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python
2 months ago
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```from math import sqrt

def sign(n):
if n == 0:
return 0
if n > 0:
return '+'
if n < 0:
return '-'

def find_cos(point1, point2, point3, point4):
x1 = abs(point1[0] - point2[0])
y1 = abs(point1[1] - point2[1])
x2 = abs(point3[0] - point4[0])
y2 = abs(point3[1] - point4[1])

return (x1 * x2 + y1 * y2) / (point_to_point(point1, point2) + point_to_point(point3, point4))

def line_intersection(l1, l2, l3, l4):
x1, y1 = l1
x2, y2 = l2
x3, y3 = l3
x4, y4 = l4

px = ((x1 * y2 - y1 * x2) * (x3 - x4) - (x1 - x2) * (x3 * y4 - y3 * x4)) / (
(x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4))
py = ((x1 * y2 - y1 * x2) * (y3 - y4) - (y1 - y2) * (x3 * y4 - y3 * x4)) / (
(x1 - x2) * (y3 - y4) - (y1 - y2) * (x3 - x4))
return [px, py]

def point_to_point(point1, point2):
return sqrt((point1[0] - point2[0]) ** 2 + (point1[1] - point2[1]) ** 2)

def point_to_segment(point, segment_p1, segment_p2):
x3, y3 = point
x1, y1 = segment_p1
x2, y2 = segment_p2
px = x2 - x1
py = y2 - y1

norm = px * px + py * py

u = ((x3 - x1) * px + (y3 - y1) * py) / float(norm)

if u > 1:
u = 1
elif u < 0:
u = 0

x = x1 + u * px
y = y1 + u * py

dx = x - x3
dy = y - y3

dist = (dx * dx + dy * dy) ** .5

return dist

def point_to_line(point, line1, line2):
x0, y0 = point
x1, y1 = line1
x2, y2 = line2

return abs((y2 - y1) * x0 - (x2 - x1) * y0 + x2 * y1 - y2 * x1) / sqrt((y2 - y1) ** 2 + (x2 - x1) ** 2)

def point_to_ray(point, ray1, ray2):
cos = find_cos(point, ray1, ray1, ray2)
if cos < 0:
return point_to_point(point, ray1)

return point_to_line(point, ray1, ray2)

def line_to_line(line1, line2, line3, line4):
x1, y1 = line1
x2, y2 = line2
x3, y3 = line3
x4, y4 = line4

k1 = abs(y2 - y1) / abs(x2 - x1)
k2 = abs(y4 - y3) / abs(x4 - x3)

if k1 == k2:
return point_to_line(line1, line3, line4)

return 0

def segment_to_line(segment1, segment2, line1, line2):
x1, y1 = segment1
x2, y2 = segment2
x3, y3 = line1
x4, y4 = line2

k1 = abs(y2 - y1) / abs(x2 - x1)
k2 = abs(y4 - y3) / abs(x4 - x3)

if k1 == k2:
return point_to_line(segment1, line1, line2)

return min(point_to_line(segment1, line1, line2), point_to_line(segment2, line1, line2))

def segment_to_segment(s1, s2, s3, s4):
x1, y1 = s1
x2, y2 = s2
x3, y3 = s3
x4, y4 = s4

return min(point_to_segment(s1, s3, s4), point_to_segment(s2, s3, s4))

def segment_to_ray(s1, s2, r1, r2):
return min(point_to_ray(s1, r1, r2), point_to_ray(s2, r1, r2))

def ray_to_ray(r1, r2, r3, r4):
x1, y1 = r1
x2, y2 = r2
x3, y3 = r3
x4, y4 = r4

k1 = abs(y2 - y1) / abs(x2 - x1)
k2 = abs(y4 - y3) / abs(x4 - x3)

if k1 == k2:
return point_to_ray(r1, r3, r4)

return 0

def ray_to_line(r1, r2, l1, l2):
x1, y1 = r1
x2, y2 = r2
x3, y3 = l1
x4, y4 = l2

k1 = abs(y2 - y1) / abs(x2 - x1)
k2 = abs(y4 - y3) / abs(x4 - x3)

intersection = line_intersection(r1, r2, l1, l2)
if k1 == k2 or not phantom_intersection(intersection, r1, r2):
return point_to_line(r1, l1, l2)

return 0

def phantom_intersection(intersection, start, end):
x, y = intersection
x1, y1 = start
x2, y2 = end

return sign(x1 - x2) == sign(x1 - x) and sign(y1 - y2) == sign(y1 - y)

def f(n):
return f'{n:.{6}f}'

a = [int(i) for i in input().split()]
b = [int(i) for i in input().split()]
c = [int(i) for i in input().split()]
d = [int(i) for i in input().split()]

from_a_to_c = point_to_point(a, c)
from_a_to_cd = point_to_segment(a, c, d)
from_a_to_cd_ray = point_to_ray(a, c, d)
from_a_to_cd_line = point_to_line(a, c, d)
from_ab_to_c = point_to_segment(c, a, b)
from_ab_to_cd = segment_to_segment(a, b, c, d)
from_ab_to_cd_ray = segment_to_ray(a, b, c, d)
from_ab_to_cd_line = segment_to_line(a, b, c, d)
from_ab_ray_to_c = point_to_ray(c, a, b)
from_ab_ray_to_cd = segment_to_ray(c, d, a, b)
from_ab_ray_to_cd_ray = ray_to_ray(a, b, c, d)
from_ab_ray_to_cd_line = ray_to_line(a, b, c, d)
from_ab_line_to_c = point_to_line(c, a, b)
from_ab_line_to_cd = segment_to_line(c, d, a, b)
from_ab_line_to_cd_ray = ray_to_line(c, d, a, b)
from_ab_line_to_cd_line = line_to_line(a, b, c, d)

print(*list(map(f, [
from_a_to_c,
from_a_to_cd,
from_a_to_cd_ray,
from_a_to_cd_line,
from_ab_to_c,
from_ab_to_cd,
from_ab_to_cd_ray,
from_ab_to_cd_line,
from_ab_ray_to_c,
from_ab_ray_to_cd,
from_ab_ray_to_cd_ray,
from_ab_ray_to_cd_line,
from_ab_line_to_c,
from_ab_line_to_cd,
from_ab_line_to_cd_ray,
from_ab_line_to_cd_line
])),
sep='\n')
```