C++ Program For Converting Roman Numerals To Decimal Lying Between 1 to 3999

Given a Romal numeral, the task is to find its corresponding decimal value.

Example :

Input: IX
Output: 9
IX is a Roman symbol which represents 9 

Input: XL
Output: 40
XL is a Roman symbol which represents 40

Input: MCMIV
Output: 1904
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:

1. Split the Roman Numeral string into Roman Symbols (character).
2. Convert each symbol of Roman Numerals into the value it represents.
3. Take symbol one by one from starting from index 0: 
   1. If current value of symbol is greater than or equal to the value of next symbol, then add this value to the running total.
   2. else subtract this value by adding the value of next symbol to the running total.

Following is the implementation of the above algorithm: 

C++

// 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;
}

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.
• Space Complexity: O(1). 
  As no extra space is required.

Another solution –

C++

// C++ Program to convert Roman
// Numerals to Numbers
#include <bits/stdc++.h>
using namespace std;

// This function returns value
// of a Roman symbol
int romanToDecimal(string& str)
{
    map<char, int> m;
    m.insert({ 'I', 1 });
    m.insert({ 'V', 5 });
    m.insert({ 'X', 10 });
    m.insert({ 'L', 50 });
    m.insert({ 'C', 100 });
    m.insert({ 'D', 500 });
    m.insert({ 'M', 1000 });
    int sum = 0;
    for (int i = 0; i < str.length(); i++)
    {
        /* If present value is less than next value,
           subtract present from next value and add
           the resultant to the sum variable.*/
        if (m[str[i]] < m[str[i + 1]])
        {
            sum+=m[str[i+1]]-m[str[i]];
            i++;
            continue;
        }
        sum += m[str[i]];
    }
    return sum;
}

// Driver Code
int main()
{
    // Considering inputs given are valid
    string str = "MCMIV";
    cout << "Integer form of Roman Numeral is " <<
             romanToDecimal(str) << endl;
    return 0;
}

Output:

Integer form of Roman Numeral is 1904

Time complexity – O(N)
Auxiliary Space – O(1)

Please refer complete article on Converting Roman Numerals to Decimal lying between 1 to 3999 for more details!