project_euler.problem_102.sol1
==============================

.. py:module:: project_euler.problem_102.sol1

.. autoapi-nested-parse::

   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:

   A(-340,495), B(-153,-910), C(835,-947)

   X(-175,41), Y(-421,-714), Z(574,-645)

   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 coordinates 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.



Functions
---------

.. autoapisummary::

   project_euler.problem_102.sol1.contains_origin
   project_euler.problem_102.sol1.solution
   project_euler.problem_102.sol1.vector_product


Module Contents
---------------

.. py:function:: contains_origin(x1: int, y1: int, x2: int, y2: int, x3: int, y3: int) -> bool

   Check if the triangle given by the points A(x1, y1), B(x2, y2), C(x3, y3)
   contains the origin.
   >>> contains_origin(-340, 495, -153, -910, 835, -947)
   True
   >>> contains_origin(-175, 41, -421, -714, 574, -645)
   False


.. py:function:: solution(filename: str = 'p102_triangles.txt') -> int

   Find the number of triangles whose interior contains the origin.
   >>> solution("test_triangles.txt")
   1


.. py:function:: vector_product(point1: tuple[int, int], point2: tuple[int, int]) -> int

   Return the 2-d vector product of two vectors.
   >>> vector_product((1, 2), (-5, 0))
   10
   >>> vector_product((3, 1), (6, 10))
   24