【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。

 1 /*

 2 五代李煜

 3 《清平乐·别来春半》

 4 别来春半，触目柔肠断。砌下落梅如雪乱，拂了一身还满。

 5 雁来音信无凭，路遥归梦难成。离恨恰如春草，更行更远还生。 

 6 */

 7 #include <cstdio>

 8 #include <cstring>

 9 #include <algorithm>

10 #include <cmath>

11 #include <queue>

12 #include <vector>

13 #include <iostream>

14 #include <string>

15 #include <ctime>

16 #define LOCAL

17 const int MAXN = 100000 + 5;

18 using namespace std;

19 typedef long long ll;

20 ll n;

21 

22 ll pow(ll a, ll b, ll p){

23     if (b == 1) return a % p;

24     ll tmp = pow(a, b / 2, p);

25     if (b % 2 == 0) return (tmp * tmp) % p;

26     else return (((tmp * tmp) % p) * (a % p)) % p;

27 }

28 //二次探测

29 bool Sec_Check(ll a, ll p){

30     ll tmp = pow(a, p, n);

31     if (tmp != 1 && tmp != (n - 1)) return 0;//不通过

32     if (tmp == (n - 1) || (p % 2 != 0)) return 1;

33     return Sec_Check(a, p / 2);

34 }

35 bool miller_rabin(ll n){

36     ll cnt = 20;

37     while (cnt--){

38         ll a = (rand()%(n - 1)) + 1;

39         if (!Sec_Check(a, n - 1)) return 0; 

40     }

41     return 1;

42 }

43 

44 int main(){

45     srand(time(0));

46     

47     while (scanf("%lld", &n) != EOF){

48         if (n == 1) printf("NO\n");

49         else if (miller_rabin(n)) printf("YES\n");

50         else printf("NO\n");

51     }

52     return 0;

53 }

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