*HDU1969 二分

Posted 2020-08-15 LuZhiyuan

Pie

Time Limit: 5000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 10043    Accepted Submission(s): 3637

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

 

 

Source

NWERC2006

题意：

共有n个半径不同的馅饼，f+1个人分，每个人只能分一块，每个人分得的面积要相同，问每个人最大能分多少。

代码：

 1 //由于每个人只能分一块，可以以最大的那块面积为上界，0位下界，二分寻找一个面积，用每一张馅饼除以这个面积就会得到能分几个人，
 2 //就这样不断二分，等于时不结束，注意二分精度不能太大会超时。
 3 #include<iostream>
 4 #include<cstdio>
 5 #include<cmath>
 6 using namespace std;
 7 const double PI=acos(-1.0);
 8 int t,n,f;
 9 double a[10004];
10 int chak(double mid)
11 {
12     int sum=0;
13     for(int i=1;i<=n;i++)
14     sum+=(int)(a[i]/mid);
15     return sum;
16 }
17 int main()
18 {
19     scanf("%d",&t);
20     while(t--)
21     {
22         scanf("%d%d",&n,&f);
23         f++;
24         double tem=0;
25         for(int i=1;i<=n;i++)
26         {
27             scanf("%lf",&a[i]);
28             a[i]=a[i]*a[i]*PI;
29             if(a[i]>tem) tem=a[i];
30         }
31         double lef=0,rig=tem,mid;
32         while(rig-lef>0.0000001)
33         {
34             mid=(lef+rig)/2;
35             int sum=chak(mid);
36             if(sum>=f) lef=mid;
37             if(sum<f) rig=mid;
38         }
39         printf("%.4lf\n",mid);
40     }
41     return 0;
42 }