Converting Roman Numerals to Decimal lying between 1 to 3999

Given a Romal numeral, find its corresponding decimal value.

Example :

Input : IX
Output : 9

Input : XL
Output : 40

Input : MCMIV
Output :  1904
M is a thousand, CM is nine hundred 
and IV is four

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

Roman numerals are based on below 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

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++

// Program to convert Roman Numerals to Numbers 
#include<bits/stdc++.h> 
using namespace std; 
  
// This function returns value of a Roman symbol 
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; 
} 
  
// Returns decimal value of roman numaral 
int romanToDecimal(string &str) 
{ 
    // Initialize result 
    int res = 0; 
  
    // Traverse given input 
    for (int i=0; i<str.length(); i++) 
    { 
        // Getting value of symbol s[i] 
        int s1 = value(str[i]); 
  
        if (i+1 < str.length()) 
        { 
            // Getting value of symbol s[i+1] 
            int s2 = value(str[i+1]); 
  
            // Comparing both values 
            if (s1 >= s2) 
            { 
                // Value of current symbol is greater 
                // or equal to the next symbol 
                res = res + s1; 
            } 
            else
            { 
                res = res + s2 - s1; 
                i++; // Value of current symbol is 
                     // less than the next symbol 
            } 
        } 
        else
        { 
            res = res + s1; 
            i++; 
        } 
    } 
    return res; 
} 
  
// Driver Program 
int main() 
{ 
    // Considering inputs given are valid 
    string str ="MCMIV"; 
    cout << "Integer form of Roman Numeral is "
         << romanToDecimal(str) << endl; 
  
    return 0; 
} 

Java

// Program to convert Roman Numerals to Numbers 
import java.util.*; 
  
public class RomanToNumber 
{ 
    // This function returns value of a Roman symbol 
    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; 
    } 
  
    // Finds decimal value of a given romal numeral 
    int romanToDecimal(String str) 
    { 
        // Initialize result 
        int res = 0; 
  
        for (int i=0; i<str.length(); i++) 
        { 
            // Getting value of symbol s[i] 
            int s1 = value(str.charAt(i)); 
  
            // Getting value of symbol s[i+1] 
            if (i+1 <str.length()) 
            { 
                int s2 = value(str.charAt(i+1)); 
  
                // Comparing both values 
                if (s1 >= s2) 
                { 
                    // Value of current symbol is greater 
                    // or equalto the next symbol 
                    res = res + s1; 
                } 
                else
                { 
                    res = res + s2 - s1; 
                    i++; // Value of current symbol is 
                    // less than the next symbol 
                } 
            } 
            else
            { 
                res = res + s1; 
                i++; 
            } 
        } 
  
        return res; 
    } 
  
    // Driver method 
    public static void main(String args[]) 
    { 
        RomanToNumber ob = new RomanToNumber(); 
  
        // Considering inputs given are valid 
        String str = "MCMIV"; 
        System.out.println("Integer form of Roman Numeral" + 
                           " is " + ob.romanToDecimal(str)); 
    } 
} 

Python

# Python program to convert Roman Numerals 
# to Numbers 
  
# This function returns value of each Roman symbol 
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)): 
  
        # Getting value of symbol s[i] 
        s1 = value(str[i]) 
  
        if (i+1 < len(str)): 
  
            # Getting value of symbol s[i+1] 
            s2 = value(str[i+1]) 
  
            # Comparing both values 
            if (s1 >= s2): 
  
                # Value of current symbol is greater 
                # or equal to the next symbol 
                res = res + s1 
                i = i + 1
            else: 
  
                # Value of current symbol is greater 
                # or equal to the next symbol 
                res = res + s2 - s1 
                i = i + 2
        else: 
            res = res + s1 
            i = i + 1
  
    return res 
  
# Driver code 
print("Integer form of Roman Numeral is"), 
print(romanToDecimal("MCMIV"))  

C#

// C# Program to convert Roman 
// Numerals to Numbers  
using System; 
  
class GFG 
{ 
// This function returns value  
// of a Roman symbol  
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; 
} 
  
// Finds decimal value of a  
// given romal numeral  
public virtual int romanToDecimal(string str) 
{ 
    // Initialize result  
    int res = 0; 
  
    for (int i = 0; i < str.Length; i++) 
    { 
        // Getting value of symbol s[i]  
        int s1 = value(str[i]); 
  
        // Getting value of symbol s[i+1]  
        if (i + 1 < str.Length) 
        { 
            int s2 = value(str[i + 1]); 
  
            // Comparing both values  
            if (s1 >= s2) 
            { 
                // Value of current symbol is greater  
                // or equalto the next symbol  
                res = res + s1; 
            } 
            else
            { 
                res = res + s2 - s1; 
                i++; // Value of current symbol is 
                     // less than the next symbol  
            } 
        } 
        else
        { 
            res = res + s1; 
            i++; 
        } 
    } 
  
    return res; 
} 
  
// Driver Code  
public static void Main(string[] args) 
{ 
    GFG ob = new GFG(); 
  
    // Considering inputs given are valid  
    string str = "MCMIV"; 
    Console.WriteLine("Integer form of Roman Numeral" +  
                      " is " + ob.romanToDecimal(str)); 
} 
} 
  
// This code is contributed by Shrikant13 

PHP

<?php 
// Program to convert Roman 
// Numerals to Numbers 
  
// This function returns  
// value of a Roman symbol 
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; 
} 
  
// Returns decimal value 
// of roman numeral 
function romanToDecimal(&$str) 
{ 
    // Initialize result 
    $res = 0; 
  
    // Traverse given input 
    for ($i = 0; $i < strlen($str); $i++) 
    { 
        // Getting value of 
        // symbol s[i] 
        $s1 = value($str[$i]); 
  
        if ($i+1 < strlen($str)) 
        { 
            // Getting value of 
            // symbol s[i+1] 
            $s2 = value($str[$i + 1]); 
  
            // Comparing both values 
            if ($s1 >= $s2) 
            { 
                // Value of current symbol  
                // is greater or equal to  
                // the next symbol 
                $res = $res + $s1; 
            } 
            else
            { 
                $res = $res + $s2 - $s1; 
                $i++; // Value of current symbol is 
                      // less than the next symbol 
            } 
        } 
        else
        { 
            $res = $res + $s1; 
            $i++; 
        } 
    } 
    return $res; 
} 
  
// Driver Code 
  
// Considering inputs 
// given are valid 
$str ="MCMIV"; 
echo "Integer form of Roman Numeral is ", 
              romanToDecimal($str), "\n"; 
  
// This code is contributed by ajit 
?> 

Output :

Integer form of Roman Numeral is 1904

References: https://en.wikipedia.org/wiki/Roman_numerals

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