def f(st=-8, top=(0,0,0,0,0), bot=(1,1,1,1,1), carry=False, rec=0):
r = 0
rec += 1
if carry:
excl = tuple(1-array(top))
bot_new = list(bot)
bot_new[st] = 0
bot_new = tuple(bot_new)
for i, e in enumerate(excl):
if e==1:
top_new = list(top)
top_new[i] = 1
top_new = tuple(top_new)
p, s = ex(st, i, excl)
r += s + p * (f(i, top_new, bot_new, False, rec))
else:
excl = bot
for i, e in enumerate(excl):
if e==1:
p, s = ex(st, i, excl)
r += s + p * (f(i, top, bot, True, rec))
#print "-"*rec + ">", st, top, bot, carry, r
return r
if __name__=="__main__":
ret = eu_format(f())
print ret
assert ret=="430.088247"
def _filter(choices, rows, cols):
return [(i, j) for (i, j) in choices if i not in (-1, rows) and j not in (-1, cols)]
def apply_mul(func, arg, mul):
for k in range(mul):
arg = func(arg)
return arg
def connectivity(n):
dim = n*n
M = zeros((dim,dim))
for i in range(n):
for j in range(n):
choices = ((i-1, j), (i+1, j), (i, j-1), (i,j+1))
choices = _filter(choices, n, n)
prob = 1.0/len(choices)
for c in choices:
M[c[0]*n+c[1], i*n+j] += prob
return M
def e213(n=30, p=50):
c = connectivity(n)
r = apply_mul(lambda x: dot(c, x), c, p-1)
o = ones((n**2, n**2))
m = o-r
return sum([prod(r) for r in m])
if __name__=="__main__":
print eu_format(e213())
