Em uma sala de bate-papo com algumas pessoas, surgiu um tópico entre eu e elas sobre quantas seqüências possíveis um regex poderia corresponder.

Sua tarefa é criar um programa que possa responder a essa pergunta.

Seu programa aceitará como entrada qualquer expressão regular, conforme definida neste documento, como uma "expressão regular estendida", como:

^[A-Za-z0-9]{8}$

e produz o número total de possíveis strings que correspondem a essa expressão, produzindo infinityse houver infinitas:

218340105584896

Seu programa também pode gerar saída too manyse houver mais de 2 ⁶³ -1 seqüências possíveis que correspondam à regex; no entanto, ele não deve produzir, a infinitymenos que haja realmente uma infinidade de cadeias.

O programa mais curto para realizar as vitórias acima.

Python 3370

Consegui que isso fosse o mais funcional possível e até alternei para o trabalho (com a verificação correta de contagem dupla!). Tanto quanto eu sei, isso funciona para tudo, exceto olhar para trás (porque isso seria loucura).

Para quem escreve sua própria solução, sinta-se à vontade para usar / melhorar meus métodos o quanto quiser.

Código:

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)

Aqui estão alguns casos de teste relevantes que confirmei:

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

* Isso é realmente diferente no golfe e no golfe devido a uma diferença de um caractere no que é definido como ascii válido. Eu acredito que o golfe é o mais correto.

Para confirmar sua precisão, mais testes podem ser feitos, informe-me sobre quaisquer erros (sinceramente, não ficaria surpreso se houvesse alguns).