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 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 main():
drawing = True
starLis = []
while 1:
if drawing:
try:
line = input()
lis = line.split(',')
lis = [int(i) for i in lis]
UnicursalPolygon(lis).draw(save=True)
except EOFError:
break
else:
try:
line = input()
lis = line.split(',')
lis = [int(i) for i in lis]
a = UnicursalPolygon(lis)
b = UnicursalPolygon(inverse_0(lis))
try:
tmp = a.is_star()
tmp2 = b.is_star()
except:
print("b failed is_star()," + str(b.perm))
continue
if tmp and tmp2:
print("star: {} inverses into a star {}".format(str(lis),str(b.perm)))
starLis.append(a)
starLis.append(b)
elif tmp:
print("star: {} does not inverse into a star {}".format(str(lis),str(b.perm)))
elif tmp2:
print("non-star: {} inverses into a star {}".format(str(lis),str(b.perm)))
else:
print(str(lis) + " neither are stars: " + str(unicursalpolygon.inverse_0(lis)))
except EOFError:
break
for perm in starLis:
perm.draw()
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
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 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))
