HDOJ 题目2289 Cup（数学，二分）

最新推荐文章于 2018-10-22 22:06:43 发布

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最新推荐文章于 2018-10-22 22:06:43 发布

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本文介绍了一道算法题目，需要根据已知的水杯顶部和底部半径、水杯高度及热水体积来计算热水的高度。通过二分查找法求解高度，并给出了完整的AC代码实现。

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Cup

Time Limit: 3000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 4431 Accepted Submission(s): 1388

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

Source

The 4th Baidu Cup final

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ac代码

#include<stdio.h>
#include<string.h>
#include<math.h>
#define pi acos(-1.0)
double area(double r1,double r2,double h1,double h)
{
	double u=(h1/h)*(r2-r1)+r1;
	return (r1*r1+u*u+r1*u)*h1*pi/3;
}
int main()
{
	int t;
	scanf("%d",&t);
	while(t--)
	{
		double r1,r2,h,v,mid,l=0,r,tv;
		scanf("%lf%lf%lf%lf",&r1,&r2,&h,&v);
		r=h;
		mid=(l+r)/2;
		tv=area(r1,r2,mid,h);
		while(fabs(tv-v)>1e-7)
		{
			if(fabs(r-l)<=1e-7)//不加这个会超时啊
				break;
			if(tv>v)
			{
				r=mid;
			}
			else
				l=mid;
			mid=(l+r)/2;
			tv=area(r1,r2,mid,h);
		}
		printf("%.6lf\n",mid);
	}
}