Problem 102
Triangle containment
Three distinct points are plotted at random on a Cartesian plane, for which -1000 ≤ x, y ≤ 1000, such that a triangle is formed.
Consider the following two triangles:
It can be verified that triangle ABC contains the origin, whereas triangle XYZ does not.
Using triangles.txt (right click and ‘Save Link/Target As…’), a 27K text file containing the co-ordinates of one thousand “random” triangles, find the number of triangles for which the interior contains the origin.
NOTE: The first two examples in the file represent the triangles in the example given above.
包含原点的三角形
从笛卡尔平面中随机选择三个不同的点，其坐标均满足-1000 ≤ x, y ≤ 1000，这三个点构成一个三角形。
考虑下面两个三角形：
可以验证三角形ABC包含原点，而三角形XYZ不包含原点。
在27K的文本文件triangles.txt（右击并选择“目标另存为……”）中包含了一千个“随机”三角形的坐标，找出其中包含原点在其内部的三角形的数量。
注意：文件中的前两个三角形就是上述样例。