← Back to blog
#python#algorithms#math

Python: Arabic number to Roman numerals

Convert a number from 1 to 3999 into Roman notation — digit by digit, with subtractive rules for 4 and 9.

The problem

Write a function that takes an integer between 1 and 3999 and returns its Roman numeral representation.

Each Arabic digit is converted separately — left to right, skipping zeros. No more than 3 identical symbols in a row.

Examples:

  • 1 → "I"
  • 1000 → "M"
  • 1666 → "MDCLXVI"
  • 1990 → "MCMXC"
  • 2008 → "MMVIII"

Approach

Split the number into digits and process them from ones upward (i.e. from the end of the string). Each position (ones, tens, hundreds, thousands) has its own symbols: I/V/X, X/L/C, C/D/M, M.

The helper get_roman_numeral handles values 0–9 for a given position:

Digit Result
0 empty string
1–3 repeat lower symbol
4 subtractive: IV, XL, CD
5–8 higher symbol + remainder of lower
9 subtractive: IX, XC, CM

We use match/case (Python 3.10+).

Solution

def get_roman_numeral(number: int, lower: str, higher: str, next_symbol: str) -> str:
    match number:
        case 0:
            return ""
        case 1 | 2 | 3:
            return lower * number
        case 4:
            return lower + higher
        case 5 | 6 | 7 | 8:
            return higher + lower * (number - 5)
        case 9:
            return lower + next_symbol
 
 
def romanNumeralsEncoder(number: int) -> str:
    result = []
    list_array = [int(x) for x in str(number)]
 
    for index, item in enumerate(reversed(list_array)):
        if index == 0:
            result.append(get_roman_numeral(item, "I", "V", "X"))
        elif index == 1:
            result.append(get_roman_numeral(item, "X", "L", "C"))
        elif index == 2:
            result.append(get_roman_numeral(item, "C", "D", "M"))
        elif index == 3:
            result.append(get_roman_numeral(item, "M", None, None))
 
    return "".join(reversed(result))

Examples

Input Output
1 I
1000 M
1666 MDCLXVI
1990 MCMXC
2008 MMVIII 
print(romanNumeralsEncoder(1))     # I
print(romanNumeralsEncoder(1666))  # MDCLXVI
print(romanNumeralsEncoder(1990))  # MCMXC
print(romanNumeralsEncoder(2008))  # MMVIII

Summary

Digit by digit, separate logic for 4 and 9 — match/case keeps the code readable without long if chains.