HDU 1071 The area

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The area

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 11337 Accepted Submission(s): 8008

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
40.69Hint
For float may be not accurate enough, please use double instead of float.

题目大意：输入三个点的坐标，这三点确定了一个抛物线，其中p1是抛物线的顶点，连接p2，p3,求闭合区域面积。

数学问题，通过三个点的坐标求得抛物线和直线的表达式，然后相减求积分即可求出面积。

/*积分问题，求抛物线与直线之间区域的面积。抛物线顶点公式  顶点为(h,k) y=a(x-h)^2+k(a≠0)直线式                      y=cx+d相减得                      f(x)=a(x-h)^2-cx+k-d区域面积就是                s=F(x3)-F(x2);*/#include<stdio.h>#include<math.h>int main(){    int t;    double x1,x2,x3,y1,y2,y3;    scanf("%d",&t);    while(t--){        scanf("%lf%lf%lf%lf%lf%lf",&x1,&y1,&x2,&y2,&x3,&y3);        double s,a,h,k,c,d;        h=x1;        k=y1;        c=(y3-y2)/(x3-x2);        d=y3-c*x3;        a=(y2-k)/( (x2-h)*(x2-h) );        s=a*(x3-h)*(x3-h)*(x3-h)/3-c*x3*x3/2+(k-d)*x3;        s-=a*(x2-h)*(x2-h)*(x2-h)/3-c*x2*x2/2+(k-d)*x2;        if(s<0) s=-s;//然而后台数据并不用考虑这种情况，或许题干说了，不过没看到。        printf("%.2lf\n",s);    }    return 0;}

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