poj2429 大数分解+dfs

  1 //Accepted    172 KB    172 ms
  2 //该程序为随机性算法，运行时间不定
  3 #include <cstdio>
  4 #include <cstring>
  5 #include <iostream>
  6 #include <ctime>
  7 #include <algorithm>
  8 using namespace std;
  9 long long factor[1000],factor_top=-1;
 10 //gcd
 11 long long gcd(long long a,long long b)
 12 {
 13     if (b==0) return a;
 14     return gcd(b,a%b);
 15 }
 16 //a*b%n n<2^62
 17 long long mult_mod(long long a,long long b,long long n)
 18 {
 19     long long exp=a%n,res=0;
 20     while (b)
 21     {
 22         if (b&1)
 23         {
 24             res+=exp;
 25             if (res>n) res-=n;
 26         }
 27         exp<<=1;
 28         if (exp>n) exp-=n;
 29         b>>=1;
 30     }
 31     return res;
 32 }
 33 //return a^b%n
 34 long long exp_mod(long long a,long long b,long long n)
 35 {
 36     long long res=1,exp=a%n;
 37     while (b>=1)
 38     {
 39         if (b&1)
 40         {
 41             res=mult_mod(res,exp,n);
 42         }
 43         exp=mult_mod(exp,exp,n);
 44         b>>=1;
 45     }
 46     return res;
 47 }
 48 //miller_rabin 算法进行素数判定
 49 //判断次数times次 一般取times=10
 50 //return true 则n为素数
 51 bool miller_rabin(long long n,long long times)
 52 {
 53     if (n==2) return true;
 54     if (n<2 || !(n&1)) return false;
 55     long long a,u=n-1,x,y;
 56     int t=0;
 57     while (u%2==0)
 58     {
 59        t++;
 60        u/=2;
 61     }
 62     srand(time(0));
 63     for (int i=0;i<times;i++)
 64     {
 65         a=rand()%(n-1)+1;
 66         x=exp_mod(a,u,n);
 67         for (int j=0;j<t;j++)
 68         {
 69             y=mult_mod(x,x,n);
 70             if (y==1 && x!=1 && x!=n-1)
 71             return false; //not prime
 72             x=y;
 73         }
 74         if (y!=1) return false;
 75     }
 76     return true;
 77 }
 78 //pollar_rho 求n的一个质因子
 79 //c 为测试函数中的常数
 80 long long pollard_rho(long long n,int c)
 81 {
 82     long long x,y,d,i=1,k=2;
 83     srand(time(0));
 84     x=rand()%(n-1)+1;
 85     y=x;
 86     while (true)
 87     {
 88          i++;
 89          x=(mult_mod(x,x,n)+c)%n;
 90          d=gcd(y-x,n);
 91          if (d>1 && d<n) return d;
 92          if (y==x) return n;
 93          if (i==k)
 94          {
 95              y=x;
 96              k<<=1;
 97          }
 98     }
 99 }
100 //找出n的所用质因子
101 void findFactor(long long n,int c)
102 {
103     if (n==1) return ;
104     if (miller_rabin(n,10))
105     {
106         factor[++factor_top]=n;
107         return ;
108     }
109     long long p=n;
110     while (p>=n)
111     {
112         p=pollard_rho(p,c--);
113     }
114     findFactor(p,c);
115     findFactor(n/p,c);
116 }
117 long long a[1000];
118 int m;
119 int cmp(long long a,long long b)
120 {
121     return a>b;
122 }
123 void slove()
124 {
125     sort(factor,factor+factor_top+1,cmp);
126     m=0;
127     a[0]=factor[0];
128     for (long long i=0;i<factor_top;i++)
129     {
130         if (factor[i]==factor[i+1])
131         {
132             a[m]*=factor[i];
133         }
134         else
135         {
136             m++;
137             a[m]=factor[i+1];
138         }
139     }
140 }
141 long long minx,ans;
142 void dfs(int s,long long num,long long t)
143 {
144     if (s==m+1)
145     {
146         if (minx==-1 || (num+t/num<minx))
147         {
148             minx=num+t/num;
149             ans=num;
150         }
151         return ;
152     }
153     dfs(s+1,a[s]*num,t);
154     dfs(s+1,num,t);
155 }
156 int main()
157 {
158     __int64 s,t,n;
159     while (scanf("%I64d%I64d",&s,&t)!=EOF)
160     {
161         n=t/s;
162         if (s==t)
163         {
164             printf("%I64d %I64d\n",s,t);
165             continue;
166         }
167         //printf("%I64d\n",gcd(t,s));
168         factor_top=-1;
169         findFactor(n,107);
170         //printf("findFactor()\n");
171         m=0;
172         slove();
173         //printf("slove()\n");
174         minx=-1;
175         dfs(0,1,n);
176         //printf("dfs()\n");
177         if (ans>n/ans) ans=n/ans;
178         printf("%I64d %I64d\n",ans*s,n/ans*s);
179     }
180     return 0;
181 }