Roman numerals/Decode
You are encouraged to solve this task according to the task description, using any language you may know.
Create a function that takes a Roman numeral as its argument and returns its value as a numeric decimal integer. You don't need to validate the form of the Roman numeral.
Modern Roman numerals are written by expressing each decimal digit of the number to be encoded separately, starting with the leftmost digit and skipping any 0s. So 1990 is rendered "MCMXC" (1000 = M, 900 = CM, 90 = XC) and 2008 is rendered "MMVIII" (2000 = MM, 8 = VIII). The Roman numeral for 1666, "MDCLXVI", uses each letter in descending order.
Ada
<lang Ada>with Ada.Text_IO;
procedure Decode_Roman_Numerals is
function Roman_To_Integer(A_Roman: String) return Integer is
function Decode_Roman_Digit (A_Char: Character) return Integer is
begin
case A_Char is
when 'M' | 'm' => return 1000;
when 'D' | 'd' => return 500;
when 'C' | 'c' => return 100;
when 'L' | 'l' => return 50;
when 'X' | 'x' => return 10;
when 'V' | 'v' => return 5;
when 'I' | 'i' => return 1;
when others => return 0;
end case;
end Decode_Roman_Digit;
L_Curr_Val: Integer;
L_Last_Val: Integer;
Result: Integer;
begin
Result := 0;
L_Last_Val := 0;
for i in reverse 1 .. A_Roman'Length loop
L_Curr_Val := Decode_Roman_Digit(A_Roman(I));
if L_Curr_Val < L_Last_Val then
Result := Result - L_Curr_Val;
else
Result := Result + L_Curr_Val;
end if;
L_Last_Val := L_Curr_Val;
end loop;
return Result;
end Roman_To_Integer;
begin
Ada.Text_IO.Put_Line(Integer'Image(Roman_To_Integer("MCMXC"))); -- 1990
Ada.Text_IO.Put_Line(Integer'Image(Roman_To_Integer("MMVIII"))); -- 2008
Ada.Text_IO.Put_Line(Integer'Image(Roman_To_Integer("MDCLXVI"))); -- 1666
end Decode_Roman_Numerals;</lang>
ALGOL 68
Note: roman to int will handle multiple subtraction, e.g. IIIIX for 6. <lang Algol68> PROC roman to int = (STRING roman) INT:
BEGIN
PROC roman digit value = (CHAR roman digit) INT:
(roman digit = "M" | 1000 |:
roman digit = "D" | 500 |:
roman digit = "C" | 100 |:
roman digit = "L" | 50 |:
roman digit = "X" | 10 |:
roman digit = "V" | 5 |:
roman digit = "I" | 1);
INT result := 0, previous value := 0, run := 0;
FOR i FROM LWB roman TO UPB roman
DO
INT value = roman digit value(roman[i]);
IF previous value = value THEN
run +:= value
ELSE
IF previous value < value THEN
result -:= run
ELSE
result +:= run
FI;
run := previous value := value
FI
OD;
result +:= run
END;
MODE TEST = STRUCT (STRING input, INT expected output);
[] TEST roman test = (
("MMXI", 2011), ("MIM", 1999),
("MCMLVI", 1956), ("MDCLXVI", 1666),
("XXCIII", 83), ("LXXIIX", 78),
("IIIIX", 6)
);
print(("Test input Value Got", newline, "--------------------------", newline));
FOR i FROM LWB roman test TO UPB roman test
DO
INT output = roman to int(input OF roman test[i]);
printf(($g, n (12 - UPB input OF roman test[i]) x$, input OF roman test[i]));
printf(($g(5), 1x, g(5), 1x$, expected output OF roman test[i], output));
printf(($b("ok", "not ok"), 1l$, output = expected output OF roman test[i]))
OD</lang>
ANTLR
Java
<lang java>/* Parse Roman Numerals
Nigel Galloway March 16th., 2012
- /
grammar ParseRN ;
options { language = Java; } @members { int rnValue; int ONE; }
parseRN: ({rnValue = 0;} rn NEWLINE {System.out.println($rn.text + " = " + rnValue);})* ;
rn : (Thousand {rnValue += 1000;})* hundreds? tens? units?;
hundreds: {ONE = 0;} (h9 | h5) {if (ONE > 3) System.out.println ("Too many hundreds");}; h9 : Hundred {ONE += 1;} (FiveHund {rnValue += 400;}| Thousand {rnValue += 900;}|{rnValue += 100;} (Hundred {rnValue += 100; ONE += 1;})*); h5 : FiveHund {rnValue += 500;} (Hundred {rnValue += 100; ONE += 1;})*;
tens : {ONE = 0;} (t9 | t5) {if (ONE > 3) System.out.println ("Too many tens");}; t9 : Ten {ONE += 1;} (Fifty {rnValue += 40;}| Hundred {rnValue += 90;}|{rnValue += 10;} (Ten {rnValue += 10; ONE += 1;})*); t5 : Fifty {rnValue += 50;} (Ten {rnValue += 10; ONE += 1;})*;
units : {ONE = 0;} (u9 | u5) {if (ONE > 3) System.out.println ("Too many ones");}; u9 : One {ONE += 1;} (Five {rnValue += 4;}| Ten {rnValue += 9;}|{rnValue += 1;} (One {rnValue += 1; ONE += 1;})*); u5 : Five {rnValue += 5;} (One {rnValue += 1; ONE += 1;})*;
One : 'I'; Five : 'V'; Ten : 'X'; Fifty : 'L'; Hundred: 'C'; FiveHund: 'D'; Thousand: 'M' ; NEWLINE: '\r'? '\n' ;</lang> Using this test data:
MMXI MCMLVI XXCIII MCMXC MMVIII MDCLXVI IIIIX MIM MDCLXVI LXXIIX M MCXI CMXI MCM MMIX MCDXLIV MMXII
Produces:
MMXI = 2011 MCMLVI = 1956 line 3:2 missing NEWLINE at 'C' XX = 20 CIII = 103
Note that this implementation does not accept XXC as eighty. The error is detected and ANTLR attempts to continue by inserting the expected NEWLINE after XX and treating CIII as a new Number.
MCMXC = 1990 MMVIII = 2008 MDCLXVI = 1666 Too many ones line 7:4 extraneous input 'X' expecting NEWLINE IIII = 4
An implementation above thinks IIIIX is 6. It isn't. ANTLR detects the surfiet of 'I' reports the errors and tries to carry on.
line 8:2 no viable alternative at input 'M' MIM = 1000 MDCLXVI = 1666 line 10:5 extraneous input 'X' expecting NEWLINE LXXII = 72 M = 1000 MCXI = 1111 CMXI = 911 MCM = 1900 MMIX = 2009 MCDXLIV = 1444 MMXII = 2012
AutoHotkey
<lang AHK>Roman_Decode(str){ res := 0 Loop Parse, str { n := {M: 1000, D:500, C:100, L:50, X:10, V:5, I:1}[A_LoopField] If ( n > OldN ) && OldN res -= 2*OldN res += n, oldN := n } return res }
test = MCMXC|MMVIII|MDCLXVI Loop Parse, test, |
res .= A_LoopField "`t= " Roman_Decode(A_LoopField) "`r`n"
clipboard := res</lang>
- Output:
MCMXC = 1990 MMVIII = 2008 MDCLXVI = 1666
AWK
<lang AWK># syntax: GAWK -f ROMAN_NUMERALS_DECODE.AWK BEGIN {
leng = split("MCMXC MMVIII MDCLXVI",arr," ")
for (i=1; i<=leng; i++) {
n = arr[i]
printf("%s = %s\n",n,roman2arabic(n))
}
exit(0)
} function roman2arabic(r, a,i,p,q,u,ua,una,unr) {
r = toupper(r)
unr = "MDCLXVI" # each Roman numeral in descending order
una = "1000 500 100 50 10 5 1" # and its Arabic equivalent
split(una,ua," ")
i = split(r,u,"")
a = ua[index(unr,u[i])]
while (--i) {
p = index(unr,u[i])
q = index(unr,u[i+1])
a += ua[p] * ((p>q) ? -1 : 1)
}
return( (a>0) ? a : "" )
}</lang>
- Output:
MCMXC = 1990 MMVIII = 2008 MDCLXVI = 1666
BBC BASIC
<lang bbcbasic> PRINT "MCMXCIX", FNromandecode("MCMXCIX")
PRINT "MMXII", FNromandecode("MMXII")
PRINT "MDCLXVI", FNromandecode("MDCLXVI")
PRINT "MMMDCCCLXXXVIII", FNromandecode("MMMDCCCLXXXVIII")
END
DEF FNromandecode(roman$)
LOCAL i%, j%, p%, n%, r%()
DIM r%(7) : r%() = 0,1,5,10,50,100,500,1000
FOR i% = LEN(roman$) TO 1 STEP -1
j% = INSTR("IVXLCDM", MID$(roman$,i%,1))
IF j%=0 ERROR 100, "Invalid character"
IF j%>=p% n% += r%(j%) ELSE n% -= r%(j%)
p% = j%
NEXT
= n%</lang>
Output:
MCMXCIX 1999 MMXII 2012 MDCLXVI 1666 MMMDCCCLXXXVIII 3888
Bracmat
<lang bracmat> ( unroman
= nbr,lastVal,val
. 0:?nbr:?lastVal
& @( low$!arg
: ?
%@?L
( ?
& (m.1000)
(d.500)
(c.100)
(l.50)
(x.10)
(v.5)
(i.1)
: ? (!L.?val) ?
& (!val:~>!lastVal|!val+-2*!lastVal)
+ !nbr
: ?nbr
& !val:?lastVal
& ~
)
)
| !nbr
)
& (M.1000)
(MCXI.1111)
(CMXI.911)
(MCM.1900)
(MCMXC.1990)
(MMVIII.2008)
(MMIX.2009)
(MCDXLIV.1444)
(MDCLXVI.1666)
(MMXII.2012)
: ?years
& (test=.out$(!arg unroman$!arg)) & ( !years
: ? (?L.?D) (?&test$!L&~) | done );</lang>
- Output:
M 1000 MCXI 1111 CMXI 911 MCM 1900 MCMXC 1990 MMVIII 2008 MMIX 2009 MCDXLIV 1444 MDCLXVI 1666 MMXII 2012
C
Note: the code deliberately did not distinguish between "I", "J" or "U", "V", doing what Romans did for fun. <lang C>#include <stdio.h>
int digits[26] = { 0, 0, 100, 500, 0, 0, 0, 0, 1, 1, 0, 50, 1000, 0, 0, 0, 0, 0, 0, 0, 5, 5, 0, 10, 0, 0 };
/* assuming ASCII, do upper case and get index in alphabet. could also be
inline int VALUE(char x) { return digits [ (~0x20 & x) - 'A' ]; }
if you think macros are evil */
- define VALUE(x) digits[(~0x20 & (x)) - 'A']
int decode(const char * roman) {
const char *bigger;
int current;
int arabic = 0;
while (*roman != '\0') {
current = VALUE(*roman);
/* if (!current) return -1;
note: -1 can be used as error code; Romans didn't even have zero
*/
bigger = roman;
/* look for a larger digit, like IV or XM */
while (VALUE(*bigger) <= current && *++bigger != '\0');
if (*bigger == '\0')
arabic += current;
else {
arabic += VALUE(*bigger);
while (roman < bigger)
arabic -= VALUE(* (roman++) );
}
roman ++;
}
return arabic;
}
int main() {
const char * romans[] = { "MCmxC", "MMVIII", "MDClXVI", "MCXLUJ" };
int i;
for (i = 0; i < 4; i++)
printf("%s\t%d\n", romans[i], decode(romans[i]));
return 0;
}</lang>
C++
<lang cpp>#include <iostream>
- include <string>
- include <algorithm>
- include <map>
static std::map<char , int> Romans;
int RomanToInt( const std::string &roman ) {
int number = 0 ;
// look for all the letters in the array
for ( std::string::const_iterator i = roman.begin( ) ; i != roman.end( ) ; i++ ) {
std::map<char , int>::const_iterator it1 = Romans.find( *i ) ;
if ( it1 == Romans.end( ) ) {
std::cerr << *i << " not a valid Roman numeral character." << std::endl ;
return -1 ;
}
int pos1 = it1->second ;
if ( i + 1 != roman.end( ) ) {
std::map<char , int>::const_iterator it2 = Romans.find( *( i + 1 ) );
if ( it2 == Romans.end( ) ) {
std::cerr << *( i + 1 ) << " not a valid Roman numeral character." << std::endl ;
return -1 ;
}
int pos2 = it2->second ;
if ( pos2 > pos1 ) {
number += pos2 - pos1 ;
i++ ;
continue ;
}
}
number += pos1 ;
}
return number ;
}
int main( ) {
Romans[ 'I' ] = 1 ; Romans[ 'V' ] = 5 ; Romans[ 'X' ] = 10 ; Romans[ 'L' ] = 50 ; Romans[ 'C' ] = 100 ; Romans[ 'D' ] = 500 ; Romans[ 'M' ] = 1000 ;
std::cout << "MCMXC in Roman numerals is " << RomanToInt( "MCMXC" ) << " in Arabic!\n" ; std::cout << "And MDCLXVI for the Romans is " << RomanToInt( "MDCLXVI" ) << " in better known Arabic figures!\n" ; return 0 ;
}</lang>
- Output:
MCMXC in Roman numerals is 1990 in Arabic! And MDCLXVI for the Romans is 1666 in better known Arabic figures!
C#
<lang csharp>using System; using System.Collections.Generic;
namespace Roman {
internal class Program
{
private static void Main(string[] args)
{
// Decode and print the numerals.
Console.WriteLine("{0}: {1}", "MCMXC", Decode("MCMXC"));
Console.WriteLine("{0}: {1}", "MMVIII", Decode("MMVIII"));
Console.WriteLine("{0}: {1}", "MDCLXVI", Decode("MDCLXVI"));
}
// Dictionary to hold our numerals and their values.
private static readonly Dictionary<char, int> RomanDictionary = new Dictionary<char, int>
{
{'I', 1},
{'V', 5},
{'X', 10},
{'L', 50},
{'C', 100},
{'D', 500},
{'M', 1000}
};
private static int Decode(string roman)
{
/* Make the input string upper-case,
* because the dictionary doesn't support lower-case characters. */
roman = roman.ToUpper();
/* total = the current total value that will be returned.
* minus = value to subtract from next numeral. */
int total = 0, minus = 0;
for (int i = 0; i < roman.Length; i++) // Iterate through characters.
{
// Get the value for the current numeral. Takes subtraction into account.
int thisNumeral = RomanDictionary[roman[i]] - minus;
/* Checks if this is the last character in the string, or if the current numeral
* is greater than or equal to the next numeral. If so, we will reset our minus
* variable and add the current numeral to the total value. Otherwise, we will
* subtract the current numeral from the next numeral, and continue. */
if (i >= roman.Length - 1 ||
thisNumeral + minus >= RomanDictionary[roman[i + 1]])
{
total += thisNumeral;
minus = 0;
}
else
{
minus = thisNumeral;
}
}
return total; // Return the total.
}
}
}</lang>
- Output:
MCMXC: 1990 MMVIII: 2008 MDCLXVI: 1666
Clojure
<lang clojure>(defn ro2ar [r]
(->> (reverse r)
(replace (zipmap "MDCLXVI" [1000 500 100 50 10 5 1]))
(partition-by identity)
(map (partial apply +))
(reduce #(if (< %1 %2) (+ %1 %2) (- %1 %2)))))</lang>
- Output:
(map ro2ar ["MDCLXVI" "MMMCMXCIX" "XLVIII" "MMVIII"]) (1666 3999 48 2008)
CoffeeScript
<lang coffeescript>roman_to_demical = (s) ->
# s is well-formed Roman Numeral >= I numbers = M: 1000 D: 500 C: 100 L: 50 X: 10 V: 5 I: 1
result = 0
for c in s
num = numbers[c]
result += num
if old_num < num
# If old_num exists and is less than num, then
# we need to subtract it twice, once because we
# have already added it on the last pass, and twice
# to conform to the Roman convention that XC = 90,
# not 110.
result -= 2 * old_num
old_num = num
result
tests =
IV: 4 XLII: 42 MCMXC: 1990 MMVIII: 2008 MDCLXVI: 1666
for roman, expected of tests
dec = roman_to_demical(roman)
console.log "error" if dec != expected
console.log "#{roman} = #{dec}"</lang>
Common Lisp
Doesn't have much in error checking: <lang lisp>(defun parse-roman (r)
(loop for l on (map 'list (lambda (c)
(getf '(#\I 1 #\V 5 #\X 10 #\L 50 #\C 100 #\D 500 #\M 1000) c)) (string-upcase r))
sum (let ((a (first l)) (b (second l)))
(if (and b (< a b)) (- a) a))))
- test code
(dolist (r '("MCMXC" "MDCLXVI" "MMVIII"))
(format t "~a: ~d~%" r (parse-roman r)))</lang>
- Output:
MCMXC: 1990 MDCLXVI: 1666 MMVIII: 2008
D
<lang d>import std.regex, std.algorithm;
int toArabic(in string s) /*pure nothrow*/ {
static immutable weights = [1000, 900, 500, 400, 100,
90, 50, 40, 10, 9, 5, 4, 1];
static immutable symbols = ["M","CM","D","CD","C","XC",
"L","XL","X","IX","V","IV","I"];
int arabic;
foreach (m; s.match(regex(r"CM|CD|XC|XL|IX|IV|[MDCLXVI]", "g")))
arabic += weights[symbols.countUntil(m.hit)];
return arabic;
}
void main() {
assert(toArabic("MCMXC") == 1990);
assert(toArabic("MMVIII") == 2008);
assert(toArabic("MDCLXVI") == 1666);
}</lang> Alternative version: <lang d>import std.regex, std.algorithm;
immutable int[string] w2s;
nothrow static this() {
w2s = ["IX": 9, "C": 100, "D": 500, "CM": 900, "I": 1,
"XC": 90, "M": 1000, "L": 50, "CD": 400, "XL": 40,
"V": 5, "X": 10, "IV": 4];
}
int toArabic(in string s) /*pure nothrow*/ {
auto ms = match(s, regex("CM|CD|XC|XL|IX|IV|[MDCLXVI]", "g"));
return reduce!((a, m) => a + w2s[m.hit])(0, ms);
}
void main() {
assert("MCMXC".toArabic == 1990);
assert("MMVIII".toArabic == 2008);
assert("MDCLXVI".toArabic == 1666);
}</lang>
Delphi/Pascal
<lang delphi>program RomanNumeralsDecode;
{$APPTYPE CONSOLE}
function RomanToInteger(const aRoman: string): Integer;
function DecodeRomanDigit(aChar: Char): Integer;
begin
case aChar of
'M', 'm': Result := 1000;
'D', 'd': Result := 500;
'C', 'c': Result := 100;
'L', 'l': Result := 50;
'X', 'x': Result := 10;
'V', 'v': Result := 5;
'I', 'i': Result := 1
else
Result := 0;
end;
end;
var
i: Integer; lCurrVal: Integer; lLastVal: Integer;
begin
Result := 0;
lLastVal := 0;
for i := Length(aRoman) downto 1 do
begin
lCurrVal := DecodeRomanDigit(aRoman[i]);
if lCurrVal < lLastVal then
Result := Result - lCurrVal
else
Result := Result + lCurrVal;
lLastVal := lCurrVal;
end;
end;
begin
Writeln(RomanToInteger('MCMXC')); // 1990
Writeln(RomanToInteger('MMVIII')); // 2008
Writeln(RomanToInteger('MDCLXVI')); // 1666
end.</lang>
Emacs Lisp
<lang lisp> (defun ro2ar (RN)
"translate a roman number RN into arabic number. Its argument RN is wether a symbol, wether a list. Returns the arabic number. (ro2ar 'C) gives 100, (ro2ar '(X X I V)) gives 24" (cond ((eq RN 'M) 1000) ((eq RN 'D) 500) ((eq RN 'C) 100) ((eq RN 'L) 50) ((eq RN 'X) 10) ((eq RN 'V) 5) ((eq RN 'I) 1) ((null (cdr RN)) (ro2ar (car RN))) ;; stop recursion ((< (ro2ar (car RN)) (ro2ar (car (cdr RN)))) (- (ro2ar (cdr RN)) (ro2ar (car RN)))) ;; "IV" -> 5-1=4 (t (+ (ro2ar (car RN)) (ro2ar (cdr RN)))))) ;; "VI" -> 5+1=6
</lang>
- Output:
(ro2ar '(M D C L X V I)) -> 1666
Euphoria
<lang euphoria>constant symbols = "MDCLXVI", weights = {1000,500,100,50,10,5,1} function romanDec(sequence roman)
integer n, lastval, arabic
lastval = 0
arabic = 0
for i = length(roman) to 1 by -1 do
n = find(roman[i],symbols)
if n then
n = weights[n]
end if
if n < lastval then
arabic -= n
else
arabic += n
end if
lastval = n
end for
return arabic
end function
? romanDec("MCMXCIX") ? romanDec("MDCLXVI") ? romanDec("XXV") ? romanDec("CMLIV") ? romanDec("MMXI")</lang>
- Output:
1999 1666 25 954 2011
F#
This implementation uses tail recursion. The accumulator (arabic) and the last roman digit (lastval) are recursively passed as each element of the list is consumed. <lang fsharp>let decimal_of_roman roman =
let rec convert arabic lastval = function
| head::tail ->
let n = match head with
| 'M' | 'm' -> 1000
| 'D' | 'd' -> 500
| 'C' | 'c' -> 100
| 'L' | 'l' -> 50
| 'X' | 'x' -> 10
| 'V' | 'v' -> 5
| 'I' | 'i' -> 1
| _ -> 0
let op = if n > lastval then (-) else (+)
convert (op arabic lastval) n tail
| _ -> arabic + lastval
convert 0 0 (Seq.toList roman)
- </lang>
Here is an alternative implementation that uses Seq(uence).fold. It threads a Tuple of the state (accumulator, last roman digit) through the list of characters. <lang fsharp>let decimal_of_roman roman =
let convert (arabic,lastval) c =
let n = match c with
| 'M' | 'm' -> 1000
| 'D' | 'd' -> 500
| 'C' | 'c' -> 100
| 'L' | 'l' -> 50
| 'X' | 'x' -> 10
| 'V' | 'v' -> 5
| 'I' | 'i' -> 1
| _ -> 0
let op = if n > lastval then (-) else (+)
(op arabic lastval, n)
let (arabic, lastval) = Seq.fold convert (0,0) roman
arabic + lastval
- </lang>
Test code: <lang fsharp>let tests = ["MCMXC"; "MMVIII"; "MDCLXVII"; "MMMCLIX"; "MCMLXXVII"; "MMX"] for test in tests do Printf.printf "%s: %d\n" test (decimal_of_roman test)
- </lang>
- Output:
MCMXC: 1990 MMVIII: 2008 MDCLXVII: 1667 MMMCLIX: 3159 MCMLXXVII: 1977 MMX: 2010
Forth
<lang forth>create (arabic)
1000 128 * char M + ,
500 128 * char D + ,
100 128 * char C + ,
50 128 * char L + ,
10 128 * char X + ,
5 128 * char V + ,
1 128 * char I + ,
does>
7 cells bounds do i @ over over 127 and = if nip 7 rshift leave else drop then 1 cells +loop dup
- >arabic
0 dup >r >r begin over over while c@ dup (arabic) rot <> while r> over r> over over > if 2* negate + else drop then + swap >r >r 1 /string repeat then drop 2drop r> r> drop
s" MCMLXXXIV" >arabic .</lang>
Fortran
<lang fortran>program Roman_decode
implicit none
write(*,*) decode("MCMXC"), decode("MMVIII"), decode("MDCLXVI")
contains
function decode(roman) result(arabic)
character(*), intent(in) :: roman integer :: i, n, lastval, arabic
arabic = 0
lastval = 0
do i = len(roman), 1, -1
select case(roman(i:i))
case ('M','m')
n = 1000
case ('D','d')
n = 500
case ('C','c')
n = 100
case ('L','l')
n = 50
case ('X','x')
n = 10
case ('V','v')
n = 5
case ('I','i')
n = 1
case default
n = 0
end select
if (n < lastval) then
arabic = arabic - n
else
arabic = arabic + n
end if
lastval = n
end do
end function decode end program Roman_decode</lang>
- Output:
1990 2008 1666
Go
For fluff, the unicode overbar is recognized as a factor of 1000, as described in WP. <lang go>package main
import (
"errors" "fmt"
)
var m = map[rune]int{
'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000,
}
func parseRoman(s string) (r int, err error) {
if s == "" {
return 0, errors.New("Empty string")
}
is := []rune(s) // easier to convert string up front
var c0 rune // c0: roman character last read
var cv0 int // cv0: value of cv
// the key to the algorithm is to process digits from right to left
for i := len(is) - 1; i >= 0; i-- {
// read roman digit
c := is[i]
k := c == 0x305 // unicode overbar combining character
if k {
if i == 0 {
return 0, errors.New(
"Overbar combining character invalid at position 0")
}
i--
c = is[i]
}
cv := m[c]
if cv == 0 {
if c == 0x0305 {
return 0, errors.New(fmt.Sprintf(
"Overbar combining character invalid at position %d", i))
} else {
return 0, errors.New(fmt.Sprintf(
"Character unrecognized as Roman digit: %c", c))
}
}
if k {
c = -c // convention indicating overbar
cv *= 1000
}
// handle cases of new, same, subtractive, changed, in that order.
switch {
default: // case 4: digit change
fallthrough
case c0 == 0: // case 1: no previous digit
c0 = c
cv0 = cv
case c == c0: // case 2: same digit
case cv*5 == cv0 || cv*10 == cv0: // case 3: subtractive
// handle next digit as new.
// a subtractive digit doesn't count as a previous digit.
c0 = 0
r -= cv // subtract...
continue // ...instead of adding
}
r += cv // add, in all cases except subtractive
}
return r, nil
}
func main() {
// parse three numbers mentioned in task description
for _, r := range []string{"MCMXC", "MMVIII", "MDCLXVI"} {
v, err := parseRoman(r)
if err != nil {
fmt.Println(err)
} else {
fmt.Println(r, "==", v)
}
}
}</lang>
- Output:
MCMXC == 1990 MMVIII == 2008 MDCLXVI == 1666
Simpler: <lang go>package main
import ( "fmt" "strings" )
var m = map[string]int{ "I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000, }
// function, per task description func from_roman(roman string) (arabic int) { last_digit := 1000 for _, r := range strings.Split(roman, "") { digit := m[r] if last_digit < digit { arabic -= 2 * last_digit } last_digit = digit arabic += digit }
return arabic }
func main() { // parse three numbers mentioned in task description for _, roman_digit := range []string{"MCMXC", "MMVIII", "MDCLXVI"} { fmt.Printf("%-10s == %d\n", roman_digit, from_roman(roman_digit)) } }</lang>
Groovy
Solution: <lang groovy>enum RomanDigits {
I(1), V(5), X(10), L(50), C(100), D(500), M(1000);
private magnitude;
private RomanDigits(magnitude) { this.magnitude = magnitude }
String toString() { super.toString() + "=${magnitude}" }
static BigInteger parse(String numeral) {
assert numeral != null && !numeral.empty
def digits = (numeral as List).collect {
RomanDigits.valueOf(it)
}
def L = digits.size()
(0..<L).inject(0g) { total, i ->
def sign = (i == L - 1 || digits[i] >= digits[i+1]) ? 1 : -1
total + sign * digits[i].magnitude
}
}
}</lang> Test: <lang groovy>println """ Digit Values = ${RomanDigits.values()} M => ${RomanDigits.parse('M')} MCXI => ${RomanDigits.parse('MCXI')} CMXI => ${RomanDigits.parse('CMXI')} MCM => ${RomanDigits.parse('MCM')} MCMXC => ${RomanDigits.parse('MCMXC')} MMVIII => ${RomanDigits.parse('MMVIII')} MMIX => ${RomanDigits.parse('MMIX')} MCDXLIV => ${RomanDigits.parse('MCDXLIV')} MDCLXVI => ${RomanDigits.parse('MDCLXVI')} """</lang>
- Output:
Digit Values = [I=1, V=5, X=10, L=50, C=100, D=500, M=1000] M => 1000 MCXI => 1111 CMXI => 911 MCM => 1900 MCMXC => 1990 MMVIII => 2008 MMIX => 2009 MCDXLIV => 1444 MDCLXVI => 1666
Haskell
<lang Haskell>import Data.List (isPrefixOf)
mapping = [("M",1000),("CM",900),("D",500),("CD",400),("C",100),("XC",90),
("L",50),("XL",40),("X",10),("IX",9),("V",5),("IV",4),("I",1)]
toArabic :: String -> Int toArabic "" = 0 toArabic str = num + toArabic xs
where (num, xs):_ = [ (num, drop (length n) str) | (n,num) <- mapping, isPrefixOf n str ]</lang>
Usage:
ghci> toArabic "MCMXC" 1990 ghci> toArabic "MMVIII" 2008 ghci> toArabic "MDCLXVI" 1666
Icon and Unicon
<lang Icon>link numbers
procedure main() every R := "MCMXC"|"MDCLXVI"|"MMVIII" do
write(R, " = ",unroman(R))
end</lang>
The code for this procedure is copied below: <lang Icon>procedure unroman(s) #: convert Roman numeral to integer
local nbr,lastVal,val
nbr := lastVal := 0
s ? {
while val := case map(move(1)) of {
"m": 1000 "d": 500 "c": 100 "l": 50 "x": 10 "v": 5 "i": 1 } do { nbr +:= if val <= lastVal then val else val - 2 * lastVal lastVal := val }
} return nbr
end</lang>
- Output:
MCMXC = 1990 MDCLXVI = 1666 MMVIII = 2008
J
<lang j>rom2d=: [: (+/ .* _1^ 0,~ 2</\ ]) 1 5 10 50 100 500 1000 {~ 'IVXLCDM'&i.</lang> Example use: <lang j> rom2d 'MCMXC' 1990
rom2d 'MDCLXVI'
1666
rom2d 'MMVIII'
2008</lang>
Java
<lang java>public class Roman { private static int decodeSingle(char letter) { switch(letter) { case 'M': return 1000; case 'D': return 500; case 'C': return 100; case 'L': return 50; case 'X': return 10; case 'V': return 5; case 'I': return 1; default: return 0; } } public static int decode(String roman) { int result = 0; String uRoman = roman.toUpperCase(); //case-insensitive for(int i = 0;i < uRoman.length() - 1;i++) {//loop over all but the last character //if this character has a lower value than the next character if (decodeSingle(uRoman.charAt(i)) < decodeSingle(uRoman.charAt(i+1))) { //subtract it result -= decodeSingle(uRoman.charAt(i)); } else { //add it result += decodeSingle(uRoman.charAt(i)); } } //decode the last character, which is always added result += decodeSingle(uRoman.charAt(uRoman.length()-1)); return result; }
public static void main(String[] args) { System.out.println(decode("MCMXC")); //1990 System.out.println(decode("MMVIII")); //2008 System.out.println(decode("MDCLXVI")); //1666 } }</lang>
- Output:
1990 2008 1666
JavaScript
<lang javascript>var Roman = {
Values: [['M', 1000], ['CM', 900], ['D', 500], ['CD', 400],
['C', 100], ['XC', 90], ['L', 50], ['XL', 40],
['X', 10], ['IX', 9], ['V', 5], ['IV', 4],
['I', 1]],
parse: function(str) {
var result = 0
for (var i=0; i<Roman.Values.length; ++i) {
var pair = Roman.Values[i]
var key = pair[0]
var value = pair[1]
var regex = RegExp('^' + key)
while (str.match(regex)) {
result += value
str = str.replace(regex, )
}
}
return result
}
}
var test_data = ['MCMXC', 'MDCLXVI', 'MMVIII'] for (var i=0; i<test_data.length; ++i) {
var test_datum = test_data[i] print(test_datum + ": " + Roman.parse(test_datum))
}</lang>
- Output:
MCMXC: 1990 MDCLXVI: 1666 MMVIII: 2008
K
<lang k> romd: {v:1 5 10 50 100 500 1000@"IVXLCDM"?/:x; +/v*_-1^(>':v),0}</lang> Example: <lang k> romd'("MCMXC";"MMVIII";"MDCLXVI") 1990 2008 1666</lang>
Liberty BASIC
As Fortran & PureBasic. <lang lb> print "MCMXCIX = "; romanDec( "MCMXCIX") '1999
print "MDCLXVI = "; romanDec( "MDCLXVI") '1666 print "XXV = "; romanDec( "XXV") '25 print "CMLIV = "; romanDec( "CMLIV") '954 print "MMXI = "; romanDec( "MMXI") '2011
end
function romanDec( roman$)
arabic =0 lastval =0
for i = len( roman$) to 1 step -1
select case upper$( mid$( roman$, i, 1))
case "M"
n = 1000
case "D"
n = 500
case "C"
n = 100
case "L"
n = 50
case "X"
n = 10
case "V"
n = 5
case "I"
n = 1
case else
n = 0
end select
if n <lastval then
arabic =arabic -n
else
arabic =arabic +n
end if
lastval =n next
romanDec =arabic
end function</lang>
MCMXCIX = 1999 MDCLXVI = 1666 XXV = 25 CMLIV = 954 MMXI = 2011
Logo
<lang logo>; Roman numeral decoder
- First, some useful substring utilities
to starts_with? :string :prefix
if empty? :prefix [output "true] if empty? :string [output "false] if not equal? first :string first :prefix [output "false] output starts_with? butfirst :string butfirst :prefix
end
to remove_prefix :string :prefix
if or empty? :prefix not starts_with? :string :prefix [output :string] output remove_prefix butfirst :string butfirst :prefix
end
- Our list of Roman numeral values
make "values [[M 1000] [CM 900] [D 500] [CD 400] [C 100] [XC 90] [L 50]
[XL 40] [X 10] [IX 9] [V 5] [IV 4] [I 1]]
- Function to do the work
to from_roman :str
local "n make "n 0
foreach :values [
local "s make "s first ?
local "v make "v last ?
while [starts_with? :str :s] [
make "n sum n :v
make "str remove_prefix :str :s
]
]
output :n
end
foreach [MCMXC MDCLXVI MMVIII] [print (sentence (word ? "|: |) from_roman ?)] bye</lang>
- Output:
MCMXC: 1990 MDCLXVI: 1666 MMVIII: 2008
Lua
<lang lua>function ToNumeral( roman )
local Num = { ["M"] = 1000, ["D"] = 500, ["C"] = 100, ["L"] = 50, ["X"] = 10, ["V"] = 5, ["I"] = 1 }
local numeral = 0
local i = 1
local strlen = string.len(roman)
while i < strlen do
local z1, z2 = Num[ string.sub(roman,i,i) ], Num[ string.sub(roman,i+1,i+1) ]
if z1 < z2 then
numeral = numeral + ( z2 - z1 )
i = i + 2
else
numeral = numeral + z1
i = i + 1
end
end
if i <= strlen then numeral = numeral + Num[ string.sub(roman,i,i) ] end
return numeral
end
print( ToNumeral( "MCMXC" ) ) print( ToNumeral( "MMVIII" ) ) print( ToNumeral( "MDCLXVI" ) )</lang>
1990 2008 1666
NetRexx
<lang NetRexx>/* NetRexx */ options replace format comments java crossref savelog symbols binary
/* 1990 2008 1666 */
years = Rexx('MCMXC MMVIII MDCLXVI')
loop y_ = 1 to years.words
Say years.word(y_).right(10) || ':' decode(years.word(y_)) end y_
return
method decode(arg) public static returns int signals IllegalArgumentException
parse arg.upper roman .
if roman.verify('MDCLXVI') \= 0 then signal IllegalArgumentException
-- always insert the value of the least significant numeral
decnum = rchar(roman.substr(roman.length, 1))
loop d_ = 1 to roman.length - 1
if rchar(roman.substr(d_, 1)) < rchar(roman.substr(d_ + 1, 1)) then do
-- Handle cases where numerals are not in descending order
-- subtract the value of the numeral
decnum = decnum - rchar(roman.substr(d_, 1))
end
else do
-- Normal case
-- add the value of the numeral
decnum = decnum + rchar(roman.substr(d_, 1))
end
end d_
return decnum
method rchar(arg) public static returns int
parse arg.upper ch +1 . select case ch when 'M' then digit = 1000 when 'D' then digit = 500 when 'C' then digit = 100 when 'L' then digit = 50 when 'X' then digit = 10 when 'V' then digit = 5 when 'I' then digit = 1 otherwise digit = 0 end
return digit</lang>
- Output:
MCMXC: 1990
MMVIII: 2008
MDCLXVI: 1666
OCaml
<lang ocaml>let decimal_of_roman roman =
let arabic = ref 0 in
let lastval = ref 0 in
for i = (String.length roman) - 1 downto 0 do
let n =
match roman.[i] with
| 'M' | 'm' -> 1000
| 'D' | 'd' -> 500
| 'C' | 'c' -> 100
| 'L' | 'l' -> 50
| 'X' | 'x' -> 10
| 'V' | 'v' -> 5
| 'I' | 'i' -> 1
| _ -> 0
in
if n < !lastval
then arabic := !arabic - n
else arabic := !arabic + n;
lastval := n
done;
!arabic
let () =
Printf.printf " %d\n" (decimal_of_roman "MCMXC"); Printf.printf " %d\n" (decimal_of_roman "MMVIII"); Printf.printf " %d\n" (decimal_of_roman "MDCLXVI");
- </lang>
Mathematica
<lang Mathematica>FromDigits["MMCDV", "Roman"]</lang> returns 2405
PARI/GP
<lang parigp>fromRoman(s)={
my(v=Vecsmall(s),key=vector(88),cur,t=0,tmp);
key[73]=1;key[86]=5;key[88]=10;key[76]=50;key[67]=100;key[68]=500;key[77]=1000;
cur=key[v[1]];
for(i=2,#v,
tmp=key[v[i]];
if(!cur, cur=tmp; next);
if(tmp>cur,
t+=tmp-cur;
cur=0
,
t+=cur;
cur=tmp
)
);
t+cur
};</lang>
Perl
<lang Perl>use 5.10.0;
{
my @trans = (
[M => 1000], [CM => 900],
[D => 500], [CD => 400],
[C => 100], [XC => 90],
[L => 50], [XL => 40],
[X => 10], [IX => 9],
[V => 5], [IV => 4],
[I => 1],
);
sub from_roman {
my $r = shift;
my $n = 0;
foreach my $pair (@trans) {
my ($k, $v) = @$pair;
$n += $v while $r =~ s/^$k//i;
}
return $n
}
}
say "$_: ", from_roman($_) for qw(MCMXC MDCLXVI MMVIII);</lang>
- Output:
MCMXC: 1990 MDCLXVI: 1666 MMVIII: 2008
Perl 6
A non-validating version: <lang perl6>sub rom-to-num($r) {
[+] gather $r.uc ~~ /
^
[
| M { take 1000 }
| CM { take 900 }
| D { take 500 }
| CD { take 400 }
| C { take 100 }
| XC { take 90 }
| L { take 50 }
| XL { take 40 }
| X { take 10 }
| IX { take 9 }
| V { take 5 }
| IV { take 4 }
| I { take 1 }
]+
$
/;
}
say "$_ => &rom-to-num($_)" for <MCMXC MDCLXVI MMVIII>;</lang>
- Output:
MCMXC => 1990 MDCLXVI => 1666 MMVIII => 2008
A validating version. Also handles older forms such as 'IIXX' and "IIII". <lang perl6>sub rom-to-num($r) {
[+] gather $r.uc ~~ /
^
( (C*)M { take 1000 - 100 * $0.chars } )*
( (C*)D { take 500 - 100 * $0.chars } )?
( (X*)C { take 100 - 10 * $0.chars } )*
( (X*)L { take 50 - 10 * $0.chars } )?
( (I*)X { take 10 - $0.chars } )*
( (I*)V { take 5 - $0.chars } )?
( I { take 1 } )*
[ $ || { return NaN } ]
/;
}
say "$_ => ", rom-to-num($_) for <MCMXC mdclxvi MMViii IIXX ILL>;</lang>
- Output:
MCMXC => 1990 mdclxvi => 1666 MMViii => 2008 IIXX => 18 ILL => NaN
PicoLisp
<lang PicoLisp>(de roman2decimal (Rom)
(let L (replace (chop Rom) 'M 1000 'D 500 'C 100 'L 50 'X 10 'V 5 'I 1)
(sum '((A B) (if (>= A B) A (- A))) L (cdr L)) ) )</lang>
Test:
: (roman2decimal "MCMXC") -> 1990 : (roman2decimal "MMVIII") -> 2008 : (roman2decimal "MDCLXVI") -> 1666
PHP
<lang PHP><?php /**
* @author Elad Yosifon <elad.yosifon@gmail.com> */
$roman_to_decimal = array( 'I' => 1, 'V' => 5, 'X' => 10, 'L' => 50, 'C' => 100, 'D' => 500, 'M' => 1000, );
/**
* @param $number * @return int */
function roman2decimal($number) { global $roman_to_decimal;
// breaks the string into an array of chars $digits = str_split($number); $lastIndex = count($digits)-1; $sum = 0;
foreach($digits as $index => $digit) { if(!isset($digits[$index])) { continue; }
if(isset($roman_to_decimal[$digit])) { if($index < $lastIndex) { $left = $roman_to_decimal[$digits[$index]]; $right = $roman_to_decimal[$digits[$index+1]]; if($left < $right) { $sum += ($right - $left); unset($digits[$index+1],$left, $right); continue; } unset($left, $right); } } $sum += $roman_to_decimal[$digit]; }
return $sum; }
/*============= OUTPUT =============*/ header('Content-Type: text/plain');
$tests = array( "I" => array(roman2decimal('I'), 1), "II" => array(roman2decimal('II'), 2), "III" => array(roman2decimal('III'), 3), "IV" => array(roman2decimal('IV'), 4), "V" => array(roman2decimal('V'), 5), "VI" => array(roman2decimal('VI'), 6), "VII" => array(roman2decimal('VII'), 7), "IX" => array(roman2decimal('IX'), 9), "X" => array(roman2decimal('X'), 10), "XI" => array(roman2decimal('XI'), 11), "XIV" => array(roman2decimal('XIV'), 14), "XV" => array(roman2decimal('XV'), 15), "XVI" => array(roman2decimal('XVI'), 16), "XVIV" => array(roman2decimal('XVIV'), 19), "XIX" => array(roman2decimal('XIX'), 19), "MDCLXVI" => array(roman2decimal('MDCLXVI'), 1666), "MCMXC" => array(roman2decimal('MCMXC'), 1990), "MMVIII" => array(roman2decimal('MMVIII'), 2008), "MMMCLIX" => array(roman2decimal('MMMCLIX'), 3159), "MCMLXXVII" => array(roman2decimal('MCMLXXVII'), 1977), );
foreach($tests as $key => $value)
{
echo "($key == {$value[0]}) => " . ($value[0] === $value[1] ? "true" : "false, should be {$value[1]}.") . "\n";
}</lang>
- Output:
(I == 1) => true (II == 2) => true (III == 3) => true (IV == 4) => true (V == 5) => true (VI == 6) => true (VII == 7) => true (IX == 9) => true (X == 10) => true (XI == 11) => true (XIV == 14) => true (XV == 15) => true (XVI == 16) => true (XVIV == 19) => true (XIX == 19) => true (MDCLXVI == 1666) => true (MCMXC == 1990) => true (MMVIII == 2008) => true (MMMCLIX == 3159) => true (MCMLXXVII == 1977) => true
PL/I
<lang PL/I> test_decode: procedure options (main); /* 28 January 2013 */
declare roman character (20) varying;
do roman = 'i', 'ii', 'iii', 'iv', 'v', 'vi', 'vii', 'viii', 'iix',
'ix', 'x', 'xi', 'xiv', 'MCMLXIV', 'MCMXC', 'MDCLXVI',
'MIM', 'MM', 'MMXIII';
put skip list (roman, decode(roman));
end;
decode: procedure (roman) returns (fixed(15));
declare roman character (*) varying; declare (current, previous) character (1); declare n fixed (15); declare i fixed binary;
previous = ; n = 0;
do i = length(roman) to 1 by -1;
current = substr(roman, i, 1);
if digit_value(current) < digit_value(previous) then
n = n - digit_value(current);
else if digit_value(current) > digit_value(previous) then
do;
n = n + digit_value(current);
previous = current;
end;
else
n = n + digit_value(current);
end;
return (n);
end decode;
digit_value: procedure (roman_char) returns (fixed);
declare roman_char character(1);
select (roman_char);
when ('M', 'm') return (1000);
when ('D', 'd') return (500);
when ('C', 'c') return (100);
when ('L', 'l') return (50);
when ('X', 'x') return (10);
when ('V', 'v') return (5);
when ('I', 'i') return (1);
otherwise return (0);
end;
end digit_value;
end test_decode; </lang>
i 1 ii 2 iii 3 iv 4 v 5 vi 6 vii 7 viii 8 iix 8 ix 9 x 10 xi 11 xiv 14 MCMLXIV 1964 MCMXC 1990 MDCLXVI 1666 MIM 1999 MM 2000 MMXIII 2013
PL/SQL
<lang PL/SQL> /*****************************************************************
* $Author: Atanas Kebedjiev $
*****************************************************************
* PL/SQL code can be run as anonymous block.
* To test, execute the whole script or create the functions and then e.g. 'select rdecode('2012') from dual;
* Please note that task definition does not describe fully some current rules, such as
* * subtraction - IX XC CM are the valid subtraction combinations
* * A subtraction character cannot be repeated: 8 is expressed as VIII and not as IIX
* * V L and D cannot be used for subtraction
* * Any numeral cannot be repeated more than 3 times: 1910 should be MCMX and not MDCCCCX
* Code below does not validate the Roman numeral itself and will return a result even for a non-compliant number
* E.g. both MCMXCIX and IMM will return 1999 but the first one is the correct notation
*/
DECLARE
FUNCTION rvalue(c IN CHAR) RETURN NUMBER IS
i INTEGER;
BEGIN
i := 0;
CASE (c)
when 'M' THEN i := 1000;
when 'D' THEN i := 500;
when 'C' THEN i := 100;
when 'L' THEN i := 50;
when 'X' THEN i := 10;
when 'V' THEN i := 5;
when 'I' THEN i := 1;
END CASE;
RETURN i;
END;
FUNCTION decode(rn IN VARCHAR2) RETURN NUMBER IS
i INTEGER; l INTEGER; cr CHAR; -- current Roman numeral as substring from r cv INTEGER; -- value of current Roman numeral
gr CHAR; -- next Roman numeral gv NUMBER; -- value of the next numeral;
dv NUMBER; -- decimal value to return
BEGIN
l := length(rn);
i := 1;
dv := 0;
while (i <= l)
LOOP
cr := substr(rn,i,1);
cv := rvalue(cr);
/* Look for a larger numeral in next position, like IV or CM
The number to subtract should be at least 1/10th of the bigger number
CM and XC are valid, but IC and XM are not */
IF (i < l) THEN
gr := substr(rn,i+1,1);
gv := rvalue(gr);
IF (cv < gv ) THEN
dv := dv - cv;
ELSE
dv := dv + cv;
END IF;
ELSE
dv := dv + cv;
END IF; -- need to add the last value unconditionally
i := i + 1;
END LOOP;
RETURN dv;
END;
BEGIN
DBMS_OUTPUT.PUT_LINE ('MMXII = ' || rdecode('MMXII')); -- 2012
DBMS_OUTPUT.PUT_LINE ('MCMLI = ' || rdecode('MCMLI')); -- 1951
DBMS_OUTPUT.PUT_LINE ('MCMLXXXVII = ' || rdecode('MCMLXXXVII')); -- 1987
DBMS_OUTPUT.PUT_LINE ('MDCLXVI = ' || rdecode('MDCLXVI')); -- 1666
DBMS_OUTPUT.PUT_LINE ('MCMXCIX = ' || rdecode('MCMXCIX')); -- 1999
END; </lang>
Prolog
<lang Prolog>decode_digit(i, 1). decode_digit(v, 5). decode_digit(x, 10). decode_digit(l, 50). decode_digit(c, 100). decode_digit(d, 500). decode_digit(m, 1000).
decode_string(Sum, _, [], Sum).
decode_string(LastSum, LastValue, [Digit|Rest], NextSum) :-
decode_digit(Digit, Value), Value < LastValue, Sum is LastSum - Value, decode_string(Sum, Value, Rest, NextSum).
decode_string(LastSum, LastValue, [Digit|Rest], NextSum) :-
decode_digit(Digit, Value), Value >= LastValue, Sum is LastSum + Value, decode_string(Sum, Value, Rest, NextSum).
decode_string(Atom, Value) :-
atom_chars(Atom, String), reverse(String, [Last|Rest]), decode_digit(Last, Start), decode_string(Start, Start, Rest, Value).
test :-
decode_string(mcmxc, 1990), decode_string(mmviii, 2008), decode_string(mdclxvi, 1666).</lang>
The program above contains its own test predicate. The respective goal succeeds. Therefore the test passes.
PureBasic
<lang PureBasic>Procedure romanDec(roman.s)
Protected i, n, lastval, arabic
For i = Len(roman) To 1 Step -1
Select UCase(Mid(roman, i, 1))
Case "M"
n = 1000
Case "D"
n = 500
Case "C"
n = 100
Case "L"
n = 50
Case "X"
n = 10
Case "V"
n = 5
Case "I"
n = 1
Default
n = 0
EndSelect
If (n < lastval)
arabic - n
Else
arabic + n
EndIf
lastval = n
Next
ProcedureReturn arabic
EndProcedure
If OpenConsole()
PrintN(Str(romanDec("MCMXCIX"))) ;1999
PrintN(Str(romanDec("MDCLXVI"))) ;1666
PrintN(Str(romanDec("XXV"))) ;25
PrintN(Str(romanDec("CMLIV"))) ;954
PrintN(Str(romanDec("MMXI"))) ;2011
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf</lang>
- Output:
1999 1666 25 954 2011
Python
<lang python>_rdecode = dict(zip('MDCLXVI', (1000, 500, 100, 50, 10, 5, 1)))
def decode( roman ):
result = 0
for r, r1 in zip(roman, roman[1:]):
rd, rd1 = _rdecode[r], _rdecode[r1]
result += -rd if rd < rd1 else rd
return result + _rdecode[roman[-1]]
if __name__ == '__main__':
for r in 'MCMXC MMVIII MDCLXVI'.split():
print( r, decode(r) )</lang>
- Output:
MCMXC 1990 MMVIII 2008 MDCLXVI 1666
Another version, which I believe has clearer logic: <lang python>roman_values = (('I',1), ('IV',4), ('V',5), ('IX',9),('X',10),('XL',40),('L',50),('XC',90),('C',100),
('CD', 400), ('D', 500), ('CM', 900), ('M',1000))
def roman_value(roman):
total=0
for symbol,value in reversed(roman_values):
while roman.startswith(symbol):
total += value
roman = roman[len(symbol):]
return total
if __name__=='__main__':
for value in "MCMXC", "MMVIII", "MDCLXVI":
print('%s = %i' % (value, roman_value(value)))
""" Output: MCMXC = 1990 MMVIII = 2008 MDCLXVI = 1666 """</lang>
Racket
<lang Racket>#lang racket (define (decode/roman number)
(define letter-values
(map cons '(#\M #\D #\C #\L #\X #\V #\I) '(1000 500 100 50 10 5 1)))
(define (get-value letter)
(cdr (assq letter letter-values)))
(define lst (map get-value (string->list number)))
(+ (last lst)
(for/fold ((sum 0))
((i (in-list lst)) (i+1 (in-list (cdr lst))))
(+ sum
(if (> i+1 i)
(- i)
i)))))
(map decode/roman '("MCMXC" "MMVIII" "MDCLXVI"))
- -> '(1990 2008 1666)</lang>
REXX
version 1
<lang REXX>/* Rexx */
Do
/* 1990 2008 1666 */ years = 'MCMXC MMVIII MDCLXVI'
Do y_ = 1 to words(years) Say right(word(years, y_), 10) || ':' decode(word(years, y_)) End y_
Return
End Exit
decode:
Procedure
Do
Parse upper arg roman . If verify(roman, 'MDCLXVI') = 0 then Do
/* always insert the value of the least significant numeral */
decnum = rchar(substr(roman, length(roman), 1))
Do d_ = 1 to length(roman) - 1
If rchar(substr(roman, d_, 1)) < rchar(substr(roman, d_ + 1, 1)) then Do
/* Handle cases where numerals are not in descending order */
/* subtract the value of the numeral */
decnum = decnum - rchar(substr(roman, d_, 1))
End
else Do
/* Normal case */
/* add the value of the numeral */
decnum = decnum + rchar(substr(roman, d_, 1))
End
End d_
End
else Do
decnum = roman 'contains invalid roman numerals'
End
Return decnum
End Exit
rchar:
Procedure
Do
Parse upper arg ch +1 .
select when ch = 'M' then digit = 1000 when ch = 'D' then digit = 500 when ch = 'C' then digit = 100 when ch = 'L' then digit = 50 when ch = 'X' then digit = 10 when ch = 'V' then digit = 5 when ch = 'I' then digit = 1 otherwise digit = 0 end
Return digit
End Exit</lang>
- Output:
MCMXC: 1990
MMVIII: 2008
MDCLXVI: 1666
version 2
This version of the (above) REXX program:
- removes 3 sets of superfluous DO-END statements
- removes dead code (3 REXX statements that can't be executed)
- replaced SUBSTR(xxx, length(xxx), 1) with RIGHT(xxx,1)
- removes a useless PARSE statement
- compresses 63 lines to 29 lines
- reordered IF statements by most likely to occur
<lang rexx>/*REXX program to convert Roman numeral number(s) to Arabic number(s). */ rYear = 'MCMXC' ; say right(rYear,9)':' rom2dec(rYear) rYear = 'mmviii' ; say right(rYear,9)':' rom2dec(rYear) rYear = 'MDCLXVI' ; say right(rYear,9)':' rom2dec(rYear) exit
rom2dec: procedure; arg roman . if verify(roman,'MDCLXVI')\==0 then do
say 'invalid Roman number:' roman
return '***error!***'
end
- =rChar(right(roman,1)) /*start with the last numeral*/
do j=1 for length(roman) - 1
x=rChar(substr(roman,j ,1)) /*the current Roman numeral. */
y=rChar(substr(roman,j+1,1)) /*the next Roman numeral. */
if x<y then # = #-x /* x<y ? Then subtract it.*/
else # = #+x /* x≥y ? Then add it. */
end /*j*/
return #
rChar: procedure; arg _ /*convert a Roman number to an Arabic dig*/ if _=='I' then return 1 if _=='V' then return 5 if _=='X' then return 10 if _=='L' then return 50 if _=='C' then return 100 if _=='D' then return 500 if _=='M' then return 1000
return 0 /*_ is an invalid Roman numeral (char). */</lang>
version 3
This REXX version allows the use of j which was being used in the later part of the Holy Roman Empire (as a trailing i in Roman numeral numbers).
Also, this program converts IIXX correctly. Note: this number was actually chiseled in Roman monuments, archways, and tombs/crypts.
Also supported are larger numbers such as (M) which is a Roman numeral(s) within a grouping symbol, in this case, a set of parenthesis.
Deep parentheses are also supported: (MM) is two million, ((MMM)) is three billion.
Normally, the Romans used an overbar (vinculum) for larger numbers (such as XX for twenty-thousand),
but the use of such a character is very problematic for computers to deal with, so parenthesis are used instead.
The Romans also had symbols for some fractions which would be a good addition to this task.
Also, lowercase u was also used for lowercase v
Also note that IIII is a legal Roman numeral construct; just check almost any old clock or "dialed" wristwatch that has Roman numerals.
<lang rexx>/*REXX program to convert Roman numerals ──► Arabic numerals (numbers).*/
numeric digits 1000 /*we can handle big nums.*/
y = 'MCMXC' ; say right(y,9)':' rom2dec(y)
y = 'mmviii' ; say right(y,9)':' rom2dec(y)
y = 'MDCLXVI' ; say right(y,9)':' rom2dec(y)
y = 'MDQLXVI' ; say right(y,9)':' rom2dec(y)
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────ROM2DEC subroutine──────────────────*/
rom2dec: procedure; h='0'x; #=0; $=1; arg n . /*uppercase N.*/
n=translate(n,'()()',"[]{}"); _ = verify(n,'MDCLXVUIJ()')
if _\==0 then return '***error!*** invalid Roman numeral:' substr(n,_,1)
@.=1; @.m=1000; @.d=500; @.c=100; @.l=50; @.x=10; @.u=5; @.v=5
do k=length(n) to 1 by -1; _=substr(n,k,1) /*examine a Roman numeral*/
/*(next) scale up or down*/
if _=='(' | _==')' then do; $=$*1000; if _=='(' then $=1; iterate; end
_=@._*$ /*scale it if necessary. */
if _>h then h=_ /*remember Roman numeral.*/
if _<h then #=#-_ /*char>next? Then sub. */
else #=#+_ /* else add. */
end /*k*/
return # /*return Arabic number. */</lang> output (input is within the REXX program):
MCMXC: 1990 mmviii: 2008 MDCLXVI: 1666 MDQLXVI: ***error!*** invalid Roman numeral: Q
Ruby
<lang ruby>def fromRoman(roman)
r = roman.dup.upcase
n = 0
until r.empty? do
case
when r.start_with?('M') then v = 1000; len = 1
when r.start_with?('CM') then v = 900; len = 2
when r.start_with?('D') then v = 500; len = 1
when r.start_with?('CD') then v = 400; len = 2
when r.start_with?('C') then v = 100; len = 1
when r.start_with?('XC') then v = 90; len = 2
when r.start_with?('L') then v = 50; len = 1
when r.start_with?('XL') then v = 40; len = 2
when r.start_with?('X') then v = 10; len = 1
when r.start_with?('IX') then v = 9; len = 2
when r.start_with?('V') then v = 5; len = 1
when r.start_with?('IV') then v = 4; len = 2
when r.start_with?('I') then v = 1; len = 1
else
raise ArgumentError.new("invalid roman numerals: " + roman)
end
n += v
r[0 .. len-1] = ""
end
n
end
[ "MCMXC", "MMVIII", "MDCLXVI" ].each {|r| pp [r, fromRoman(r)]}</lang>
- Output:
["MCMXC", 1990] ["MMVIII", 2008] ["MDCLXVI", 1666]
Run BASIC
<lang runbasic>print "MCMXCIX = "; romToDec( "MCMXCIX") '1999 print "MDCLXVI = "; romToDec( "MDCLXVI") '1666 print "XXV = "; romToDec( "XXV") '25 print "CMLIV = "; romToDec( "CMLIV") '954 print "MMXI = "; romToDec( "MMXI") '2011
function romToDec(roman$)
for i = len(roman$) to 1 step -1 x$ = mid$(roman$, i, 1) n = 0 if x$ = "M" then n = 1000 if x$ = "D" then n = 500 if x$ = "C" then n = 100 if x$ = "L" then n = 50 if x$ = "X" then n = 10 if x$ = "V" then n = 5 if x$ = "I" then n = 1 if n < preNum then num = num - n else num = num + n preNum = n next romToDec =num
end function</lang>
Scala
<lang Scala>def fromRoman( r:String ) : Int = {
val arabicNumerals = List("CM"->900,"M"->1000,"CD"->400,"D"->500,"XC"->90,"C"->100,
"XL"->40,"L"->50,"IX"->9,"X"->10,"IV"->4,"V"->5,"I"->1)
var s = r
arabicNumerals.foldLeft(0){ (n,t) => {
val l = s.length; s = s.replaceAll(t._1,""); val c = (l - s.length)/t._1.length // Get the frequency
n + (c*t._2) // Add the arabic numerals up
} }
}
// A small test
def test( roman:String ) = println( roman + " => " + fromRoman( roman ) )
test("MCMXC") test("MMVIII") test("MDCLXVI")</lang>
- Output:
MCMXC => 1990 MMVIII => 2008 MDCLXVI => 1666
Seed7
<lang seed7>$ include "seed7_05.s7i";
const func integer: ROMAN parse (in string: roman) is func
result
var integer: arabic is 0;
local
var integer: index is 0;
var integer: number is 0;
var integer: lastval is 0;
begin
for index range length(roman) downto 1 do
case roman[index] of
when {'M', 'm'}: number := 1000;
when {'D', 'd'}: number := 500;
when {'C', 'c'}: number := 100;
when {'L', 'l'}: number := 50;
when {'X', 'x'}: number := 10;
when {'V', 'v'}: number := 5;
when {'I', 'i'}: number := 1;
otherwise: raise RANGE_ERROR;
end case;
if number < lastval then
arabic -:= number;
else
arabic +:= number;
end if;
lastval := number;
end for;
end func;
const proc: main is func
begin writeln(ROMAN parse "MCMXC"); writeln(ROMAN parse "MMVIII"); writeln(ROMAN parse "MDCLXVI"); end func;</lang>
Original source: [1]
- Output:
1990 2008 1666
SNOBOL4
<lang SNOBOL4>* Roman to Arabic
define('arabic(n)s,ch,val,sum,x') :(arabic_end)
arabic s = 'M1000 D500 C100 L50 X10 V5 I1 '
n = reverse(n)
arab1 n len(1) . ch = :f(arab2)
s ch break(' ') . val
val = lt(val,x) (-1 * val)
sum = sum + val; x = val :(arab1)
arab2 arabic = sum :(return) arabic_end
- Test and display
tstr = 'MMX MCMXCIX MCDXCII MLXVI CDLXXVI "
tloop tstr break(' ') . r span(' ') = :f(out)
astr = astr r '=' arabic(r) ' ' :(tloop)
out output = astr end</lang>
- Output:
MMX=2010 MCMXCIX=1999 MCDXCII=1492 MLXVI=1066 CDLXXVI=476
Here's an alternative version, which is maybe more SNOBOL4-idiomatic and less like one might program it in a more common language: <lang SNOBOL4>* Roman to Arabic define("arabic1(romans,arabic1)rdigit,adigit,b4") romans1 = " 0 IX9 IV4 III3 II2 I1 VIII8 VII7 VI6 V5" :(arabic1_end) arabic1 ident(romans) :s(return) romans (break("IV") | rem) . b4 rem . rdigit = b4
romans1 " " rdigit any("0123456789") . adigit
arabic1 = adigit arabic1
romans = replace(romans,"MDCLX","CLXVI") :(arabic1)
arabic1_end
- Test and display
tstr = "MMX MCMXCIX MCDXCII MLXVI CDLXXVI "
tloop tstr break(' ') . r span(' ') = :f(out)
astr = astr r '=' arabic1(r) ' ' :(tloop)
out output = astr end</lang> The output is the same as in the earlier version.
The following version takes advantage of some of the so-called "SPITBOL extensions", which are to be found in most modern implementations. This allows removing several labels and explicit transfers of control, and moves some of the looping into the pattern matcher. Again, the output is the same. <lang SNOBOL4>* Roman to Arabic define("arabic1(romans,arabic1)rdigit,adigit,b4") romans1 = " 0 IX9 IV4 III3 II2 I1 VIII8 VII7 VI6 V5" :(arabic1_end) arabic1 ident(romans) :s(return) romans (break("IV") | rem) . b4 rem . rdigit = replace(b4,"MDCLX","CLXVI")
romans1 " " rdigit any("0123456789") . adigit
arabic1 = adigit arabic1 :(arabic1) arabic1_end
- Test and display
tstr = " MMX MCMXCIX MCDXCII MLXVI CDLXXVI "
tstr span(' ') break(' ') $ r *?(astr = astr r '=' arabic1(r) ' ') fail
output = astr
end</lang>
Tcl
As long as we assume that we have a valid roman number, this is most easily done by transforming the number into a sum and evaluating the expression: <lang tcl>proc fromRoman rnum {
set map {M 1000+ CM 900+ D 500+ CD 400+ C 100+ XC 90+ L 50+ XL 40+ X 10+ IX 9+ V 5+ IV 4+ I 1+}
expr [string map $map $rnum]0}
}</lang> Demonstrating: <lang tcl>foreach r {MCMXC MDCLXVI MMVIII} {
puts "$r\t-> [fromRoman $r]"
}</lang>
- Output:
MCMXC -> 1990 MDCLXVI -> 1666 MMVIII -> 2008
TI-83 BASIC
Using the Rom‣Dec function "real(21," from Omnicalc. <lang ti83b>PROGRAM:ROM2DEC
- Input Str1
- Disp real(21,Str1)</lang>
Using TI-83 BASIC <lang ti83b>PROGRAM:ROM2DEC
- Input "ROMAN:",Str1
- {1000,500,100,50,10,5,1}➞L1
- 0➞P
- 0➞Y
- For(I,length(Str1),1,-1)
:inString("MDCLXVI",sub(Str1,I,1))➞X
:If X≤0:Then
:Disp "BAD NUMBER"
:Stop
:End
:L1(x)➞N
:If N<P:Then
:Y–N➞Y
:Else
:Y+N➞Y
:End
:N➞P
- End
- Disp Y</lang>
TUSCRIPT
<lang tuscript>$$ MODE TUSCRIPT LOOP roman_number="MCMXC'MMVIII'MDCLXVI" arab_number=DECODE (roman_number,ROMAN) PRINT "Roman number ",roman_number," equals ", arab_number ENDLOOP</lang>
- Output:
Roman number MCMXC equals 1990 Roman number MMVIII equals 2008 Roman number MDCLXVI equals 1666
Vedit macro language
<lang vedit>// Main program for testing the function // do {
Get_Input(10, "Enter a roman numeral: ", NOCR+STATLINE)
Call("Roman_to_Arabic")
Reg_Type(10) Message(" = ") Num_Type(#1)
} while(#1) Return
// Convert Roman numeral into numeric value // in: @10 = Roman numeral // out: #1 = numeric value //
- Roman_to_Arabic:
Buf_Switch(Buf_Free)
Ins_Text("M1000 D500 C100 L50 X10 V5 I1") Ins_Newline
Reg_Ins(10) Ins_Char(' ')
#1 = #2 = 0
Repeat(ALL) {
#3 = #2 // #3 = previous character
Goto_Line(2) // roman numeral to be converted
if (At_EOL) {
Break // all done
}
Reg_Copy_Block(11, CP, CP+1, DELETE) // next character in roman numeral
if (Search(@11, BEGIN+ADVANCE+NOERR)) { // find character from the table
#2 = Num_Eval(SUPPRESS) // corresponding numeric value
if (#2 > #3) { // larger than previous digit?
#1 -= #3 // substract previous digit
} else {
#1 += #3 // add previous digit
}
}
}
Reg_Empty(11)
Buf_Quit(OK)
Return</lang>
- Output:
iv = 4 xii = 12 MDCLXVI = 1666 MCMXC = 1990 MMXI = 2011
XPL0
<lang XPL0>string 0; \use zero-terminated strings code CrLf=9, IntOut=11;
func Roman(Str); \Convert Roman numeral string to decimal value char Str; int I, Val, Val0, Sum; [I:= 0; Sum:= 0; Val0:= 5000; loop [case Str(I) of
^M: Val:= 1000;
^D: Val:= 500;
^C: Val:= 100;
^L: Val:= 50;
^X: Val:= 10;
^V: Val:= 5;
^I: Val:= 1
other return Sum; \zero string terminator
I:= I+1;
Sum:= Sum + Val;
if Val > Val0 then Sum:= Sum - 2*Val0;
Val0:= Val;
];
];
[IntOut(0, Roman("MCMXC")); CrLf(0);
IntOut(0, Roman("MMVIII")); CrLf(0);
IntOut(0, Roman("MDCLXVI")); CrLf(0);
]</lang>
Output:
1990 2008 1666
Zsh
<lang zsh>function parseroman () {
local max=0 sum i j
local -A conv
conv=(I 1 V 5 X 10 L 50 C 100 D 500 M 1000)
for j in ${(Oas::)1}; do
i=conv[$j]
if (( i >= max )); then
(( sum+=i ))
(( max=i ))
else
(( sum-=i ))
fi
done
echo $sum
}</lang>
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