Miller Rabin素数检测

 1 #include<iostream>
 2 #include<cstdio>
 3 #include<queue>
 4 #include<cstring>
 5 #include<algorithm>
 6 #include<cmath>
 7 #include<cstdlib>
 8 #include<ctime> 
 9 #define lson l, m, rt<<1
10 #define rson m+1, r, rt<<1|1
11 #define INF 0x3f3f3f3f
12 typedef long long LL;
13 using namespace std;/* *************************************************
14 * Miller_Rabin 算法进行素数测试
15 * 速度快，可以判断一个 < 2^63 的数是不是素数
16 *
17 **************************************************/
18 const int S = 8; 
19 LL mult_mod(LL  a,LL   b,LL   c)
20 {
21     a %= c;
22     b %= c;
23     LL ret = 0;
24     LL tmp = a;
25     while(b)
26     {
27         if(b & 1)
28         {
29         ret += tmp;
30         if(ret > c)ret -= c;
31         }
32         tmp <<= 1;
33         if(tmp > c)tmp -= c;
34         b >>= 1;
35     }
36     return ret;
37 }
38 LL  pow_mod(LL   a,LL   n,LL   mod)
39 {
40     LL ret = 1;
41     LL temp = a%mod;
42     while(n)
43     {
44         if(n & 1)ret = mult_mod(ret,temp,mod);
45         temp = mult_mod(temp,temp,mod);
46         n >>= 1;
47     }
48     return ret;
49 }
50 bool check(LL a,LL n,LL x,LL t)
51 {
52     LL ret = pow_mod(a,x,n);
53     LL last = ret;
54     for(int i = 1;i <= t;i++)
55     {
56     ret = mult_mod(ret,ret,n);
57     if(ret == 1 && last != 1 && last != n-1)return true;
58     last = ret;
59     }
60     if(ret != 1)return true;
61     else return false;
62 }
63 bool MiLLer_Rabin(LL n)
64 {
65     if( n < 2)return false;
66     if( n == 2)return true;
67     if( (n&1) == 0)return false;
68     LL x = n - 1;
69     LL t = 0;
70     while( (x&1)==0 ){x >>= 1; t++;}
71     srand(time(NULL));
72     for(int i = 0;i < S;i++)
73     {
74         LL a = rand()%(n-1) + 1;
75         if( check(a,n,x,t) )
76         return false;
77     }
78     return true;
79 }
80 int main()
81 {
82     LL n, m;
83     while(cin >> n){
84         LL cnt=0;
85         for(int i = 0; i < n; i++){
86             cin >> m;
87             if(MiLLer_Rabin(m))
88                 cnt++; 
89         }
90         cout << cnt << endl;
91     }
92 }