 0;
}