Converting Roman Numerals to Decimal lying between 1 to 3999
Last Updated :
29 Feb, 2024
Given a Roman numeral, the task is to find its corresponding decimal value.
Example :
Input: IX
Output: 9
Explanation: IX is a Roman symbol which represents 9
Input: XL
Output: 40
Explanation: XL is a Roman symbol which represents 40
Input: MCMIV
Output: 1904
Explanation: M is a thousand, CM is nine hundred and IV is four
Roman numerals are based on the following symbols.
SYMBOL VALUE
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
Approach: A number in Roman Numerals is a string of these symbols written in descending order(e.g. M’s first, followed by D’s, etc.). However, in a few specific cases, to avoid four characters being repeated in succession(such as IIII or XXXX), subtractive notation is often used as follows:
- I placed before V or X indicates one less, so four is IV (one less than 5) and 9 is IX (one less than 10).
- X placed before L or C indicates ten less, so forty is XL (10 less than 50) and 90 is XC (ten less than a hundred).
- C placed before D or M indicates a hundred less, so four hundred is CD (a hundred less than five hundred) and nine hundred is CM (a hundred less than a thousand).
Algorithm to convert Roman Numerals to Integer Number:
- Split the Roman Numeral string into Roman Symbols (character).
- Convert each symbol of Roman Numerals into the value it represents.
- Take symbol one by one from starting from index 0:
- If current value of symbol is greater than or equal to the value of next symbol, then add this value to the running total.
- else subtract this value by adding the value of next symbol to the running total.
Following is the implementation of the above algorithm:
C++
#include <bits/stdc++.h>
using namespace std;
int value( char r)
{
if (r == 'I' )
return 1;
if (r == 'V' )
return 5;
if (r == 'X' )
return 10;
if (r == 'L' )
return 50;
if (r == 'C' )
return 100;
if (r == 'D' )
return 500;
if (r == 'M' )
return 1000;
return -1;
}
int romanToDecimal(string& str)
{
int res = 0;
for ( int i = 0; i < str.length(); i++) {
int s1 = value(str[i]);
if (i + 1 < str.length()) {
int s2 = value(str[i + 1]);
if (s1 >= s2) {
res = res + s1;
}
else {
res = res + s2 - s1;
i++;
}
}
else {
res = res + s1;
}
}
return res;
}
int main()
{
string str = "MCMIV" ;
cout << "Integer form of Roman Numeral is "
<< romanToDecimal(str) << endl;
return 0;
}
|
C
#include <stdio.h>
#include <string.h>
int value( char r)
{
if (r == 'I' )
return 1;
if (r == 'V' )
return 5;
if (r == 'X' )
return 10;
if (r == 'L' )
return 50;
if (r == 'C' )
return 100;
if (r == 'D' )
return 500;
if (r == 'M' )
return 1000;
return -1;
}
int romanToDecimal( char str[])
{
int res = 0;
for ( int i = 0; i < strlen (str); i++)
{
int s1 = value(str[i]);
if (i + 1 < strlen (str))
{
int s2 = value(str[i + 1]);
if (s1 >= s2)
{
res = res + s1;
}
else
{
res = res + s2 - s1;
i++;
}
}
else {
res = res + s1;
}
}
return res;
}
int main()
{
char str[10] = "MCMIV" ;
printf ( "Integer form of Roman Numeral is %d" ,romanToDecimal(str));
return 0;
}
|
Java
import java.util.*;
public class RomanToNumber {
int value( char r)
{
if (r == 'I' )
return 1 ;
if (r == 'V' )
return 5 ;
if (r == 'X' )
return 10 ;
if (r == 'L' )
return 50 ;
if (r == 'C' )
return 100 ;
if (r == 'D' )
return 500 ;
if (r == 'M' )
return 1000 ;
return - 1 ;
}
int romanToDecimal(String str)
{
int res = 0 ;
for ( int i = 0 ; i < str.length(); i++) {
int s1 = value(str.charAt(i));
if (i + 1 < str.length()) {
int s2 = value(str.charAt(i + 1 ));
if (s1 >= s2) {
res = res + s1;
}
else {
res = res + s2 - s1;
i++;
}
}
else {
res = res + s1;
}
}
return res;
}
public static void main(String args[])
{
RomanToNumber ob = new RomanToNumber();
String str = "MCMIV" ;
System.out.println( "Integer form of Roman Numeral"
+ " is "
+ ob.romanToDecimal(str));
}
}
|
Python
def value(r):
if (r = = 'I' ):
return 1
if (r = = 'V' ):
return 5
if (r = = 'X' ):
return 10
if (r = = 'L' ):
return 50
if (r = = 'C' ):
return 100
if (r = = 'D' ):
return 500
if (r = = 'M' ):
return 1000
return - 1
def romanToDecimal( str ):
res = 0
i = 0
while (i < len ( str )):
s1 = value( str [i])
if (i + 1 < len ( str )):
s2 = value( str [i + 1 ])
if (s1 > = s2):
res = res + s1
i = i + 1
else :
res = res + s2 - s1
i = i + 2
else :
res = res + s1
i = i + 1
return res
print ( "Integer form of Roman Numeral is" ),
print (romanToDecimal( "MCMIV" ))
|
C#
using System;
class GFG {
public virtual int value( char r)
{
if (r == 'I' )
return 1;
if (r == 'V' )
return 5;
if (r == 'X' )
return 10;
if (r == 'L' )
return 50;
if (r == 'C' )
return 100;
if (r == 'D' )
return 500;
if (r == 'M' )
return 1000;
return -1;
}
public virtual int romanToDecimal( string str)
{
int res = 0;
for ( int i = 0; i < str.Length; i++) {
int s1 = value(str[i]);
if (i + 1 < str.Length) {
int s2 = value(str[i + 1]);
if (s1 >= s2) {
res = res + s1;
}
else {
res = res + s2 - s1;
i++;
}
}
else {
res = res + s1;
i++;
}
}
return res;
}
public static void Main( string [] args)
{
GFG ob = new GFG();
string str = "MCMIV" ;
Console.WriteLine( "Integer form of Roman Numeral"
+ " is "
+ ob.romanToDecimal(str));
}
}
|
Javascript
<script>
function value(r) {
if (r == 'I' )
return 1;
if (r == 'V' )
return 5;
if (r == 'X' )
return 10;
if (r == 'L' )
return 50;
if (r == 'C' )
return 100;
if (r == 'D' )
return 500;
if (r == 'M' )
return 1000;
return -1;
}
function romanToDecimal( str)
{
var res = 0;
for (i = 0; i < str.length; i++)
{
var s1 = value(str.charAt(i));
if (i + 1 < str.length) {
var s2 = value(str.charAt(i + 1));
if (s1 >= s2) {
res = res + s1;
}
else
{
res = res + s2 - s1;
i++;
}
} else {
res = res + s1;
}
}
return res;
}
var str = "MCMIV" ;
document.write( "Integer form of Roman Numeral"
+ " is " + romanToDecimal(str));
</script>
|
PHP
<?php
function value( $r )
{
if ( $r == 'I' )
return 1;
if ( $r == 'V' )
return 5;
if ( $r == 'X' )
return 10;
if ( $r == 'L' )
return 50;
if ( $r == 'C' )
return 100;
if ( $r == 'D' )
return 500;
if ( $r == 'M' )
return 1000;
return -1;
}
function romanToDecimal(& $str )
{
$res = 0;
for ( $i = 0; $i < strlen ( $str ); $i ++)
{
$s1 = value( $str [ $i ]);
if ( $i +1 < strlen ( $str ))
{
$s2 = value( $str [ $i + 1]);
if ( $s1 >= $s2 )
{
$res = $res + $s1 ;
}
else
{
$res = $res + $s2 - $s1 ;
$i ++;
}
}
else
{
$res = $res + $s1 ;
$i ++;
}
}
return $res ;
}
$str = "MCMIV" ;
echo "Integer form of Roman Numeral is " ,
romanToDecimal( $str ), "\n" ;
?>
|
Output
Integer form of Roman Numeral is 1904
Complexity Analysis:
- Time Complexity: O(n), where n is the length of the string.
Only one traversal of the string is required.
- Auxiliary Space: O(1), As no extra space is required.
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