pollard_rho和Miller_Rabin

Miller_Rabin就是以概论大小来判断素数 可以判断2^63范围的数

pollard_rho推荐两个很好的博客来理解：整数分解费马方法以及Pollard rho和[ZZ]Pollard Rho算法思想

 //#pragma comment(linker, "/STACK:167772160")//手动扩栈~~~~hdu 用c++交
 #include<cstdio>
 #include<cstring>
 #include<cstdlib>
 #include<iostream>
 #include<queue>
 #include<stack>
 #include<cmath>
 #include<set>
 #include<algorithm>
 #include<vector>
 #include<malloc.h>
 using namespace std;
 #define clc(a,b) memset(a,b,sizeof(a))
 #define inf 0x3f3f3f3f
 #define LL long long
 const double eps = 1e-;
 const double pi = acos(-);
 // inline int r(){
 //     int x=0,f=1;char ch=getchar();
 //     while(ch>'9'||ch<'0'){if(ch=='-') f=-1;ch=getchar();}
 //     while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
 //     return x*f;
 // }
 const int Times = ;
 const int N = ;

 LL ct, cnt;
 LL fac[N], num[N];//fac记录素因子，num记录每个因子的次数

 LL gcd(LL a, LL b)
 {
     return b? gcd(b, a % b) : a;
 }
 //return a*b%m
 LL multi(LL a, LL b, LL m)
 {
     LL ans = ;
     a %= m;
     while(b)
     {
         if(b & )
         {
             ans = (ans + a) % m;
             b--;
         }
         b >>= ;
         a = (a + a) % m;
     }
     return ans;
 }

 LL quick_mod(LL a, LL b, LL m)
 {
     LL ans = ;
     a %= m;
     while(b)
     {
         if(b & )
         {
             ans = multi(ans, a, m);
             b--;
         }
         b >>= ;
         a = multi(a, a, m);
     }
     return ans;
 }
 //判断素数
 bool Miller_Rabin(LL n)
 {
     if(n == ) return true;
     if(n <  || !(n & )) return false;
     LL m = n - ;
     int k = ;
     while((m & ) == )
     {
         k++;
         m >>= ;
     }
     for(int i=; i<Times; i++)
     {
         LL a = rand() % (n - ) + ;
         LL x = quick_mod(a, m, n);
         LL y = ;
         for(int j=; j<k; j++)
         {
             y = multi(x, x, n);
             if(y ==  && x !=  && x != n - ) return false;
             x = y;
         }
         if(y != ) return false;
     }
     return true;
 }
 //分解素数
 LL pollard_rho(LL n, LL c)
 {
     LL i = , k = ;
     LL x = rand() % (n - ) + ;
     LL y = x;
     while(true)
     {
         i++;
         x = (multi(x, x, n) + c) % n;
         LL d = gcd((y - x + n) % n, n);
         if( < d && d < n) return d;
         if(y == x) return n;
         if(i == k)
         {
             y = x;
             k <<= ;
         }
     }
 }

 void find(LL n, int c)
 {
     if(n == ) return;
     if(Miller_Rabin(n))
     {
         fac[ct++] = n;
         return ;
     }
     LL p = n;
     LL k = c;
     while(p >= n) p = pollard_rho(p, c--);
     find(p, k);
     find(n / p, k);
 }

 int main()
 {
     LL n;
     while(cin>>n)
     {
         ct = ;
         find(n, );
         sort(fac, fac + ct);
         num[] = ;
         int k = ;
         for(int i=; i<ct; i++)
         {
             if(fac[i] == fac[i-])
                 ++num[k-];
             else
             {
                 num[k] = ;
                 fac[k++] = fac[i];
             }
         }
         cnt = k;
         for(int i=; i<cnt; i++)
             cout<<fac[i]<<"^"<<num[i]<<" ";
         cout<<endl;
     }
     return ;
 }