Python/project_euler/problem_102/sol1.py
Christian Clauss cecf43d648
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Python

"""
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.
"""
from __future__ import annotations
from pathlib import Path
def 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
"""
return point1[0] * point2[1] - point1[1] * point2[0]
def 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
"""
point_a: tuple[int, int] = (x1, y1)
point_a_to_b: tuple[int, int] = (x2 - x1, y2 - y1)
point_a_to_c: tuple[int, int] = (x3 - x1, y3 - y1)
a: float = -vector_product(point_a, point_a_to_b) / vector_product(
point_a_to_c, point_a_to_b
)
b: float = +vector_product(point_a, point_a_to_c) / vector_product(
point_a_to_c, point_a_to_b
)
return a > 0 and b > 0 and a + b < 1
def solution(filename: str = "p102_triangles.txt") -> int:
"""
Find the number of triangles whose interior contains the origin.
>>> solution("test_triangles.txt")
1
"""
data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
triangles: list[list[int]] = []
for line in data.strip().split("\n"):
triangles.append([int(number) for number in line.split(",")])
ret: int = 0
triangle: list[int]
for triangle in triangles:
ret += contains_origin(*triangle)
return ret
if __name__ == "__main__":
print(f"{solution() = }")