Miller-Rabin素性测试算法

 1 #include <iostream>
 2 #include <time.h>
 3 #include <algorithm>
 4 #include <stdio.h>
 5 
 6 typedef long long LL;
 7 
 8 using namespace std;
 9 
10 const int times = 20;
11 LL fac[1001];
12 int cnt;
13 
14 LL mul(LL a,LL b,LL mod){
15     LL ans = 0;
16     while (b){
17         if (b & 1){
18             ans = (ans + a) % mod;
19         }
20         a = (a<<1) % mod;
21         b >>= 1;
22     }
23     return ans;
24 }
25 
26 
27 LL pow(LL a,LL b,LL mod){
28     LL ans = 1;
29     while (b){
30         if (b & 1){
31             ans = mul(ans,a,mod);
32         }
33         b >>= 1;
34         a = mul(a,a,mod);
35     }
36     return ans;
37 }
38 
39 
40 bool witness(LL a,LL n){
41     LL temp = n - 1;
42     int j = 0;
43     while (temp % 2 == 0){  // 其实就是得到 m
44         j++;
45         temp /= 2;
46     }
47     LL x = pow(a,temp,n);   
48     if (x == 1 || x == n-1){   // 判断a^m
49         return true;
50     }
51     while (j--){
52         x = mul(x,x,n);  // 进一步判断 a^(2m)  a^(4m) ...
53         if (x == n-1)
54             return true;
55     }
56     return false;
57 }
58 
59 bool miller_rabin(LL n){
60     if (n == 2){ //  如果是2肯定是素数
61         return true;
62     }
63     if (n<2 || n % 2 == 0){ //如果小于2或者是大于2的偶数肯定不是素数
64         return false;
65     }
66     for (int i=0;i<times;i++){ //随机化检验
67         LL a = rand() % (n-1) + 1;
68         if (!witness(a,n))
69             return false;
70     }
71     return true;
72 }
73 
74 int main(){
75     LL tar;
76     while (cin >> tar){
77         if (miller_rabin(tar)){
78             cout << "Yes,Prime!" << endl;
79         } else
80             cout << "No" << endl;
81     }
82     return 0;
83 }