hdu 4430 Yukari's Birthday 枚举+二分

2012年ACM亚洲赛长春现场赛K题

Yukari's Birthday

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

            http://acm.zju.edu.cn/onlinejudge/showProblem.do?problemId=4888

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
18
111
1111

Sample Output
1 17
2 10
3 10

Source

2012 Asia ChangChun Regional Contest

枚举r,然后通过二分来求k.

需要注意的是二分时初始右边界不能太大，不然会导致计算过程超出long long

还有就是提交时输入输出在zoj上要要用%lld，而hdu要用%I64d，不然会Wrong Answer

代码：

#include<stdio.h>#include<string.h>#include<stdlib.h>#include<math.h>long long powLL(long long a,int b){long long res=1;for(int i=0;i<b;i++)res*=a;return res;}int main(void){long long n,r,k;while(scanf("%lld",&n)!=EOF){r=1;k=n-1;for(int i=2;i<=45;i++){long long ll,rr,mm;ll=2;rr=(long long)pow(n,1.0/i);while(ll<=rr){mm=(long long)(ll+rr)/2;long long 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("%lld %lld\n",r,k);}return 0;}