素数判断的多种方法

包括线性筛，朴素判断方法，以及miller-rabin（非加强版）

#include <iostream>
#include <cstdlib>
#include <vector>
#include <map>
using namespace std;

inline bool sqrt_judge(int x)  //复杂度O(sqrt(n))
{
    if(x == 2) return 1;
    if(x == 1) return 0;
    for(int i = 2; i*i <= x; i++) if(x % i == 0) return 0;
    return 1;
}

inline int Pow(int x, int P)
{
    int ans = 1;
    for(int i = 1; i <= P; i++) ans = ans*x%(P+1);
    return ans;
}

inline bool Miller_Rabin(int x)  //不稳定随机判断，复杂度O(1)
{
    if(x == 2) return 1;
    if(x == 1) return 0;
    int p[7] = {2, 3, 5, 7, 11, 13, 17};
    for(int i = 0; i < 7 && p[i] != x; i++) if(Pow(x, p[i]-1) != 1) return 0;
    return 1;
}
vector <int> prime;
map <int, int> check;
void Select()  //素数筛，筛选复杂度O(n)，判断复杂度O(1)
{
    prime.clear(); check.clear();
    for(int i = 2; i <= 100000; i++)
    {
        if(! check[i]) prime.push_back(i);
        for(auto x : prime)
        {
            if(i * x > 100000) break;
            check[i * x] = 1;
            if(i % x == 0) break;
        }
    }
}

int main()
{
    Select();
    int n;
    while(cin>>n)
    {
        int ans = 0, i;
        switch(rand()%3)
        {
            case 0: for(i = 1; i < n; i++) if(sqrt_judge(i)) ans += i; break;
            case 1: for(i = 1; i < n; i++) if(Miller_Rabin(i)) ans += i; break;
            case 2: for(auto x : prime) if(x < n) ans += x; else break; break;
        }
        cout<<ans<<endl;
    }
}