Poj 3122 Pie【基础二分】水题

最新推荐文章于 2022-09-14 21:43:44 发布

mengxiang000000

最新推荐文章于 2022-09-14 21:43:44 发布

阅读量992

点赞数

CC 4.0 BY-SA版权

分类专栏：二分查找文章标签： Poj 3122 pku 3122

本文链接：https://blog.youkuaiyun.com/mengxiang000000/article/details/52432334

二分查找专栏收录该内容

142 篇文章

订阅专栏

本文介绍了一道经典的分饼问题，旨在将不同大小的饼均匀分配给多人，确保每个人得到相同体积的一份。通过二分查找算法高效求解最大可能的分配体积。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

Pie

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15500		Accepted: 5310		Special Judge

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

Source

Northwestern Europe 2006

题目大意:有n块饼，每块饼的半径给你了，然后让你将这些饼分给m+1个人，要求每人分到的大小要一样，而且不能拼接，问最大可以切多大。

思路：

直接二分查找即可，注意如果eps控制到1e-8会出现TLE的情况。精度控制到1e-5即可。

Ac代码：

#include<stdio.h>
#include<string.h>
#include<math.h>
using namespace std;
double a[100000];
const double PI =acos(-1);
int n,m;
int Slove(double mid)
{
    int sum=0;
    for(int i=0;i<n;i++)
    {
        sum+=a[i]*a[i]*PI/mid;
    }
    if(sum>=m+1)return 1;
    else return 0;
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        for(int i=0;i<n;i++)
        {
            scanf("%lf",&a[i]);
        }
        double ans=0;
        double mid;
        double l=0;
        double r=1000000000;
        while(r-l>=1e-5)
        {
            mid=(l+r)/2;
            if(Slove(mid)==1)
            {
                l=mid;
                ans=mid;
            }
            else r=mid;
        }
        printf("%.4f\n",ans);
    }
}