How to Convert Integer to Roman

In this problem, we are given an integer, and our task is to give a string representing the integer in the Roman Number system. Let us see some examples to understand the problem.

Input: 10

Output: X

Input: 4

Output: IV

Input: 60

Output: LX

Input: 1903

Output: MCMIII

Here is a list of standard Roman numerals and their conversion to an integer system.

Approach - 1

We will convert the integer to Roman numbers by extracting the digits of places. We will convert the digits into units, tens, hundreds, and thousands of places as we have standard Roman symbols for these places. Then, we will check further if the digit follows the addition or subtraction rule. For example, the digits 3, 8, 13, etc., follow the addition rule, while the digits 4, 9, and 14 follow the subtraction rule.

Let us see the algorithm of this approach.

To extract the number of places from the integer, we will compare the given integer with the standard Roman symbol values. Firstly, we will compare it with 1000, then 900, then 500, then 400, 100, 90, 50, 40, 10, 9, 5, 4, 1. In these numbers, we have included integers like 900, 400, 90, 40, 9, and 4 because these are the standard numbers to follow the subtraction rule. It will be easy to check the place value separately for these integer values, too. Let us understand the algorithm with an example.

Let us take the example of integer 1903.

Integer = 1903

Roman = ""

• Firstly, we will compare the integer with the base value 1000. Since 1903 > 1000, we will proceed as follows:
  • Divide the number with the base value, i.e., 1903 / 1000.
  • Store the remainder and quotient. Remainder = 903, Quotient = 1
  • The Roman symbol will be the representation of the base value times the quotient, which will be M.
  • Hence, Roman = "M".
  • Integer = Remainder = 903.
• In the next iteration, we will again compare the integer with the base values. This time, the base value that is smaller and closest to the integer is 900 since 903 > 900.
  • Divide the number with the base value, i.e., 903 / 900.
  • Store the remainder and quotient. Remainder = 3, Quotient = 1
  • The Roman symbol will be the representation of the base value times the quotient, which will be CM.
  • Hence, Roman = "MCM".
  • Integer = Remainder = 3.
• In this iteration, we will again compare, and this time, the appropriate base value is 1 since 3 > 1.
  • Divide the number with the base value, i.e., 3 / 1.
  • Store the remainder and quotient. Remainder = 0, Quotient = 3
  • The Roman symbol will be the representation of the base value times the quotient, which will be I * 3 = III.
  • Hence, Roman = "MCMIII".
  • Integer = Remainder = 0.
• Since the integer is 0, we have successfully converted it to its Roman representation.

Hence, the Roman representation of the integer 1903 is MCMIII.

Below is the implementation of the above-mentioned approach in Python.

Code

Output:

The roman representation of 1903 is: MCMIII

Approach - 2

In this approach, we will extract the main significant digit of the given number. The main significant digits are the digits that are placed in the highest place value of the number. For example, in the number 350, the main significant digit is 3, and in the number 45, the main significant digit is 4. We will maintain an iterator to update the divisor according to the current number so that when we divide the number by the divisor, we get the main significant digit. This time, we are adding two more Roman symbols representing the numbers 5000 and 10000. These numbers are represented by G and H, respectively.

Here is the implementation of the above-mentioned approach in Python.

Code

Output:

The Roman value for the integer is: MCMIII

Approach - 3

In this approach, we will use the built-in function to convert the integer to the Roman number. This built-in function is available in the module called Roman. We first need to install this module, and then we can use the function toRoman() to convert the integer to its Roman representation.

To install the package, we will use the pip command. The command is:

We just need to pass the integer value to the function, and it will return the Roman equivalent of the integer passed as an argument to the function.

Code

Output:

The Roman value for the integer is: MCMIII