Java Program for Converting Roman Numerals to Decimal Lying Between 1 to 3999

The characters used in an arrangement of number notation based on the pre-Roman Roman system is called Roman numerals. The letters M, D, C, L, X, V, and I stand for 1000, 500, 1000, 50, 10, 5, and 1, respectively, and will discuss all main symbols in the below section. In this problem, we are given a string of Roman numerals and our task is to convert Roman numerals to decimals in the range of 1 to 3999.

Let’s see examples with explanations below to understand the problem in a better way.

Input 1

str = "MCMIX"

Output 1

1909

Explanation

M is the Roman representation of 1000,

CM is the Roman representation of 900,

IX is the Roman representation of 9.

Input 2

str = "IV"

Output

2

Explanation

IV is the Roman representation of 4.

Input 3

str = "VI"

Output 3

6

SYMBOL	VALUE
I	1
IV	4
IX	9
V	5
X	10
XL	40
XC	90
L	50
C	100
CD	400
CM	900
D	500
M	1000

Approach

We have seen the example above for the given Roman numeral string, let us move to the approach.

As per the observation, the Roman numeral's symbol follows the descending order to represent the numbers (e.g. C's come first, the X's, etc.). However, it also follows subtractive notation in certain situations to prevent 4 characters from continuously repeated in a row(for example CCCC or IIII):

• I comes before V or X to indicate one less.

  Example: 4 = IV (1 less than five),

  9 = IX ( 1 less than ten)

• X comes before L or C to indicate ten less.

  Example: 40 = XL (ten less than fifty),

  90 = XC (10 less than 100)

• C comes before D and M to indicate 100 less

  Example: 400 = CD (hundred less than five hundred)

  900 = CM (hundred less than thousand)

Let's see the code below for a better understanding of the above approach.

Example

Below is a Java Program to convert Roman Numerals to Decimal Lying Between 1 to 3999.

import java.util.*;

// Create a class for initializing the function to return the Roman symbol's value.
public class Solution{
   // This function is created to return a Roman symbol's value.
   int romanValue(char ch)    {
      if(ch=='I')
         return 1;
      else if(ch=='V')
         return 5;
      else if(ch=='X')
         return 10;
      else if(ch=='L')
         return 50;
      else if(ch=='C')
         return 100;
      else if(ch=='D')
         return 500;
      else if(ch=='M')
         return 1000;
      return -1;
   } 
   
   // This function is created for the conversion of Roman numerals to decimal numerals
   int convertRomanToDecimal(String str) {
      // Initialize decimal value 
      int decVal = 0;
      int n = str.length(); // Getting the size of the string
      for (int i = 0; i < n; i++) {
         // check if i+1 charchter exist and getting value of roman symbol str[i] and str[i+1]
         if (i + 1 < n && romanValue(str.charAt(i)) < romanValue(str.charAt(i + 1)))  {
            //subtract the current value from the next value and add the decVal variable
            decVal = decVal + romanValue(str.charAt(i + 1)) - romanValue(str.charAt(i));
            i++; // Increment the index of the string to point to the next char
         }
         // If i+1 char not exist
         else {
            decVal = decVal + romanValue(str.charAt(i)); // add the first char value
         }
      } 
      return decVal; // Return decimal value
   } 
   public static void main(String args[]) {
      Solution ob = new Solution(); 
      String str = "MCMIX"; // Given string
      System.out.println("Roman Numeral: " + str);
      // Print the decimal form and call the function of conversion
      System.out.println("The decimal Numeral form of the Roman Numeral" + " is " + ob.convertRomanToDecimal(str));
   }
}

Output

Roman Numeral: MCMIX
The decimal Numeral form of the Roman Numeral is 1909

Time and Space Complexity

The time complexity of the above code is O(N), as only one traverse of the string is required. Where N is the size of the given Roman numeral string. As no extra space is used the space complexity of the above code is O(1).

Another Solution using Hashmap

Example

import java.util.Map;
import java.util.HashMap;
public class Solution {
   public static final Map<Character,
      Integer> romanValue = new HashMap<Character,
   Integer>() {
      {
         put ( 'M', 1000 );
         put ( 'D', 500 );
         put ( 'C', 100 );
         put ( 'L', 50 );
         put ( 'X', 10 );
         put ( 'V', 5 );
         put ( 'I', 1 );
      }
   };
   // Function is created for conversion of the Roman numeral to decimal numeral
   private static int convertRomanToDecimal(String str) {
      // Initialize decimal value
      int decVal = 0;
      for (int i = 0; i < str.length(); i++) {
         // store numeric value of roman symbol str[i]
         int first = romanValue.get(str.charAt(i));
         // check if i+1 charchter exist or not
         if (i + 1 < str.length()) {
            // store numeric value of roman symbol str[i+1]
            int second = romanValue.get(str.charAt(i + 1));
            // check which value is greater first or second
            if (first <= second) {
               // if first value <= second add first value to variable decVal
               decVal = decVal + first;
            } else  {
               // Value of first char is less than to the the second char
               decVal = decVal + second - first;
               i++; // Increment the index of string to point to next char
            }
         }
         // If i+1 char not exist
         else {
            decVal = decVal + first; // add the first char value
         }
      }
      return decVal; // Return decimal value
   }
   public static void main(String args[]) {
      String str = "MMMIX"; // Given string
      System.out.println("Roman Numeral: " + str);
      // print the decimal form and call function of conversion
      System.out.println("Decimal Numeral form of Roman Numeral" +
         " is " + convertRomanToDecimal(str));
    }
}

Output

Roman Numeral: MMMIX
Decimal Numeral form of Roman Numeral is 3009

Conclusion

In this tutorial, we have implemented a Java program for Converting Roman Numerals to Decimal Lying Between 1 to 3999. We have implemented an approach with two solutions. First with normal function and second with hashmap function.