Acdream 1234 Two Cylinders（自适应辛普森积分法）

发布时间：2020-12-13 21:13:07 所属栏目：PHP教程来源：网络整理

导读：传送门 Two Cylinders Special Judge Time Limit: 2000/1000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others) Submit Statistic Next Problem Problem Description In this problem your task is very simple. Consider two infinite cylinders

传送门
Two Cylinders
Special Judge Time Limit: 2000/1000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)
Submit Statistic Next Problem
Problem Description

  In this problem your task is very simple.
  Consider two infinite cylinders in three-dimensional space,of radii R1 and R2 respectively,located in such a way that their axes intersect and are perpendicular.
  Your task is to find the volume of their intersection.

Input

  Input file contains two real numbers R1 and R2 (1 <= R1,R2 <= 100).

Output

  Output the volume of the intersection of the cylinders. Your answer must be accurate up to 10⑷.

Sample Input

1 1
Sample Output

5.3333
Source

Andrew Stankevich Contest 3
Manager

mathlover

题目大意：
给了两个圆柱的半径 r1,r2，他们的轴线垂直相交，让你求的是相交部份的体积。

解题思路：
这个题目首先我们对其积分：得到1个公式：

\int r 0 r 12 ? x 2 ? ? ? ? ? ? ? \sqrt ? r 22 ? x 2 ? ? ? ? ? ? ? \sqrt d y

我们现在用正常的积分公式积不出来，我们就能够采取辛普森积分法进行积分，可以当作模板用
My Code:

/**
求两个交叉圆柱的体积
**/
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
const double eps = 1e⑼;///精度
using namespace std;
double r1,r2;
double f(double x)///积分函数
{
    return 8.0*(sqrt(r1*r1-x*x))*(sqrt(r2*r2-x*x));
}
double simpson(double x,double y)
{
    return (y-x)*(f(x)+f(y)+4*f((x+y)/2))/6.0;
}
double jifen(double x,double y)///积分区间[x,y]
{
    double ans = simpson(x,y);///2分区间积分减小误差
    double mid = (x+y)/2.0;
    double left = simpson(x,mid);
    double right = simpson(mid,y);
    if(fabs(ans-(left+right)) < eps)
        return ans;
    return jifen(x,mid)+jifen(mid,y);
}
int main()
{
    while(~scanf("%lf%lf",&r1,&r2))
    {
        if(r1<r2) swap(r1,r2);
        printf("%.6lfn",jifen(0.0,r2));
    }
    return 0;
}

（编辑：李大同）

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