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First solution in Creative category for Black Holes by _Chico_
from itertools import combinations
from math import acos, hypot, pi
left = lambda a, b: min(a[0], b[0])
area = lambda r: r**2 * pi
def distance(a, b):
x1, y1, _ = a
x2, y2, _ = b
return hypot(x1-x2, y1-y2)
def intersection_area(a, b, d):
r1, r2 = a[-1], b[-1]
if r1 + r2 <= d:
return 0
if r1 > d + r2:
return area(r2)
# http://mathworld.wolfram.com/Circle-CircleIntersection.html
s = (2 * d * r1)**2 - (d**2 + r1**2 - r2**2)**2
d1 = (d**2 + r1**2 - r2**2) / (2 * d * r1)
d2 = (d**2 + r2**2 - r1**2) / (2 * d * r2)
return r1**2 * acos(d1) + r2**2 * acos(d2) - 0.5 * s**0.5
def checkio(data):
holes = [list(hole) for hole in data]
while True:
pairs = sorted((distance(a, b), left(a, b), a, b)
for a, b in combinations(holes, 2))
for d, _, a, b in pairs:
smaller, bigger = sorted((a, b), key=lambda x: x[-1])
A1, A2 = area(bigger[-1]), area(smaller[-1])
A_inter = intersection_area(bigger, smaller, d)
if A_inter >= 0.55 * A2 and A1 >= 1.2 * A2:
bigger[-1] = ((A1 + A2) / pi)**0.5
holes.remove(smaller)
break
else:
break
return [(x, y, round(r, 2)) for (x, y, r) in holes]
May 18, 2021
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