Integer to Roman Number

Contents

ProblemExamplesSolutionAlgorithmCodeTimeSpace

Problem Statement❯

Given a positive integer num, your task is to convert it into a Roman numeral as per the classical Roman numeral system.

  • Roman numerals use combinations of letters from the Latin alphabet: I, V, X, L, C, D, and M.
  • There are specific rules for combining symbols to represent numbers, including using subtraction (e.g., IV for 4, IX for 9).

Note: The input number will be a positive integer between 1 and 3999 (inclusive). If the input is outside this range or invalid (like 0 or negative), return an appropriate message or handle it gracefully.

Examples❯

Input Output Description
1 I Smallest valid Roman numeral
4 IV Special case using subtraction rule
9 IX Another subtraction case
58 LVIII L = 50, V = 5, III = 3 → 50 + 5 + 3
1994 MCMXCIV M = 1000, CM = 900, XC = 90, IV = 4
3999 MMMCMXCIX Largest number representable in standard Roman numerals
0 Invalid input Roman numerals start from 1, so 0 is not valid
-5 Invalid input Negative numbers can't be converted

Solution❯

Roman numerals are based on combining letters that represent certain values. The key symbols are: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000.

To convert an integer into Roman numerals, we need to break it down from the highest possible value and work our way down. For example, for the number 58:

  • The highest Roman symbol less than 58 is L = 50
  • Next is V = 5
  • Then III = 3 gives us the remaining 3
  • So, 58 becomes LVIII

Some numbers need subtraction to avoid four repetitions of the same symbol. For instance:

  • 4 is not IIII, but IV (5 - 1)
  • 9 is IX, 40 is XL, 90 is XC, and so on

So, to build the Roman numeral:

  1. We create a list of integer values and their matching Roman symbols, arranged from largest to smallest
  2. We loop through these values, and at each step, we subtract as many times as the value fits into the number
  3. For each subtraction, we append the corresponding Roman symbol to the result

This continues until the number becomes 0. For example:

1994 is broken into: M (1000) + CM (900) + XC (90) + IV (4) → MCMXCIV

What if the input is invalid?

If the input is 0, negative, or not a number (like an empty string or null), it cannot be converted to a Roman numeral because Roman numerals only support positive integers from 1 to 3999. In such cases, return a clear message like "Invalid input".

This approach is simple, efficient, and gives the correct result for any input within the valid range.

Algorithm Steps❯

  1. Create two arrays: one for the integer values and one for corresponding Roman symbols, both sorted in descending order.
  2. Initialize an empty string to hold the result.
  3. Loop over the integer values array:
  4. → While the input number is greater than or equal to the current integer value:
  5. → Subtract that value and append the corresponding Roman symbol to the result.
  6. Repeat until the number becomes 0.
  7. Return the result string.

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
def int_to_roman(num):
    val = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
    syms = ["M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"]
    roman = ""
    for i in range(len(val)):
        while num >= val[i]:
            roman += syms[i]  # Append the matching symbol
            num -= val[i]     # Subtract the value
    return roman

# Example
print(int_to_roman(1994))  # Output: MCMXCIV

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)The number of iterations is limited to a small fixed set of Roman numeral values (13 in total).
Average CaseO(1)Regardless of the input size, the logic loops through at most 13 Roman symbols.
Worst CaseO(1)Even for the maximum input (3999), the loop runs a constant number of times.

Space Complexity

O(1)

Explanation: Only a few variables and fixed arrays are used. No additional memory scales with input.