HDOJ-----1969二分

最新推荐文章于 2017-12-27 21:49:12 发布

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本文介绍了一个算法问题，涉及如何公平地将不同大小的圆柱形蛋糕等分为若干份，每份体积相同，确保每个人都能获得同样大小的一份蛋糕。通过二分查找的方法，在给定的精度范围内找到最大的可能体积。

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Pie

Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 9433 Accepted Submission(s): 3418

Problem Description

My birthday is coming up and traditionally I'm serving pie. Not just one pie, no, I have a number N of them, of various tastes and of various sizes. F of my friends are coming to my party and each of them gets a piece of pie. This should be one piece of one pie, not several small pieces since that looks messy. This piece can be one whole pie though.

My friends are very annoying and if one of them gets a bigger piece than the others, they start complaining. Therefore all of them should get equally sized (but not necessarily equally shaped) pieces, even if this leads to some pie getting spoiled (which is better than spoiling the party). Of course, I want a piece of pie for myself too, and that piece should also be of the same size.

What is the largest possible piece size all of us can get? All the pies are cylindrical in shape and they all have the same height 1, but the radii of the pies can be different.

Input

One line with a positive integer: the number of test cases. Then for each test case:
---One line with two integers N and F with 1 <= N, F <= 10 000: the number of pies and the number of friends.
---One line with N integers ri with 1 <= ri <= 10 000: the radii of the pies.

Output

For each test case, output one line with the largest possible volume V such that me and my friends can all get a pie piece of size V. The answer should be given as a floating point number with an absolute error of at most 10^(-3).

Sample Input

3
3 3
4 3 3
1 24
5
10 5
1 4 2 3 4 5 6 5 4 2

Sample Output

25.1327
3.1416
50.2655

就是给出N块圆柱型蛋糕的直径，高都是1，F个朋友，算上自己，是F+1个人，每人相同的体积，蛋糕不能拼接，从0到最大的那一块蛋糕之间二分就可以了

#include<cstdio>
#include<cmath>
#include<algorithm>
const double PI = acos(-1.0);//这是这道题最丧心病狂的地方，PI定义为3.1415926就WA，精度简直变态
using namespace std;
double ss[10010];
int t, N, F, x;
int judge(double a){
	int ans = 0;
	for(int i = 0; i < N; i++){
		ans += (int)(ss[i] / a);
	}
	return ans;
}
bool cmp(double x, double y){
	return x < y;
}
int main(){
	double s, e, m, v;
	scanf("%d", &t);
	while(t--){
		scanf("%d%d", &N, &F);
		s = e = 0;
		F++;
		for(int i = 0; i < N; i++){
			scanf("%d", &x);
			ss[i] = x*x*PI;
		}
		sort(ss, ss+N, cmp);
		e = ss[N-1];
		while(e-s > .000001){
			m = (e+s) / 2;
			if(judge(m) >= F){
				s = m;
			}
			else{
				e = m;
			}
		}
		printf("%.4lf\n", s);
	}
	return 0;
}