How do you match only valid roman numerals with a regular expression?

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

You can use the following regex for this:

^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} 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}

You could, of course, use something like M* to allow any number (including zero) of thousands, if you want to allow bigger numbers.

Next is (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

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

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

---

Just keep in mind that that regex will also match an empty string. If you don't want this (and your regex engine is modern enough), you can use positive look-behind and look-ahead:

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

(the other alternative being to just check that the length is not zero beforehand).

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

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 4

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.

Answer 5

Fortunately, the range of numbers is limited to 1..3999 or thereabouts. Therefore, you can build up the regex piece-meal.

<opt-thousands-part><opt-hundreds-part><opt-tens-part><opt-units-part>

Each of those parts will deal with the vagaries of Roman notation. For example, using Perl notation:

<opt-hundreds-part> = m/(CM|DC{0,3}|CD|C{1,3})?/;

Repeat and assemble.

Added: The <opt-hundreds-part> can be compressed further:

<opt-hundreds-part> = m/(C[MD]|D?C{0,3})/;

Since the 'D?C{0,3}' clause can match nothing, there's no need for the question mark. And, most likely, the parentheses should be the non-capturing type - in Perl:

<opt-hundreds-part> = m/(?:C[MD]|D?C{0,3})/;

Of course, it should all be case-insensitive, too.

You can also extend this to deal with the options mentioned by James Curran (to allow XM or IM for 990 or 999, and CCCC for 400, etc).

<opt-hundreds-part> = m/(?:[IXC][MD]|D?C{0,4})/;

Answer 6

import re
pattern = '^M{0,3}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$'
if re.search(pattern, 'XCCMCI'):
    print 'Valid Roman'
else:
    print 'Not valid Roman'

For people who really want to understand the logic, please take a look at a step by step explanation on 3 pages on diveintopython.

The only difference from original solution (which had M{0,4}) is because I found that 'MMMM' is not a valid Roman numeral (also old Romans most probably have not thought about that huge number and will disagree with me). If you are one of disagreing old Romans, please forgive me and use {0,4} version.

Answer 7

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 8

Some really amazing answers here but none fit the bill for me since I needed to be able to match only valid Roman numerals within a string without matching empty strings and only match numerals that are on their own (i.e. not within a word).

Let me present you to Reilly's Modern roman numerals strict expression:

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

Out of the box it was pretty close to what I needed but it will only match standalone Roman numerals and when changed to match in string it will match empty strings at certain points (where a word begins with an uppercase V, M etc.) and will also give partial matches of invalid Roman numerals such as MMLLVVDD, XXLLVVDD, MMMMDLVX, XVXDLMM and MMMCCMLXXV.

So, after a bit of modification I and ended up with this:

(?<![MDCLXVI])(?=[MDCLXVI])M{0,3}(?:C[MD]|D?C{0,3})(?:X[CL]|L?X{0,3})(?:I[XV]|V?I{0,3})[^ ]\b

The added negative lookbehind will ensure that it doesn't do partial matches of invalid Roman numerals and locking down the first M to 3 since that is the highest it goes in the Roman numeral standard form.

As of right now, this is the only regular expression that passes my extensive test suit of over 4000 tests that includes all possible Roman numerals from 1-3999, Roman numerals within strings and invalid Roman numerals like the ones I mentioned above.

Here's a screenshot of it in action from https://regex101.com/:

Answer 9

I've seen multiple answers that doesn't cover empty strings or uses lookaheads to solve this. And I want to add a new answer that does cover empty strings and doesn't use lookahead. The regex is the following one:

^(I[VX]|VI{0,3}|I{1,3})|((X[LC]|LX{0,3}|X{1,3})(I[VX]|V?I{0,3}))|((C[DM]|DC{0,3}|C{1,3})(X[LC]|L?X{0,3})(I[VX]|V?I{0,3}))|(M+(C[DM]|D?C{0,3})(X[LC]|L?X{0,3})(I[VX]|V?I{0,3}))$

I'm allowing for infinite M, with M+ but of course someone could change to M{1,4} to allow only 1 or 4 if desired.

Below is a visualization that helps to understand what it is doing, preceded by two online demos:

Debuggex Demo

Regex 101 Demo

Answer 10

Im answering this question Regular Expression in Python for Roman Numerals here
because it was marked as an exact duplicate of this question.

It might be similar in name, but this is a specific regex question / problem
as can be seen by this answer to that question.

The items being sought can be combined into a single alternation and then
encased inside a capture group that will be put into a list with the findall()
function.
It is done like this :

>>> import re
>>> target = (
... r"this should pass v" + "\n"
... r"this is a test iii" + "\n"
... )
>>>
>>> re.findall( r"(?m)\s(i{1,3}v*|v)$", target )
['v', 'iii']

The regex modifications to factor and capture just the numerals are this :

 (?m)
 \s 
 (                     # (1 start)
      i{1,3} 
      v* 
   |  v
 )                     # (1 end)
 $

Answer 11

The following expression worked for me to validate the roman number.

^M{0,4}(C[MD]|D?C{0,3})(X[CL]|L?X{0,3})(I[XV]|V?I{0,3})$

Here,

• M{0,4} will match thousands
• C[MD]|D?C{0,3} will match Hundreds
• X[CL]|L?X{0,3} will match Tens
• I[XV]|V?I{0,3} will match Units

Below is a visualization that helps to understand what it is doing, preceded by two online demos:

Debuggex Demo

Regex 101 Demo

Python Code:

import re
regex = re.compile("^M{0,4}(C[MD]|D?C{0,3})(X[CL]|L?X{0,3})(I[XV]|V?I{0,3})$")
matchArray = regex.match("MMMCMXCIX")

Answer 12

The positive look-behind and look-ahead suggested by @paxdiablo in order to avoid matching empty strings seems not working to me.

I have fixed it by using negative look-ahead instead :

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

NB: if you append something (eg. "foobar" at the end of the regex, then obviously you'll have to replace (?!$) by (?!f) (where f is the first character of "foobar").

Answer 13

Steven Levithan uses this regex in his post which validates roman numerals prior to "deromanizing" the value:

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

Answer 14

This works in Java and PCRE regex engines and should now work in the latest JavaScript but may not work in all contexts.

(?<![A-Z])(M*(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3}))(?![A-Z])

The first part is the atrocious negative lookbehind. But, for logical purposes it is the easiest to understand. Basically, the first (?<!) is saying don't match the middle ([MATCH]) if there are letters coming before the middle ([MATCH]) and the last (?!) is saying don't match the middle ([MATCH]) if there are letters coming after it.

The middle ([MATCH]) is just the most commonly used regex for matching the sequence of Roman Numerals. But now, you don't want to match that if there are any letters around it.

See for yourself. https://regexr.com/4vce5

Answer 15

The problem of the solution from Jeremy and Pax is, that it does also match "nothing".

The following regex expects at least one roman numeral:

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

Answer 16

I would write functions to my work for me. Here are two roman numeral functions in PowerShell.

function ConvertFrom-RomanNumeral
{
  <#
    .SYNOPSIS
        Converts a Roman numeral to a number.
    .DESCRIPTION
        Converts a Roman numeral - in the range of I..MMMCMXCIX - to a number.
    .EXAMPLE
        ConvertFrom-RomanNumeral -Numeral MMXIV
    .EXAMPLE
        "MMXIV" | ConvertFrom-RomanNumeral
  #>
    [CmdletBinding()]
    [OutputType([int])]
    Param
    (
        [Parameter(Mandatory=$true,
                   HelpMessage="Enter a roman numeral in the range I..MMMCMXCIX",
                   ValueFromPipeline=$true,
                   Position=0)]
        [ValidatePattern("^M{0,3}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})$")]
        [string]
        $Numeral
    )

    Begin
    {
        $RomanToDecimal = [ordered]@{
            M  = 1000
            CM =  900
            D  =  500
            CD =  400
            C  =  100
            XC =   90
            L  =   50
            X  =   10
            IX =    9
            V  =    5
            IV =    4
            I  =    1
        }
    }
    Process
    {
        $roman = $Numeral + " "
        $value = 0

        do
        {
            foreach ($key in $RomanToDecimal.Keys)
            {
                if ($key.Length -eq 1)
                {
                    if ($key -match $roman.Substring(0,1))
                    {
                        $value += $RomanToDecimal.$key
                        $roman  = $roman.Substring(1)
                        break
                    }
                }
                else
                {
                    if ($key -match $roman.Substring(0,2))
                    {
                        $value += $RomanToDecimal.$key
                        $roman  = $roman.Substring(2)
                        break
                    }
                }
            }
        }
        until ($roman -eq " ")

        $value
    }
    End
    {
    }
}

function ConvertTo-RomanNumeral
{
  <#
    .SYNOPSIS
        Converts a number to a Roman numeral.
    .DESCRIPTION
        Converts a number - in the range of 1 to 3,999 - to a Roman numeral.
    .EXAMPLE
        ConvertTo-RomanNumeral -Number (Get-Date).Year
    .EXAMPLE
        (Get-Date).Year | ConvertTo-RomanNumeral
  #>
    [CmdletBinding()]
    [OutputType([string])]
    Param
    (
        [Parameter(Mandatory=$true,
                   HelpMessage="Enter an integer in the range 1 to 3,999",
                   ValueFromPipeline=$true,
                   Position=0)]
        [ValidateRange(1,3999)]
        [int]
        $Number
    )

    Begin
    {
        $DecimalToRoman = @{
            Ones      = "","I","II","III","IV","V","VI","VII","VIII","IX";
            Tens      = "","X","XX","XXX","XL","L","LX","LXX","LXXX","XC";
            Hundreds  = "","C","CC","CCC","CD","D","DC","DCC","DCCC","CM";
            Thousands = "","M","MM","MMM"
        }

        $column = @{Thousands = 0; Hundreds = 1; Tens = 2; Ones = 3}
    }
    Process
    {
        [int[]]$digits = $Number.ToString().PadLeft(4,"0").ToCharArray() |
                            ForEach-Object { [Char]::GetNumericValue($_) }

        $RomanNumeral  = ""
        $RomanNumeral += $DecimalToRoman.Thousands[$digits[$column.Thousands]]
        $RomanNumeral += $DecimalToRoman.Hundreds[$digits[$column.Hundreds]]
        $RomanNumeral += $DecimalToRoman.Tens[$digits[$column.Tens]]
        $RomanNumeral += $DecimalToRoman.Ones[$digits[$column.Ones]]

        $RomanNumeral
    }
    End
    {
    }
}