hdu 2289 Cup(二分)

最新推荐文章于 2018-06-25 01:08:22 发布

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本文介绍了一种通过二分查找算法计算圆台形水杯中水位高度的方法。已知圆台上下底面半径、高度及水体积，利用数学公式结合二分法精确求解水的高度。

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Cup

Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4554 Accepted Submission(s): 1426

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

题意：已知一个圆台（杯子）的上下圆的半径是R,r,圆台的高H，水的体积，求水的高度。

水的高度不会超过最大高度，最大高度是100，不小于0，所以，在这个区间内进行二分，找出最接近的答案。

#include<stdio.h>
#include<math.h>
#include<iostream>
using namespace std;
#define PI acos(-1.0)//这里写成3.1415926或3.1415927不过 
#define eps 1e-9
double bin(double r,double R,double h,double H)
{
	double u=(R-r)*h/H+r;
	return PI*h*(r*r+u*r+u*u)/3;
}
int main()
{
	int T;
	double r,R,H,V,vv;
	scanf("%d",&T);
	while(T--)
	{
		double low;
		double high;
		double mid;
		low=0.0;
		high=100.0;
		scanf("%lf%lf%lf%lf",&r,&R,&H,&V);
		while(high-low>eps)
		{
			mid=(low+high)/2;
			vv=bin(r,R,mid,H);
			if(fabs(vv-V)<=eps)
				break;
			else if(vv>V)
				high=mid;
			else if(vv<V)
				low=mid;
		}
		printf("%.6lf\n",mid);
	}
	return 0;
}