52 lines
1.3 KiB
Python
52 lines
1.3 KiB
Python
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from math import acos, sqrt, pi, atan
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import matplotlib.pyplot as plt
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def triangle(euler_text_line):
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ps = list(map(int, euler_text_line.split(",")))
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ps = [(ps[0], ps[1]), (ps[2], ps[3]), (ps[4], ps[5])]
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return ps
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def angle_x(x, y):
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if x > 0 and y == 0:
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return 0
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elif x < 0 and y == 0:
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return pi
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elif x == 0 and y > 0:
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return pi / 2
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elif x == 0 and y < 0:
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return 3 / 2 * pi
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elif x > 0 and y > 0:
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return atan(y / x)
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elif x < 0 and y > 0:
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return pi - atan(y / abs(x))
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elif x < 0 and y < 0:
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return pi + atan(abs(y) / abs(x))
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elif x > 0 and y < 0:
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return 2 * pi - atan(abs(y) / x)
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else:
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raise Exception("Unhandled case")
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def contains_origin(triangle):
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a, b, c = triangle
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angles = sorted([angle_x(*a), angle_x(*b), angle_x(*c)])
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a = angles[1] - angles[0]
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b = angles[2] - angles[1]
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c = angles[0] + 2 * pi - angles[2]
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return not (a + b < pi or b + c < pi or c + a < pi)
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def euler_102():
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with open("../txt/e102.txt", "r") as f:
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triangles = list(map(triangle, f.readlines()))
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return len([1 for t in triangles if contains_origin(t)])
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if __name__ == "__main__":
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solution = euler_102()
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print("e102.py: " + str(solution))
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assert(solution == 228)
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