How do you match only valid roman numerals with a

Question

Thinking about my other problem, i decided I can't even create a regular expression that will match roman numerals (let alone a context-free grammar that will generate them)

The problem is matching only valid roman numerals. Eg, 990 is NOT "XM", it's "CMXC"

My problem in making the regex for this is that in order to allow or not allow certain characters, I need to look back. Let's take thousands and hundreds, for example.

I can allow M{0,2}C?M (to allow for 900, 1000, 1900, 2000, 2900 and 3000). However, If the match is on CM, I can't allow following characters to be C or D (because I'm already at 900).

How can I express this in a regex?
If it's simply not expressible in a regex, is it expressible in a context-free grammar?

Answer 1

Try:

^M{0,4}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$

Breaking it down:

---

M{0,4}

This specifies the thousands section and basically restrains it to between 0 and 4000. It's a relatively simple:

   0: <empty>  matched by M{0}
1000: M        matched by M{1}
2000: MM       matched by M{2}
3000: MMM      matched by M{3}
4000: MMMM     matched by M{4}

---

(CM|CD|D?C{0,3})

Slightly more complex, this is for the hundreds section and covers all the possibilities:

  0: <empty>  matched by D?C{0} (with D not there)
100: C        matched by D?C{1} (with D not there)
200: CC       matched by D?C{2} (with D not there)
300: CCC      matched by D?C{3} (with D not there)
400: CD       matched by CD
500: D        matched by D?C{0} (with D there)
600: DC       matched by D?C{1} (with D there)
700: DCC      matched by D?C{2} (with D there)
800: DCCC     matched by D?C{3} (with D there)
900: CM       matched by CM

---

(XC|XL|L?X{0,3})

Same rules as previous section but for the tens place:

 0: <empty>  matched by L?X{0} (with L not there)
10: X        matched by L?X{1} (with L not there)
20: XX       matched by L?X{2} (with L not there)
30: XXX      matched by L?X{3} (with L not there)
40: XL       matched by XL
50: L        matched by L?X{0} (with L there)
60: LX       matched by L?X{1} (with L there)
70: LXX      matched by L?X{2} (with L there)
80: LXXX     matched by L?X{3} (with L there)
90: XC       matched by XC

---

(IX|IV|V?I{0,3})

This is the units section, handling 0 through 9 and also similar to the previous two sections (Roman numerals, despite their seeming weirdness, follow some logical rules once you figure out what they are):

0: <empty>  matched by V?I{0} (with V not there)
1: I        matched by V?I{1} (with V not there)
2: II       matched by V?I{2} (with V not there)
3: III      matched by V?I{3} (with V not there)
4: IV       matched by IV
5: V        matched by V?I{0} (with V there)
6: VI       matched by V?I{1} (with V there)
7: VII      matched by V?I{2} (with V there)
8: VIII     matched by V?I{3} (with V there)
9: IX       matched by IX

Answer 2

Actually, your premise is flawed. 990 IS "XM", as well as "CMXC".

The Romans were far less concerned about the "rules" than your third grade teacher. As long as it added up, it was OK. Hence "IIII" was just as good as "IV" for 4. And "IIM" was completely cool for 998.

(If you have trouble dealing with that... Remember English spellings were not formalized until the 1700s. Until then, as long as the reader could figure it out, it was good enough).

Answer 3

As Jeremy and Pax pointed out above ... '^M{0,4}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$' should be the solution you're after ...

The specific URL that should have been attached (IMHO) is http://thehazeltree.org/diveintopython/7.html

Example 7.8 is the short form using {n,m}

Answer 4

In my case, I was trying to find and replace all occurences of roman numbers by one word inside the text, so I couldn't use the start and end of lines. So the @paxdiablo solution found many zero-length matches. I ended up with the following expression:

(?=\b[MCDXLVI]{1,6}\b)M{0,4}(?:CM|CD|D?C{0,3})(?:XC|XL|L?X{0,3})(?:IX|IV|V?I{0,3})

My final Python code was like this:

import re
text = "RULES OF LIFE: I. STAY CURIOUS; II. NEVER STOP LEARNING"
text = re.sub(r'(?=\b[MCDXLVI]{1,6}\b)M{0,4}(?:CM|CD|D?C{0,3})(?:XC|XL|L?X{0,3})(?:IX|IV|V?I{0,3})', 'ROMAN', text)
print(text)

Output:

RULES OF LIFE: ROMAN. STAY CURIOUS; ROMAN. NEVER STOP LEARNING

Answer 5

Just to save it here:

(^(?=[MDCLXVI])M*(C[MD]|D?C{0,3})(X[CL]|L?X{0,3})(I[XV]|V?I{0,3})$)

Matches all the Roman numerals. Doesn't care about empty strings (requires at least one Roman numeral letter). Should work in PCRE, Perl, Python and Ruby.

Online Ruby demo: http://rubular.com/r/KLPR1zq3Hj

Online Conversion: http://www.onlineconversion.com/roman_numerals_advanced.htm

Answer 6

To avoid matching the empty string you'll need to repeat the pattern four times and replace each 0 with a 1 in turn, and account for V, L and D:

(M{1,4}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})|M{0,4}(CM|C?D|D?C{1,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})|M{0,4}(CM|CD|D?C{0,3})(XC|X?L|L?X{1,3})(IX|IV|V?I{0,3})|M{0,4}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|I?V|V?I{1,3}))

In this case (because this pattern uses ^ and $) you would be better off checking for empty lines first and don't bother matching them. If you are using word boundaries then you don't have a problem because there's no such thing as an empty word. (At least regex doesn't define one; don't start philosophising, I'm being pragmatic here!)

---

In my own particular (real world) case I needed match numerals at word endings and I found no other way around it. I needed to scrub off the footnote numbers from my plain text document, where text such as "the Red Sea^cl and the Great Barrier Reef^cli" had been converted to the Red Seacl and the Great Barrier Reefcli. But I still had problems with valid words like Tahiti and fantastic are scrubbed into Tahit and fantasti.