HDU 2289 CUP 二分

Cup

Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 6684    Accepted Submission(s): 2062

Problem Description

The WHU ACM Team has a big cup, with which every member drinks water. Now, we know the volume of the water in the cup, can you tell us it height? The radius of the cup's top and bottom circle is known, the cup's height is also known.

Input

The input consists of several test cases. The first line of input contains an integer T, indicating the num of test cases.
Each test case is on a single line, and it consists of four floating point numbers: r, R, H, V, representing the bottom radius, the top radius, the height and the volume of the hot water.
Technical Specification
1. T ≤ 20.
2. 1 ≤ r, R, H ≤ 100; 0 ≤ V ≤ 1000,000,000.
3. r ≤ R.
4. r, R, H, V are separated by ONE whitespace.
5. There is NO empty line between two neighboring cases.

Output

For each test case, output the height of hot water on a single line. Please round it to six fractional digits.

Sample Input

1
100 100 100 3141562

Sample Output

99.999024

题目大意：给出一个杯子的上下半径r,R，杯子的高度H，装入V升水，求水的高度

思路：二分或数学方法

二分

#include <stdio.h>
#include <math.h>
double r, R, H, V;
#define PI 3.1415926535897932
double vv(double h)
{
 double x=r+(R-r)*h/H;
 return (PI*h*(x*x+r*x+r*r)/3.0);
}
double f(double z, double y)
{
    double mid;
    while((y-z)>1e-10)
        {
            mid=(z+y)/2.0;
            if(vv(mid)<V)
                z=mid;
            else
                y=mid;
        }
        return mid;
}
int main()
{
    int a;
    scanf("%d", &a);
    while(a--)
    {
        scanf("%lf%lf%lf%lf", &r, &R, &H, &V);
        printf("%lf
", f(0,H));
    }
    return 0;
}