zoukankan      html  css  js  c++  java
  • 杭电1071-The area

    问题描述:
     
    Ignatius bought a land last week, but he didn't know the area of the land because the land is enclosed by a parabola and a straight line. The picture below shows the area. Now given all the intersectant points shows in the picture, can you tell Ignatius the area of the land?

    Note: The point P1 in the picture is the vertex of the parabola.

     
    Input
    The input contains several test cases. The first line of the input is a single integer T which is the number of test cases. T test cases follow.
    Each test case contains three intersectant points which shows in the picture, they are given in the order of P1, P2, P3. Each point is described by two floating-point numbers X and Y(0.0<=X,Y<=1000.0).
     
    Output
    For each test case, you should output the area of the land, the result should be rounded to 2 decimal places.
     
    Sample Input
    2
    5.000000 5.000000
    0.000000 0.000000
    10.000000 0.000000
    10.000000 10.000000
    1.000000 1.000000
    14.000000 8.222222
     
    Sample Output
    33.33 40.69
    Hint
    For float may be not accurate enough, please use double instead of float.
    问题分析:
    注意:
              已知抛物线与直线相交两点和抛物线顶点,顶点P1(-b/(2a), (4ac-b^2)/4a)。
              抛物线方程:y=ax^2+bx+c;
              直线方程:y=kx+h;
              已知p1,p2,p3可以求出a,b,c,k,h
              y1=ax1^2+bx1+c
              y2=ax2^2+bx2+c
              y1-y2=(x1-x2)(a(x1+x2)+b)
              又x1=-b/2a,
              所以a=(y2-y1)/(x2-x1)^2
              面积用积分公式化简为:
              S=a/3*(x3^3–x2^3)+(b-k)/2*(x3^2–x2^2)+(c-h)*(x3-x2);
    AC代码:
    #include <cstdlib>
    #include <iostream>
    #include<iomanip>
    using namespace std;

    int main(int argc, char *argv[])
    {
        double x1,x2,x3,y1,y2,y3,area;
        double a,b,c,k,h;
        int n;
        cin>>n;
        while(n--)
        {
           cin>>x1>>y1;
           cin>>x2>>y2;
           cin>>x3>>y3;
           a=(y2-y1)/((x2-x1)*(x2-x1));
           b=-2*a*x1;
           c=y1-a*x1*x1-b*x1;
           k=(y3-y2)/(x3-x2);
           h=y3-k*x3;
           area=a/3*(x3*x3*x3-x2*x2*x2)+(b-k)/2*(x3*x3-x2*x2)+(c-h)*(x3-x2);
           cout<<fixed<<setprecision(2)<<area<<endl;
        }
        system("PAUSE");
        return EXIT_SUCCESS;
    }

  • 相关阅读:
    oracle RAC 更换IP
    12C oracle 12.1.0.2版本打补丁
    node name配置错误,导致grid日志在报警
    input_subsys 输入子系统框架分析
    www.bing.com
    getopt函数使用说明
    FreeType 矢量字体 测试移植(1)
    字符的编码方式
    在开发板上显示字符和中文
    块设备驱动程序的框架
  • 原文地址:https://www.cnblogs.com/wft1990/p/4313644.html
Copyright © 2011-2022 走看看