HDU 4430 Yukari's Birthday（二分）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4430

题目大意：给定n个蜡烛，围绕蛋糕的中心插同心圆，从里往外分别是第1圈、第2圈、...第r圈，第 i 圈要插k^i 个蜡烛，且r*k最小。求出r和k。注意，中心点可以放，也可以不放

Sample Input

18

111

1111

 

Sample Output

1 17

2 10

3 10

代码如下：

# include<cstdio>
# include<cstring>
# include<cmath>
# include<algorithm>
# define LL long long
using namespace std;

LL pow1(LL a,int b){
    LL ans=1;
    for(int i=0;i<b;i++)
        ans*=a;
    return ans;
}
int main(){
    LL n,r,k;
    while(scanf("%I64d",&n)!=EOF){
        r=1;
        k=n-1;
        LL left,right,mid;
        for(int i=2;i<=41;i++){
            left=2;
            right=(long long)pow(n,1.0/i);
            while(left<=right){
                mid=(long long)(left+right)/2;
                LL temp=(mid-pow1(mid,i+1))/(1-mid);
                if(temp==n||temp==n-1){
                    if(i*mid<r*k){
                        r=i;
                        k=mid;
                    }
                    break;
                }
                else if(temp<n) left=mid+1;
                else right=mid-1;
            }
        }
        printf("%I64d %I64d
",r,k);
    }
    return 0;
}