HDU 2.1.8 The area

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本文介绍了一个计算由抛物线和直线围成土地面积的问题。给定三个交点坐标，通过解析几何的方法求解出抛物线方程，并计算出特定区域内由抛物线与直线围成的土地面积。

The area

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

Total Submission(s): 1305 Accepted Submission(s): 1038

Problem Description

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.

//#define LOCAL  
#include<stdio.h>  
  
double x1, x2, x3, y1, y2, y3, a, k, b, ans;  
int n;  
double f(double x)  
{  
    return a*x*x*x / 3 - (a*x1 + k / 2)*x*x + (a*x1*x1 + y1 - b)*x;  
}  
int main()  
{  
#ifdef LOCAL  
    freopen("H://dataIn.txt", "r", stdin);  
    freopen("H://dataOut.txt", "w", stdout);  
#endif  
    scanf("%d", &n);  
    while(n--)  
    {  
        scanf("%lf%lf%lf%lf%lf%lf", &x1, &y1, &x2, &y2, &x3, &y3);  
        a = (y2 - y1) / (x2 - x1) / (x2 - x1);  
        k = (y3 - y2) / (x3 - x2);  
        b = y3 - k*x3;  
        printf("%.2lf\n", f(x3) - f(x2));  
    }  
    return 0;  
}