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Simplified version of previous solution (no unnecessary sqrt(), abs(), round()) solution in Clear category for Similar Triangles by jakubbortlik
from itertools import combinations
from typing import List, Tuple
Coords = List[Tuple[int, int]]
def get_squared_sizes(coords) -> tuple:
"""Return sorted list of second powers of triangle side sizes."""
return sorted(
(x1 - x2) ** 2 + (y1 - y2) ** 2
for (x1, y1), (x2, y2) in combinations(coords, 2)
)
def similar_triangles(coords_1: Coords, coords_2: Coords) -> bool:
"""Return True if all ratios of pairs of sides in two triangles are the same."""
sizes1, sizes2 = get_squared_sizes(coords_1), get_squared_sizes(coords_2)
ratios = {a / b for a, b in zip(sizes1, sizes2)}
return len(ratios) == 1
if __name__ == "__main__":
print("Example:")
print(similar_triangles([(0, 0), (1, 2), (2, 0)], [(3, 0), (4, 2), (5, 0)]))
# These "asserts" are used for self-checking and not for an auto-testing
assert (
similar_triangles([(0, 0), (1, 2), (2, 0)], [(3, 0), (4, 2), (5, 0)]) is True
), "basic"
assert (
similar_triangles([(0, 0), (1, 2), (2, 0)], [(3, 0), (4, 3), (5, 0)]) is False
), "different #1"
assert (
similar_triangles([(0, 0), (1, 2), (2, 0)], [(2, 0), (4, 4), (6, 0)]) is True
), "scaling"
assert (
similar_triangles([(0, 0), (0, 3), (2, 0)], [(3, 0), (5, 3), (5, 0)]) is True
), "reflection"
assert (
similar_triangles([(1, 0), (1, 2), (2, 0)], [(3, 0), (5, 4), (5, 0)]) is True
), "scaling and reflection"
assert (
similar_triangles([(1, 0), (1, 3), (2, 0)], [(3, 0), (5, 5), (5, 0)]) is False
), "different #2"
print("Coding complete? Click 'Check' to earn cool rewards!")
Nov. 22, 2022
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