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semistar_test.py
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semistar_test.py
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#!/usr/bin/env python3
from unicursalpolygon.utils import get_csv_line, inverse_0
def semistar_property(k, perm, inv, neigh, n):
i = inv[k]
j = inv[(k+1)%n]
val = lambda x : (x - perm[i]) % n
intersection = neigh[i].intersection(neigh[j])
if len(intersection) == 0:
a = val(min(neigh[i], key=val))
b = val(max(neigh[j], key=val))
return a < b
elif len(intersection) == 1:
a = val(neigh[i].difference(intersection).pop())
b = val(neigh[j].difference(intersection).pop())
common = val(intersection.pop())
return not ((a > common) and (b < common))
else:
assert("SIZE OF INTERSECTION IS NOT 0/1" == 0)
def test_semistar_property(perm):
n = len(perm)
inv = inverse_0(perm)
neigh = [{perm[(i-1) % n], perm[(i+1) % n]} for i in range(n)]
return all(semistar_property(i, perm, inv, neigh, n) for i in range(n))
def triple_intersection(n,p,q,r):
#assert(n > r)
#assert(r > p)
#assert(p > q)
from sympy import acos,sin,cos,pi,sqrt,simplify,trigsimp,cancel
# simplify is slow
def simplify(a):
return a
return cancel(trigsimp(a))
def sub(v1,v2):
return simplify(v1[0]-v2[0]), simplify(v1[1]-v2[1])
def add(v1,v2):
return simplify(v1[0]+v2[0]), simplify(v1[1]+v2[1])
def dot(v1,v2):
return simplify(v1[0]*v2[0] + v1[1]*v2[1])
def scale(k,v):
return simplify(k*v[0]), simplify(k*v[1])
def length(v):
return simplify(sqrt(v[0]**2 + v[1]**2))
# 0q and 1p will intersect in c
# length of 0c
magnitude = simplify(sin((n-p)*pi/n) * 2 * sin(2*pi/n/2) / sin((p-q+1) * pi/n))
# angle of oc of length 1
unit_v = (simplify(-sin(q * pi / n)), simplify(cos(q * pi /n)))
# the point/vector c is [1,0] + magnitude*unit_v
intersection = add((1,0),scale(magnitude,unit_v))
# then we can find c0 vector
c0 = sub((1,0),intersection)
# and cr vector
cr = sub((cos(r*2*pi/n), sin(r*2*pi/n)), intersection)
# the angle between c0 and cr
theta = simplify(acos(dot(c0,cr)/(length(c0)*length(cr))))
# Now the arc r0 and s'q create a interior angle theta
# satisfying (r0 + s'q)/2 = theta
# or (n-r+q-s') * pi /n = theta
# so s' = -theta * n/pi + n -r + q
# this s' can be compared to s, if s is less than s' then rs intersects 0c1
return n - r + q - theta*n/pi
def test_star_property(orig):
from sympy import S
n = len(orig)
for i in range(n):
val = lambda x : (x - i) % n
perm = [val(x) for x in orig]
neigh = [{perm[(i-1) % n], perm[(i+1) % n]} for i in range(n)]
inv = inverse_0(perm)
q = min(neigh[inv[0]])
p = max(neigh[inv[1]])
if not p > q:
#print(i, "semistar")
return False
for r in range(p+1, n):
sprime = triple_intersection(n,p,q,r)
#print(sprime)
s_set = neigh[inv[r]]
if any(0 < sprime - S(s) and s > 1 for s in s_set):
#print(i, "star", p,q,r,s_set,float(sprime))
return False
return True
def embeddingless_star(orig):
res = 1
reslis = []
n = len(orig)
for i in range(n):
val = lambda x : (x - i) % n
invval = lambda x : (x + i) % n
perm = [val(x) for x in orig]
neigh = [{perm[(i-1) % n], perm[(i+1) % n]} for i in range(n)]
inv = inverse_0(perm)
q = min(neigh[inv[0]])
p = max(neigh[inv[1]])
if not p > q:
#print(i, "semistar")
return False
if n-p-1 > 0 and q-2 > 0:
reslis.append(i)
res = 2
for r in range(p+1, n):
lis = [s for s in neigh[inv[r]] if 1 < s and s < q]
if len(lis):
#print("O:{} I:{} p:{} q:{} r:{} s:{}".format(i, i+1, invval(p), invval(q), invval(r), [invval(_) for _ in lis]))
return False
return res
def get_significant_adjacent_points(O, perm, inv, neigh, n, val):
I = (O+1) % n
q = min(neigh[inv[O]], key=val)
p = max(neigh[inv[I]], key=val)
return p,q
def meddling_middlepoint(perm):
n = len(perm)
inv = inverse_0(perm)
neigh = [{perm[(i-1) % n], perm[(i+1) % n]} for i in range(n)]
for O in range(n):
val = lambda x : (x - O) % n
p,q = get_significant_adjacent_points(O,perm,inv,neigh,n,val)
if val(p) - val(q) == 1:
val = lambda x : (x - q) % n
pp,qq = get_significant_adjacent_points(q,perm,inv,neigh,n,val)
if (qq,pp) == (O, (O+1)%n):
return True
return False
def nova_badness(orig):
res = []
n = len(orig)
for i in range(n):
val = lambda x : (x - i) % n
invval = lambda x : (x + i) % n
perm = [val(x) for x in orig]
neigh = [{perm[(i-1) % n], perm[(i+1) % n]} for i in range(n)]
inv = inverse_0(perm)
q = min(neigh[inv[0]])
p = max(neigh[inv[1]])
if not p > q:
#print(i, "semistar")
return -1 # not a semistar
if n-p-1 > 0 and q-2 > 0:
pass
tmp = 0
for r in range(p+1, n):
lis = [s for s in neigh[inv[r]] if 1 < s and s < q]
tmp += len(lis)
res.append(tmp)
return sum(res),res
from enum import IntEnum
class Star(IntEnum):
nothing = 0
neighbour_avoidance = 1
semistar_middlepoint = 2
semistar = 3
star = 4
nova = 5
def avoid_neigh(perm):
n = len(perm)
return all((perm[i] + 1) % n != perm[(i+1) % n] and (perm[i] - 1) % n != perm[(i+1)%n] for i in range(n))
def classify_permutation(perm):
from unicursalpolygon.models.unicursalpolygon import UnicursalPolygon
if not avoid_neigh(perm):
return Star.nothing
elif not test_semistar_property(perm):
return Star.neighbour_avoidance
elif embeddingless_star(perm):
return Star.nova
elif UnicursalPolygon(perm).is_star():
return Star.star
else:
return Star.semistar
def classify2_permutation(perm):
from unicursalpolygon.models.unicursalpolygon import UnicursalPolygon
if not avoid_neigh(perm):
return Star.nothing
elif not test_semistar_property(perm):
return Star.neighbour_avoidance
badness,lis = nova_badness(perm)
if badness == 0:
return Star.nova
elif meddling_middlepoint(perm):
return Star.semistar_middlepoint, badness, lis
elif UnicursalPolygon(perm).is_star():
return Star.star, badness, lis
else:
return Star.semistar, badness, lis
if __name__ == "__main__":
while 1:
try:
perm = get_csv_line()
except:
break
starclass = classify2_permutation(perm)
s = ",".join(str(p) for p in perm)
print(s, starclass)