HDU 4430 Yukari's Birthday

Yukari's Birthday

Time Limit: 12000/6000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 5449    Accepted Submission(s): 1309

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 <stdio.h>#include <string.h>#include <math.h>#include <algorithm>using namespace std;#define ll __int64ll n;ll bin(ll s){    ll l = 2,r = n,mid,i;    while(l<=r)    {        mid = (l+r)/2;        ll sum = 1,ans = 0;;        for(i = 1; i<=s; i++)        {            if(n/sum<mid)            {                ans = n+1;                break;            }            sum*=mid;            ans+=sum;            if(ans>n)//放置溢出                break;        }        if(ans == n || ans == n-1) return mid;        else if(ans<n-1) l = mid+1;        else r = mid-1;    }    return -1;}int main(){    ll s,k,l,r,mid,i;    while(~scanf("%I64d",&n))    {        l = 1,r = n-1;        for(i = 2; i<=45; i++)        {            k = bin(i);            if(k!=-1 && i*k<l*r)            {                l = i,r = k;            }        }        printf("%I64d %I64d\n",l,r);    }    return 0;}