56 lines
1.1 KiB
Python
56 lines
1.1 KiB
Python
from collections import namedtuple
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Point = namedtuple("P", ["x", "y"])
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Vector = namedtuple("V", ["x", "y"])
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def generate_triangles(n):
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all_points = [Point(x, y)
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for x in range(0, n + 1)
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for y in range(0, n + 1)
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]
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all_points = all_points[1:] # remove (0, 0)
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all_pairs = []
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for i in range(len(all_points)):
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for j in range(i + 1, len(all_points)):
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p = (all_points[i], all_points[j])
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yield p
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def vector(p1, p2):
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return Vector(p2.x - p1.x, p2.y - p1.y)
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def dot_product(v1, v2):
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return v1.x * v2.x + v1.y * v2.y
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def has_right_angle(p, q):
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o = Point(0, 0)
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oq = vector(o, q)
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op = vector(o, p)
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qp = vector(q, p)
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if dot_product(oq, op) == 0:
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return True
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elif dot_product(oq, qp) == 0:
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return True
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elif dot_product(op, qp) == 0:
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return True
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return False
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def euler_091():
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count = 0
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ts = generate_triangles(50)
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for t in ts:
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if has_right_angle(*t):
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count += 1
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return count
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if __name__ == "__main__":
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solution = euler_091()
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print("e091.py: " + str(solution))
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assert(solution == 14234)
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