Python 3370
I got this to be about as functional as I could, and even got alternation to work (with correct double-count checking!). As far as I know this works for everything except lookarounds (because that would be crazy).
For anyone writing their own solution feel free to use/improve my methods as much as you like.
Code:
R=range;L=len;E=enumerate;I=int;F="Infinity";S=sum;H=chr;D=ord;J=lambda l:''.join(l);U=lambda s:J([H(i)if H(i) not in s else''for i in R(1,128)]);s=' \n\t';c=J((H(i)if H(i)not in s else'')for i in R(1,32));d,l,u=[J(H(i)for i in R(*n))for n in [[48,59],[97,123],[65,91]]];p='`~!@#$%^&*()-_=+[{]}\\|;:\'",<.>/?';Y={'\\s':s,'\\S':c+s+p+u+l+d,'\\d':d,'\\D':U(d),'\\w':u+l+'_','\\W':U(u+l+'_'),'[:alnum:]':u+l+d,'[:alpha:]':u+l,'[:ascii:]':U(''),'[:blank:]':' \t','[:cntrl:]':c,'[:digit:]':d,'[:graph:]':p+d+l+u,'[:lower:]':l,'[:print:]':p+d+l+u+s,'[:punct:]':p,'[:space:]':s,'[:upper:]':u,'[:word:]':l+u+'_','[:xdigit:]':d+'ABCDEF'};C=lambda l,n:[d+[l[i]]for i in R(L(l))for d in C(l[i+1:],n-1)]if n>0 else[[]];O=lambda x:S([all((c in s)for s in [(e[1]if any(e[1] not in Y for e in x)else Y[e[1]])if e[0]=='e'else(e[1]if e[0]=='t'else((Y[e[1]]if e[1]in Y else B(e[1]))if e[0]=='['else''))for e in x])for c in Y['[:ascii:]']])
def X(r):
x=[];l=0;c=''
for h in r:
l+=I(h in'([')-I(h in')]')
if l<1 and'|'==h:x+=[c];c=''
else:c+=h
x+=[c]
if L(x)>1:
o=0;m=[];u=[]
for e in x:
p,b=X(e)
if p==F:return F,[]
o+=p;m+=[('(',b)];u+=[b]
return o-S([(-1)**(i%2)*T(s) for i in R(2,L(u)+1)for s in C(u,i)]),[('|',m)]
u=[];o=[];m=[];w=1
while r!='':
h=r[0];z=0
if h in'([{':
l=1;i=1
while l>0:k=r[i];l+=(k==h)-(k=={'(':')','[':']','{':'}'}[h]);i+=1
u+=[(h,r[1:i-1])];z=i
elif h=='\\':u+=[('e','\\'+eval("'\\%s'"%r[1]))]if r[1]in'nt'else[('e','\\'+r[1])];z=2
elif h in ['*','+','?']:u+=[('{',h)];z=1
elif h in'^$':return 0
elif h=='.':u+=[('[','[:ascii:]')];z=1
else:u+=[('t',h)];z=1
r=r[z:]
for t,g in u:
if t=='(':p,b=X(g);o+=[p];m+=[('(',b)]
elif t=='e':o+=[L(Y[g])]if g in Y else[1]
elif t=='[':o+=[N(g)]
elif t=='{':
n=o[-1]
try:o[-1]=S([n**r for r in Q(g)])
except:return F,[]
elif t=='t':o+=[1]
if t!='(':m+=[(t,g)]
for c in o:
if c==F:return F,[]
w*=c
return w,m
def N(s):
if s in Y:return L(Y[s])
if(s[0],s[-1])==('[',']'):return 1
n=(s[0]=='^');a=0
if n:s=s[1:]
while s!='':
if L(s)>=3 and s[1]=='-':a+=D(s[2])-D(s[0])+1;s=s[3:];continue
a+=1;s=s[1:]
return 256*n+(-1)**n*a
def Q(s):
if s=='?':return[0,1]
if s[0]in'*+':return None
if ','in s:
l,h=s.split(',')
return None if h==''else R(I(l),I(h)+1)
return[I(s)]
def B(s):
n=(s[0]=='^')
if n:s=s[1:]
a='';w=''
while s!='':
h=s[0]
if 3<=L(s)and'-'==s[1]:
for i in R(D(s[0]),D(s[2])+1):a+=H(i)
s=s[3:];continue
a+=h;s=s[1:]
return J([c*(c not in a)for c in Y['[:ascii:]']])if n else a
def T(x):
if all(e==[] for e in x):return 1
for i,e in E(x):
if L(e)>=2 and e[1][0]=='{':return S([T([[e[0]]*n+e[2:]]+x[:i]+x[i+1:])for n in Q(e[1][1])])
if L(e)>=1:
if e[0][0] == '(':return T([e[0][1]+e[1:]]+x[:i]+x[i+1:])
if e[0][0]== '|':
t=S(T([[s]+e[1:]]+x[:i]+x[i+1:])for s in e[0][1])
u=[[s]for s in e[0][1]]
return t-S((-1)**(j%2)*T(b)for j in R(2,L(u)+1)for b in C(u,j))
if any(e==[]for e in x):return 0
return O([e[0]for e in x])*T([e[1:]for e in x])
r=raw_input();e=[];l=0;c=''
for h in r:
l+=I(h in'([')-I(h in')]')
if l<1 and'|'==h:e+=[c];c=''
else:c+=h
e+=[c];o=[];x=[]
for f in e:
if '^'!=f[0]or'$'!=f[-1]:print F;quit()
n,m=X(f[1:-1])
if n==F:print F;quit()
o+=[n];x+=[m]
print S(o)-S([(-1)**(i%2)*T(s) for i in R(2,L(x)+1)for s in C(x,i)])
Ungolfed:
controlchars = ''
for i in range(1,32):
if chr(i) not in '\t\n':
controlchars += chr(i)
CLASSES={
'\\s':' \t\n',
'\\S':controlchars+'!"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~',
'\\d':'0123456789',
'\\D':controlchars+'\n\t !"#$%&\'()*+,-./:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~',
'\\w':'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_',
'\\W':controlchars+'\n\t !"#$%&\'()*+,-./:;<=>?@[\\]^`{|}~',
'[:alnum:]':'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789',
'[:alpha:]':'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ',
'[:ascii:]':controlchars+'\n\t !"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~',
'[:blank:]':' \t',
'[:cntrl:]':controlchars,
'[:digit:]':'0123456789',
'[:graph:]':'!"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~',
'[:lower:]':'abcdefghijklmnopqrstuvwxyz',
'[:print:]':'\n\t !"#$%&\'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\\]^_`abcdefghijklmnopqrstuvwxyz{|}~',
'[:punct:]':'`~!@#$%^&*()-_=+[{]}\\|;:\'",<.>/?',
'[:space:]':' \t\n',
'[:upper:]':'ABCDEFGHIJKLMNOPQRSTUVWXYZ',
'[:word:]':'abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789_',
'[:xdigit:]':'0123456789ABCDEF'
}
DELIMIT = {
'(':')',
')':'(',
'[':']',
']':'[',
'{':'}',
'}':'{'
}
def combos(lst,num):
if num == 0:
return [[]]
combs = []
for i in range(len(lst)):
for c in combos(lst[i+1:],num-1):
combs.append([lst[i]]+c)
return combs
def count_regex(regex):
exprs = []
level = 0
current = ''
for char in regex:
if char in '([':
level += 1
if char in ')]':
level -= 1
if char == '|' and level == 0:
exprs.append(current)
current = ''
else:
current += char
exprs.append(current)
comps = []
expanded = []
for e in exprs:
if (e[0] != '^' or e[-1] != '$'):
return 'Infinity'
num,member = count_expr(e[1:-1])
if num == 'Infinity':
return 'Infinity'
comps.append(num)
expanded.append(member)
total = sum(comps)
for i in range(2,len(expanded)+1):
for subset in combos(expanded,i):
if i % 2 == 0:
total -= count_doubles(subset)
else:
total += count_doubles(subset)
return total
def count_expr(expr):
exprs = []
level = 0
current = ''
for char in expr:
if char in '([':
level += 1
if char in ')]':
level -= 1
if char == '|' and level == 0:
exprs.append(current)
current = ''
else:
current += char
exprs.append(current)
if len(exprs) != 1:
comps = 0
members = []
sub = []
for e in exprs:
comp,memb = count_expr(e)
if comp == 'Infinity':
return 'Infinity',[]
comps += comp
members.append(('(',memb))
sub.append(memb)
for i in range(2,len(sub)+1):
for subset in combos(sub,i):
if i % 2 == 0:
comps -= count_doubles(subset)
else:
comps += count_doubles(subset)
return comps,[('|',members)]
sub = []
while expr != '':
char = expr[0]
if char in ['(','[','{']:
level = 1
i = 1
while level > 0:
nchar = expr[i]
if nchar == char: level += 1
if nchar == DELIMIT[char]: level -= 1
i += 1
sub.append((char,expr[1:i-1]))
expr = expr[i:]
elif char == '\\':
if expr[1] == 'n':
sub.append(('e','\\'+'\n'))
expr = expr[2:]
elif expr[1] == 't':
sub.append(('e','\\'+'\t'))
expr = expr[2:]
else:
sub.append(('e','\\'+expr[1]))
expr = expr[2:]
elif char in ['*','+','?']:
sub.append(('{',char))
expr = expr[1:]
else:
if char in '^$':
return 0
if char == '.':
sub.append(('[','[:ascii:]'))
expr = expr[1:]
else:
sub.append(('t',char))
expr = expr[1:]
components = []
members = []
for t,string in sub:
if t == '(':
comp,memb = count_expr(string)
components.append(comp)
members.append(('(',memb))
elif t == 'e':
if string in CLASSES:
components.append(len(CLASSES[string]))
else:
components.append(1)
elif t == '[':
components.append(count_class(string))
elif t == '{':
num = components[-1]
try:
components[-1] = sum([num**r for r in count_quantifier(string)])
except TypeError:
return 'Infinity',[]
elif t == 't':
components.append(1)
if t != '(':
members.append((t,string))
total = 1
for c in components:
if c == 'Infinity':
return 'Infinity',[]
total *= c
return total,members
def count_class(string):
if string in CLASSES:
return len(CLASSES[string])
if string[0] == '[' and string[-1] == ']':
return 1
negate = (string[0] == '^')
if negate: string = string[1:]
avail_count = 0
while string != '':
char = string[0]
if len(string) >= 3:
if string[1] == '-':
first,last = string[0],string[2]
avail_count += ord(last)-ord(first)+1
string = string[3:]
continue
avail_count += 1
string = string[1:]
if negate:
return 256-avail-count
return avail_count
def count_quantifier(string):
if string == '?':
return [0,1]
if string[0] in '*+':
return None
if ',' in string:
low,high = string.split(',')
if high == '':
return None
return range(int(low),int(high)+1)
return [int(string)]
def bracket_string(string):
negate = (string[0] == '^')
if negate: string = string[1:]
avail = ''
while string != '':
char = string[0]
if len(string) >= 3:
if string[1] == '-':
first,last = string[0],string[2]
for i in range(ord(first),ord(last)+1):
avail += chr(i)
string = string[3:]
continue
avail += char
string = string[1:]
if negate:
new = ''
for c in CLASSES['[:ascii:]']:
if c not in avail:
new += c
return new
return avail
def overlap(es):
chars=['' for i in range(len(es))]
for i,e in enumerate(es):
if e[0] == 'e':
if any(e[1] not in CLASSES for e in es):
chars[i] = e[1]
else:
chars[i] = CLASSES[e[1]]
for i,e in enumerate(es):
if e[0] == 't':
chars[i] = e[1]
for i,e in enumerate(es):
if e[0] == '[':
if e[1] in CLASSES:
chars[i] = CLASSES[e[1]]
else:
chars[i] = bracket_string(e[1])
total = 0
for c in CLASSES['[:ascii:]']:
has = True
for chs in chars:
if c not in chs:
has = False
break
if has:
total += 1
return total
def count_doubles(exprs):
if all(e==[] for e in exprs):
return 1
for i,expr in enumerate(exprs):
if len(expr) >= 2 and expr[1][0] == '{':
rng = count_quantifier(expr[1][1])
total = 0
for n in rng:
total += count_doubles([ [expr[0]]*n+expr[2:] ] + exprs[:i] + exprs[i+1:])
return total
for i,expr in enumerate(exprs):
if len(expr) >= 1 and expr[0][0] == '(':
return count_doubles([ expr[0][1]+expr[1:] ] + exprs[:i] + exprs[i+1:] )
if any(e==[] for e in exprs):
return 0
for i,expr in enumerate(exprs):
if expr[0][0] == '|':
total = 0
subs = []
for sub_expr in expr[0][1]:
subs.append([sub_expr])
total += count_doubles([ [sub_expr]+expr[1:] ] + exprs[:i] + exprs[i+1:])
for j in range(2,len(subs)+1):
for subset in combos(subs,j):
if j % 2 == 0:
total -= count_doubles(subset)
else:
total += count_doubles(subset)
return total
over = overlap([e[0] for e in exprs])
if over == 0:
return 0
return over * count_doubles([e[1:] for e in exprs])
reg = raw_input('Regex: ')
print count_regex(reg)
Here are some relevant test cases I have confirmed:
Regex: ^[A-Za-z0-9]{8}$
218340105584896
Regex: ^([a-b]*)$
Infinity
Regex: ^([0-9]|[a-e])([a-e]|[A-E])$|^[a-f]{2}$
161
Regex: ^[a-z]{2}$|^[0-9]?[a-z]{2,3}$|^a[a-z]?$
200773
Regex: ^([a-z]|[a-e]|[A-E]|[3-4]|[D-G])$
35
Regex: ^\(.)\(.)\2\1$
16129*
Regex: ^(a)\1?$
2
Regex: ^[[:space:]]$|^\t$
3
*This is actually different in the golfed and ungolfed due to a one character difference in what is defined as valid ascii. I believe the golfed is the more correct one.
To confirm its accuracy further tests could be done, please let me know of any errors (I honestly would not be surprised if there were quite a few).
^[A-Za-z0-9]{8}$
? Otherwise the answer would beinfinity
. \$\endgroup\$