POJ-3122-Pie

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


1. 二分枚举时间。由于最后和面积有关系。所以一开始数组就保存的是平方值。
2. 判断过程中，计算饼子数量。如果数量大于人数。返回true。表示mid比较小。此时保存的是l值。

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
#define M 10002
const double PI=3.14159265359;
const double eps = 1e-7;
double a[M];
int n,f;
bool cmp(int a,int b)
{
    return a>b;
}
bool check(double mid)
{
    int sum=0;
    for(int i =0;i<n;i++)
    {
        if(a[i]>=mid)
            sum+=(int)a[i]/mid;
    }
    return sum>=f;
}
int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%d%d",&n,&f);

        double maxx = 0;
        for(int i=0;i<n;i++)
        {
                scanf("%lf",&a[i]);
                a[i] = a[i]*a[i];
                maxx= max(maxx,a[i]);
        }

        f++;
        double l=0,r = maxx,mid;
        while(r-l>=eps)
        {
            mid = (l+r)/2;
            if(check(mid))
                l = mid;
            else
                r = mid;
        }
        printf("%.4f
", l *PI);
    }
    return 0;
}