poj 1181(大数判素数 ，分解)

  1 //miller_rabin 判断一个大数是否是素数

  2 //pollard_rho 大数因子分解

  3 #include<cstdio>

  4 #include<cstdlib>

  5 #include<cstring>

  6 #include<cmath>

  7 #include<algorithm>

  8 

  9 using namespace std;

 10 

 11 #define LL long long

 12 const LL Max = (LL) 1 << 62;

 13 LL p[10]={2,3,5,7,11,13,17,19,23,29};

 14 

 15 //计算a*b%n

 16 inline LL multi_mod(LL a,LL b,LL mod)

 17 {

 18     LL sum=0;

 19     while(b)

 20     {

 21         if(b&1)    sum = (sum + a) % mod;

 22         a <<= 1;

 23         b >>= 1;

 24         if (a >= mod) a %= mod;

 25     }

 26     return sum;

 27 }

 28 

 29 //计算a^b%n;

 30 inline LL quick_mod(LL a,LL b,LL mod)

 31 {

 32     LL sum = 1;

 33     while(b)

 34     {

 35         if(b & 1) sum = multi_mod(sum, a, mod);

 36         a = multi_mod(a, a, mod);

 37         b >>= 1;

 38     }

 39     return sum;

 40 }

 41 

 42 bool miller_rabin(LL n)

 43 {

 44     LL u,m,buf;

 45     int k = 0;

 46     //将n分解为m*2^k

 47     if(n==2)   return true;

 48     if(n<2 || !(n&1))    return false;

 49     m = n - 1;

 50     while(!(m&1))

 51         k++,m >>= 1;

 52     for(int i = 0; i < 9; ++i)

 53     {

 54         if(p[i] >= n) return true;

 55         u = quick_mod(p[i], m, n);

 56         if(u==1) continue;

 57         for(int j = 0; j < k; ++j)

 58         {

 59             buf = multi_mod(u, u, n);

 60             if(buf == 1 && u != 1 && u != n - 1)

 61                 return false;

 62             u = buf;

 63         }

 64         //如果p[i]^(n-1)%n!=1那么n为合数

 65         if(u - 1) return false;

 66     }

 67     return true;

 68 }

 69 

 70 LL gcd(LL a, LL b)

 71 {

 72     return b == 0 ? a: gcd(b, a%b);

 73 }

 74 //寻找n的一个因子，该因子并不一定是最小的，所以下面要二分查找最小的那个因子

 75 LL pollard(LL n )

 76 {

 77    LL x,y,c=0,d,i=1,k=2;

 78    while(c==0 || c==2 ) c = abs( rand())%(n-1) + 1;

 79    x = y = (rand( )%( n-1 )) + 1;

 80    do

 81    {

 82       i++;

 83       d = gcd( y + n - x, n );

 84       if( d >1 && d < n )

 85           return d; 

 86       if( i == k )

 87       {

 88          y = x; k <<= 1;        

 89       }    

 90       x = (multi_mod( x , x, n )+n-c )%n;

 91     }while( x != y );

 92     return n; 

 93 }

 94 

 95 LL pollard_min(LL n)

 96 {

 97     LL p,a,b=Max;

 98     if(n==1)    return Max;

 99     if(miller_rabin(n))    return n;

100     p = pollard(n);

101     a = pollard_min(p);//二分查找

102     b = pollard_min(n / p);

103     return a < b ? a : b;

104 }

105 

106 int main(void)

107 {

108     LL T;

109     LL n;

110     scanf("%lld",&T);

111     while(T--)

112     {

113         scanf("%lld",&n);

114         if(miller_rabin(n))

115         {

116             puts("Prime");

117         }

118         else printf("%lld\n",pollard_min(n));

119     }

120     return 0;

121 }