Converting Roman Numerals to Decimal lying between 1 to 3999

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++

// 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 {
                // Value of current symbol is
                // less than the next symbol
                res = res + s2 - s1;
                i++;
            }
        }
        else {
            res = res + s1;
        }
    }
    return res;
}

// Driver Code
int main()
{
    // Considering inputs given are valid
    string str = "MCMIV";
    cout << "Integer form of Roman Numeral is "
         << romanToDecimal(str) << endl;

    return 0;
}

C

// Program to convert Roman
// Numerals to Numbers
#include <stdio.h>
#include <string.h>

// 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(char str[])
{
    // Initialize result
    int res = 0;

    // Traverse given input
    for (int i = 0; i < strlen(str); i++)
    {
        // Getting value of symbol s[i]
        int s1 = value(str[i]);

        if (i + 1 < strlen(str))
        {
            // 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
            {
                // Value of current symbol is
                // less than the next symbol
                res = res + s2 - s1;
                i++;
            }
        }
        else {
            res = res + s1;
        }
    }
    return res;
}

// Driver Code
int main()
{
    // Considering inputs given are valid
    char str[10] = "MCMIV";
    printf("Integer form of Roman Numeral is %d",romanToDecimal(str));


    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 roman 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 {
                    // Value of current symbol is
                    // less than the next symbol
                    res = res + s2 - s1;
                    i++;
                }
            }
            else {
                res = res + s1;
            }
        }

        return res;
    }

    // Driver Code
    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 roman 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

Javascript

<script>
// Program to convert Roman
// Numerals to Numberspublic
    // 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;
    }

    // Finds decimal value of a
    // given roman numeral
    function romanToDecimal( str)
    {

        // Initialize result
        var res = 0;

        for (i = 0; i < str.length; i++)
        {

            // Getting value of symbol s[i]
            var s1 = value(str.charAt(i));

            // Getting value of symbol s[i+1]
            if (i + 1 < str.length) {
                var 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
                {

                    // Value of current symbol is
                    // less than the next symbol
                    res = res + s2 - s1;
                    i++;
                }
            } else {
                res = res + s1;
            }
        }

        return res;
    }

    // Driver Code

        // Considering inputs given are valid
        var str = "MCMIV";
        document.write("Integer form of Roman Numeral"
        + " is " + romanToDecimal(str));

// This code is contributed by umadevi9616
</script>

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

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.