问题
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?
回答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
回答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).
回答3:
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 $) you would be better off checking for empty lines first and don't bother matching them. If you are using word boundaries then you don't have a problem because there's no such thing as an empty word. (At least regex doesn't define one; don't start philosophising, I'm being pragmatic here!)
In my own particular (real world) case I needed match numerals at word endings and I found no other way around it. I needed to scrub off the footnote numbers from my plain text document, where text such as "the Red Seacl and the Great Barrier Reefcli" had been converted to the Red Seacl and the Great Barrier Reefcli. But I still had problems with valid words like Tahiti and fantastic are scrubbed into Tahit and fantasti.
回答4:
Just to save it here:
(^(?=[MDCLXVI])M*(C[MD]|D?C{0,3})(X[CL]|L?X{0,3})(I[XV]|V?I{0,3})$)
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
回答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})/;
回答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})$'
if re.search(pattern, 'XCCMCI'):
print 'Valid Roman'
else:
print 'Not valid Roman'
For people who really want to understand the logic, please take a look at a step by step explanation on 3 pages on diveintopython.
The only difference from original solution (which had M{0,4}) is because I found that 'MMMM' is not a valid Roman numeral (also old Romans most probably have not thought about that huge number and will disagree with me). If you are one of disagreing old Romans, please forgive me and use {0,4} version.
回答7:
Im answering this question Regular Expression in Python for Roman Numerals here
because it was marked as an exact duplicate of this question.
It might be similar in name, but this is a specific regex question / problem
as can be seen by this answer to that question.
The items being sought can be combined into a single alternation and then
encased inside a capture group that will be put into a list with the findall()
function.
It is done like this :
>>> import re
>>> target = (
... r"this should pass v" + "\n"
... r"this is a test iii" + "\n"
... )
>>>
>>> re.findall( r"(?m)\s(i{1,3}v*|v)$", 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)
$
回答8:
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})$' should be the solution you're after ...
The specific URL that should have been attached (IMHO) is http://thehazeltree.org/diveintopython/7.html
Example 7.8 is the short form using {n,m}
回答9:
In my case, I was trying to find and replace all occurences of roman numbers by one word inside the text, so I couldn't use the start and end of lines. So the @paxdiablo solution found many zero-length matches. I ended up with the following expression:
(?=\b[MCDXLVI]{1,6}\b)M{0,4}(?:CM|CD|D?C{0,3})(?:XC|XL|L?X{0,3})(?:IX|IV|V?I{0,3})
My final Python code was like this:
import re
text = "RULES OF LIFE: I. STAY CURIOUS; II. NEVER STOP LEARNING"
text = re.sub(r'(?=\b[MCDXLVI]{1,6}\b)M{0,4}(?:CM|CD|D?C{0,3})(?:XC|XL|L?X{0,3})(?:IX|IV|V?I{0,3})', 'ROMAN', text)
print(text)
Output:
RULES OF LIFE: ROMAN. STAY CURIOUS; ROMAN. NEVER STOP LEARNING
回答10:
Steven Levithan uses this regex in his post which validates roman numerals prior to "deromanizing" the value:
/^M*(?:D?C{0,3}|C[MD])(?:L?X{0,3}|X[CL])(?:V?I{0,3}|I[XV])$/
回答11:
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])$
回答12:
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
{
}
}
来源：https://stackoverflow.com/questions/59310128/regular-expression-in-python-for-roman-numerals