2012年亚洲长春区域赛：K Yukari's Birthday

K - Yukari's Birthday

Time Limit:6000MS     Memory Limit:0KB     64bit IO Format:%lld & %llu

UVALive 6076

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 r1 concentric circles. They place kⁱcandles equidistantly on the i-th circle, where k2, 1ir. 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 x 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 18n10¹².

Output 

For each test case, output r and k.

Sample Input 

 
18
111
1111

Sample Output 

 
1 17
2 10
3 10

 解题思路：利用等比数列求和公式求出n或n-1的表达式：n (或n-1) = k * ( K^r -  1) / ( k - 1) ；

可以得出k是n或n-1的一个因子，则我们可以枚举r（枚举k会超时）

解题代码：

// File Name: K - Yukari's Birthday
// Author: sheng
// Created Time: 2013年04月18日 星期四 13时47分51秒

#include <stdio.h>
#include <math.h>
long long a,b,n;
void f(long long n)
{
    long long f,s,i,k,j;
    for (i=2;i<=50;i++)
    {
        s=0;f=1;
        k=(long long)pow(n,1.0/i);
        for (j=1;j<=i;j++)
        {
            f*=k;
            s+=f;
            if (s==n && i*k<a*b)
            {
                a=i;
                b=k;
                break;
            }
        }
    }
}
int main()
{
    while (~scanf("%lld",&n))
    {
        a=1;b=n-1;
        f(n);
        f(n-1);
        printf("%lld %lld\n",a,b);
    }
    return 0;
}