HDU-3864 D_num Miller_Rabin和Pollard_rho

　　题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3864

　　题意：给定一个数n，求n的因子只有四个的情况。

　　Miller_Rabin和Pollard_rho模板题，复杂度O(n^(1/4))，注意m^3=n的情况。

  1 //STATUS:C++_AC_62MS_232KB

  2 #include <functional>

  3 #include <algorithm>

  4 #include <iostream>

  5 //#include <ext/rope>

  6 #include <fstream>

  7 #include <sstream>

  8 #include <iomanip>

  9 #include <numeric>

 10 #include <cstring>

 11 #include <cassert>

 12 #include <cstdio>

 13 #include <string>

 14 #include <vector>

 15 #include <bitset>

 16 #include <queue>

 17 #include <stack>

 18 #include <cmath>

 19 #include <ctime>

 20 #include <list>

 21 #include <set>

 22 #include <map>

 23 using namespace std;

 24 //#pragma comment(linker,"/STACK:102400000,102400000")

 25 //using namespace __gnu_cxx;

 26 //define

 27 #define pii pair<int,int>

 28 #define mem(a,b) memset(a,b,sizeof(a))

 29 #define lson l,mid,rt<<1

 30 #define rson mid+1,r,rt<<1|1

 31 #define PI acos(-1.0)

 32 //typedef

 33 typedef long long LL;

 34 typedef unsigned long long ULL;

 35 //const

 36 const int N=2000010;

 37 const int INF=0x3f3f3f3f;

 38 const int MOD=1000000007,STA=8000010;

 39 const LL LNF=1LL<<60;

 40 const double EPS=1e-8;

 41 const double OO=1e15;

 42 const int dx[4]={-1,0,1,0};

 43 const int dy[4]={0,1,0,-1};

 44 const int day[13]={0,31,28,31,30,31,30,31,31,30,31,30,31};

 45 //Daily Use ...

 46 inline int sign(double x){return (x>EPS)-(x<-EPS);}

 47 template<class T> T gcd(T a,T b){return b?gcd(b,a%b):a;}

 48 template<class T> T lcm(T a,T b){return a/gcd(a,b)*b;}

 49 template<class T> inline T lcm(T a,T b,T d){return a/d*b;}

 50 template<class T> inline T Min(T a,T b){return a<b?a:b;}

 51 template<class T> inline T Max(T a,T b){return a>b?a:b;}

 52 template<class T> inline T Min(T a,T b,T c){return min(min(a, b),c);}

 53 template<class T> inline T Max(T a,T b,T c){return max(max(a, b),c);}

 54 template<class T> inline T Min(T a,T b,T c,T d){return min(min(a, b),min(c,d));}

 55 template<class T> inline T Max(T a,T b,T c,T d){return max(max(a, b),max(c,d));}

 56 //End

 57 

 58 LL factor[100];   //质因数分解结果（刚返回时是无序的）

 59 int tol;   //质因数的个数。数组小标从0开始

 60 const int S=10;

 61 

 62 LL gcd(LL a,LL b)

 63 {

 64     if(a==0)return 1;

 65     if(a<0) return gcd(-a,b);

 66     while(b)

 67     {

 68         LL t=a%b;

 69         a=b;

 70         b=t;

 71     }

 72     return a;

 73 }

 74 

 75 LL mult_mod(LL a,LL b,LL c)

 76 {

 77     a%=c;

 78     b%=c;

 79     LL ret=0;

 80     while(b)

 81     {

 82         if(b&1){ret+=a;ret%=c;}

 83         a<<=1;

 84         if(a>=c)a%=c;

 85         b>>=1;

 86     }

 87     return ret;

 88 }

 89 

 90 //计算  x^n %c

 91 LL pow_mod(LL x,LL n,LL mod)//x^n%c

 92 {

 93     if(n==1)return x%mod;

 94     x%=mod;

 95     LL tmp=x;

 96     LL ret=1;

 97     while(n)

 98     {

 99         if(n&1) ret=mult_mod(ret,tmp,mod);

100         tmp=mult_mod(tmp,tmp,mod);

101         n>>=1;

102     }

103     return ret;

104 }

105 //以a为基,n-1=x*2^t      a^(n-1)=1(mod n)  验证n是不是合数

106 //一定是合数返回true,不一定返回false

107 bool check(LL a,LL n,LL x,LL t)

108 {

109     LL ret=pow_mod(a,x,n);

110     LL last=ret;

111     for(int i=1;i<=t;i++)

112     {

113         ret=mult_mod(ret,ret,n);

114         if(ret==1&&last!=1&&last!=n-1) return true;//合数

115         last=ret;

116     }

117     if(ret!=1) return true;

118     return false;

119 }

120 

121 // Miller_Rabin()算法素数判定

122 //是素数返回true.(可能是伪素数，但概率极小)

123 //合数返回false;

124 bool Miller_Rabin(LL n)

125 {

126     if(n<2)return false;

127     if(n==2)return true;

128     if((n&1)==0) return false;//偶数

129     LL x=n-1;

130     LL t=0;

131     while((x&1)==0){x>>=1;t++;}

132     for(int i=0;i<S;i++)

133     {

134         LL a=rand()%(n-1)+1;//rand()需要stdlib.h头文件

135         if(check(a,n,x,t))

136             return false;//合数

137     }

138     return true;

139 }

140 

141 LL Pollard_rho(LL x,LL c)

142 {

143     LL i=1,k=2;

144     LL x0=rand()%x;

145     LL y=x0;

146     while(1)

147     {

148         i++;

149         x0=(mult_mod(x0,x0,x)+c)%x;

150         LL d=gcd(y-x0,x);

151         if(d!=1&&d!=x) return d;

152         if(y==x0) return x;

153         if(i==k){y=x0;k+=k;}

154     }

155 }

156 //对n进行素因子分解

157 void findfac(LL n)

158 {

159     if(Miller_Rabin(n))//素数

160     {

161         factor[tol++]=n;

162         return;

163     }

164     LL p=n;

165     while(p>=n)p=Pollard_rho(p,rand()%(n-1)+1);

166     findfac(p);

167     findfac(n/p);

168 }

169 

170 LL n;

171 

172 int main(){

173 //    freopen("in.txt","r",stdin);

174     srand(time(NULL));

175     int i,j;

176     LL a,b;

177     while(~scanf("%I64d",&n))

178     {

179         if(n==1){

180             printf("is not a D_num\n");

181             continue;

182         }

183         tol=0;

184         findfac(n);

185         if(tol!=2 && tol!=3){

186             printf("is not a D_num\n");

187             continue;

188         }

189         sort(factor,factor+tol);

190         if(tol==2 && factor[0]!=factor[1]){

191             printf("%I64d %I64d %I64d\n",factor[0],factor[1],n);

192         }

193         else if(tol==3 && factor[0]==factor[1] && factor[1]==factor[2]){

194             printf("%I64d %I64d %I64d\n",factor[0],factor[0]*factor[0],n);

195         }

196         else printf("is not a D_num\n");

197     }

198     return 0;

199 }