HDU 1071 The area

Posted 2020-10-03 Reqaw’s Blog

题目链接：

http://acm.hdu.edu.cn/showproblem.php?pid=1071

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.

题意描述：
给出如图中位置的三个点，计算斜线部分的面积

 

解题思路：

有三个点得出抛物线和直线的方程，求出原函数，利用牛顿-莱布尼茨公式计算即可。

AC代码：

 1 #include<stdio.h>
 2 int main()
 3 {
 4     int T;
 5     double x1,x2,x3,y1,y2,y3,a,b,c,k,h,ans;
 6     scanf("%d",&T);
 7     while(T--)
 8     {
 9         scanf("%lf%lf",&x1,&y1);
10         scanf("%lf%lf",&x2,&y2);
11         scanf("%lf%lf",&x3,&y3);
12         k=(y3-y2)/(x3-x2);
13         h=y3-k*x3;
14         a=(y2-y1)/( (x2*x2-x1*x1)-2*x1*(x2-x1) );
15         b=-2*a*x1;
16         c=y1-a*x1*x1-b*x1;
17         ans=(a*x3*x3*x3/3+(b-k)*x3*x3/2+(c-h)*x3)-(a*x2*x2*x2/3+(b-k)*x2*x2/2+(c-h)*x2);
18         printf("%.2lf\n",ans);
19     }
20     return 0;
21  }