【HOJ1356】【Miller_rabin素性测试】Prime Judge

Given a positive integer, your job is writing a program to determine whether it is a prime number or not.

Input

There are several tests. Each test consists of a positive integer n(no more than 2^31) on a single line. Input is terminated by end of file.

Output

For each integer in the input, print a "YES" if it is a prime number, otherwise print a "NO" instead.

Sample Input

4
5
6

Sample Output

NO
YES
NO
【分析】
素性测试最基本的应用，主要精髓在于费马小定理和二次探测理论。

/*
五代李煜
《清平乐·别来春半》
别来春半，触目柔肠断。砌下落梅如雪乱，拂了一身还满。
雁来音信无凭，路遥归梦难成。离恨恰如春草，更行更远还生。 
*/
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <queue>
#include <vector>
#include <iostream>
#include <string>
#include <ctime>
#define LOCAL
const int MAXN = 100000 + 5;
using namespace std;
typedef long long ll;
ll n;

ll pow(ll a, ll b, ll p){
    if (b == 1) return a % p;
    ll tmp = pow(a, b / 2, p);
    if (b % 2 == 0) return (tmp * tmp) % p;
    else return (((tmp * tmp) % p) * (a % p)) % p;
}
//二次探测
bool Sec_Check(ll a, ll p){
    ll tmp = pow(a, p, n);
    if (tmp != 1 && tmp != (n - 1)) return 0;//不通过
    if (tmp == (n - 1) || (p % 2 != 0)) return 1;
    return Sec_Check(a, p / 2);
}
bool miller_rabin(ll n){
    ll cnt = 20;
    while (cnt--){
        ll a = (rand()%(n - 1)) + 1;
        if (!Sec_Check(a, n - 1)) return 0; 
    }
    return 1;
}

int main(){
    srand(time(0));
    
    while (scanf("%lld", &n) != EOF){
        if (n == 1) printf("NO\n");
        else if (miller_rabin(n)) printf("YES\n");
        else printf("NO\n");
    }
    return 0;
}