mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 17:20:16 +00:00
cecf43d648
* Pyupgrade to Python 3.9
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
82 lines
2.3 KiB
Python
82 lines
2.3 KiB
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() = }")
|