10250 - The Other Two Trees

最新推荐文章于 2025-07-26 12:45:55 发布

SIO__Five

最新推荐文章于 2025-07-26 12:45:55 发布

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本文介绍了一个几何问题的解决方法：已知四边形相邻正方形中两棵树的坐标，通过简单的数学计算找到其余两棵树的坐标。文章提供了一段C++代码实现，用于处理输入坐标并输出计算结果。

Problem E

The Other Two Trees

Input: standard input

Output: standard output

Time Limit: 2 seconds

You have a quadrilateral shaped land whose opposite fences are of equal length. You have four neighbors whose lands are exactly adjacent to your four fences, that means you have a common fence with all of them. For example if you have a fence of length d in one side, this fence of length d is also the fence of the adjacent neighbor on that side. The adjacent neighbors have no fence in common among themselves and their lands also don’t intersect. The main difference between their land and your land is that their lands are all square shaped. All your neighbors have a tree at the center of their lands. Given the Cartesian coordinates of trees of two opposite neighbors, you will have to find the Cartesian coordinates of the other two trees.

Input

The input file contains several lines of input. Each line contains four floating point or integer numbers x1, y1, x2, y2, where (x1, y1), (x2, y2) are the coordinates of the trees of two opposite neighbors. Input is terminated by end of file.

Output

For each line of input produce one line of output which contains the line “Impossible.” without the quotes, if you cannot determine the coordinates of the other two trees. Otherwise, print four floating point numbers separated by a single space with ten digits after the decimal pointax1, ay1, ax2, ay2, where (ax1, ay1) and (ax2, ay2) are the coordinates of the other two trees. The output will be checked with special judge program, so don’t worry about the ordering of the points or small precision errors. The sample output will make it clear.

Sample Input

10 0 -10 0

Sample Output

0.0000000000 10.0000000000 0.0000000000 -10.0000000000

0.0000000000 10.0000000000 -0.0000000000 -10.0000000000

0.0000000000 -10.0000000000 0.0000000000 10.0000000000

一个四边形，然后以每个边向外做四个正方形。四棵树，每棵种在正方形的中心，告诉你相对的两棵的坐标，求另外两棵的坐标。

其实就是很水的几何题，自己画一下图就晓得啦。

#include<iostream>
#include<cstdio>
#include<cmath>
using namespace std;
int main ()
{
    double x1,y1,x2,y2,ax1,ay1,bx2,by2,a,b,x,y;
    while(cin>>x1>>y1>>x2>>y2)
    {
        if (x1==x2 && y1==y2) printf("Impossible.\n");
        else
        {
            x=(x1+x2)/2;
            y=(y1+y2)/2;
            ax1=x+(y1-y);
            bx2=x-(y1-y);
            ay1=y-(x1-x);
            by2=y+(x1-x);
            printf("%.10lf %.10lf %.10lf %.10lf\n",ax1,ay1,bx2,by2);
        }
    }
    return 0;
}