Pie--hdu1969(二分法)

Bertha 。 2022-08-04 08:55 167阅读 0赞

Pie

**Time Limit: 5000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)  
Total Submission(s): 6158 Accepted Submission(s): 2343**

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

4 3 3

1 24

10 5

1 4 2 3 4 5 6 5 4 2

Sample Output

25.1327

3.1416

50.2655

这一题大意是：总共有m个蛋糕，要分给K+1个人，求能分给每个人，且面积最大的蛋糕面积！

用二分法来查找！

1 #include<cstdio>
     2 #include<cstring>
     3 #include<algorithm>
     4 #include<cmath>
     5 #define PI acos(-1.0)//PI的精度最好大点
     6 using namespace std;
     7 
     8 double L[50000] , man;
     9 int n,k,i;
    10 
    11 bool F(double x)
    12 {
    13     int sum=0;
    14     for(i=0;i<n;i++)
    15     sum+=(int)(L[i]/x);//sum的作用是记录当要求的面积为x时，最多能分多少整块
    16     return sum>=(k+1);//如果能分的比要求的多就返回真
    17 }
    18 void qw()
    19 {
    20     double l=0,r=man,mid;
    21     while(r-l>1e-7)//二分法
    22     {
    23         mid=(l+r)/2;
    24         if(F(mid))
    25         l=mid;
    26         else
    27         r=mid;
    28     }
    29     printf("%.4lf\n",r);
    30 }
    31 int main()
    32 {
    33     int N,T;
    34     scanf("%d",&N);
    35     while(N--)
    36     {
    37         scanf("%d%d",&n,&k);
    38         man =0;
    39         for(i=0;i<n;i++){
    40             scanf("%d",&T);
    41             L[i] = PI*T*T;
    42             
    43             if(man < L[i]) man = L[i];//找出最大的蛋糕面积
    44         }
    45         qw();
    46     }
    47     return 0;
    48 }