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82 lines
2.3 KiB
Python
82 lines
2.3 KiB
Python
"""
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Three distinct points are plotted at random on a Cartesian plane,
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for which -1000 ≤ x, y ≤ 1000, such that a triangle is formed.
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Consider the following two triangles:
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A(-340,495), B(-153,-910), C(835,-947)
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X(-175,41), Y(-421,-714), Z(574,-645)
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It can be verified that triangle ABC contains the origin, whereas
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triangle XYZ does not.
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Using triangles.txt (right click and 'Save Link/Target As...'), a 27K text
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file containing the coordinates of one thousand "random" triangles, find
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the number of triangles for which the interior contains the origin.
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NOTE: The first two examples in the file represent the triangles in the
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example given above.
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"""
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from __future__ import annotations
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from pathlib import Path
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def vector_product(point1: tuple[int, int], point2: tuple[int, int]) -> int:
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"""
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Return the 2-d vector product of two vectors.
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>>> vector_product((1, 2), (-5, 0))
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10
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>>> vector_product((3, 1), (6, 10))
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24
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"""
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return point1[0] * point2[1] - point1[1] * point2[0]
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def contains_origin(x1: int, y1: int, x2: int, y2: int, x3: int, y3: int) -> bool:
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"""
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Check if the triangle given by the points A(x1, y1), B(x2, y2), C(x3, y3)
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contains the origin.
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>>> contains_origin(-340, 495, -153, -910, 835, -947)
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True
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>>> contains_origin(-175, 41, -421, -714, 574, -645)
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False
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"""
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point_a: tuple[int, int] = (x1, y1)
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point_a_to_b: tuple[int, int] = (x2 - x1, y2 - y1)
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point_a_to_c: tuple[int, int] = (x3 - x1, y3 - y1)
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a: float = -vector_product(point_a, point_a_to_b) / vector_product(
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point_a_to_c, point_a_to_b
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)
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b: float = +vector_product(point_a, point_a_to_c) / vector_product(
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point_a_to_c, point_a_to_b
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)
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return a > 0 and b > 0 and a + b < 1
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def solution(filename: str = "p102_triangles.txt") -> int:
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"""
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Find the number of triangles whose interior contains the origin.
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>>> solution("test_triangles.txt")
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1
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"""
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data: str = Path(__file__).parent.joinpath(filename).read_text(encoding="utf-8")
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triangles: list[list[int]] = []
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for line in data.strip().split("\n"):
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triangles.append([int(number) for number in line.split(",")])
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ret: int = 0
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triangle: list[int]
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for triangle in triangles:
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ret += contains_origin(*triangle)
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return ret
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if __name__ == "__main__":
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print(f"{solution() = }")
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