Yukari's Birthday(精度处理） （二分）

Yukari's Birthday

Time Limit: 12000/6000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2910    Accepted Submission(s): 610

Problem Description

Today is Yukari's n-th birthday. Ran and Chen hold a celebration party for her. Now comes the most important part, birthday cake! But it's a big challenge for them to place n candles on the top of the cake. As Yukari has lived for such a long long time, though she herself insists that she is a 17-year-old girl.
To make the birthday cake look more beautiful, Ran and Chen decide to place them like r ≥ 1 concentric circles. They place kⁱ candles equidistantly on the i-th circle, where k ≥ 2, 1 ≤ i ≤ r. And it's optional to place at most one candle at the center of the cake. In case that there are a lot of different pairs of r and k satisfying these restrictions, they want to minimize r × k. If there is still a tie, minimize r.

 

Input

There are about 10,000 test cases. Process to the end of file.
Each test consists of only an integer 18 ≤ n ≤ 10¹².

 

Output

For each test case, output r and k.

 

Sample Input

181111111

 

Sample Output

1 172 103 10
 # include<iostream> # include<cstdio> # include<cstring> # include<algorithm> # include<cmath> # define  lh   __int64 using namespace std; lh powll(lh x,int y) {     lh res=1;     for(int i=0;i<y;i++)     {         res*=x;     }     return res; } int main() {     lh n;    lh r,k;     while(~scanf("%I64d",&n))     {         r=1;         k=n-1;        lh ll,rr,mm;        for(int i=2;i<=45;i++)        {            ll=2;            rr=(lh)pow(n,1.0/i);               //规定上界            while(ll<=rr)            {                 mm=(lh)(ll+rr)/2;                 lh ans=(mm-powll(mm,i+1))/(1-mm);                 if(ans==n||ans==n-1)                 {                     if(i*mm<r*k)                     {                         r=i;                         k=mm;                     }                     break;                 }                 else if(ans>n)                      rr=mm-1;                 else                      ll=mm+1;            }        }         printf("%I64d %I64d\n",r,k);    }     return 0; }