Convert a number to Roman numerals in C#

Converting a number to Roman numerals in C# is a common programming problem that involves mapping integer values to their corresponding Roman numeral representations. Roman numerals use specific symbols like I, V, X, L, C, D, and M to represent numbers.

Roman Numeral System

Roman numerals follow specific rules where certain combinations represent subtraction (like IV for 4, IX for 9). The key is to use a mapping of values in descending order, including these special cases

Using an Iterative Approach

This approach uses a predefined dictionary to map Roman numerals to their integer values in descending order. We iteratively subtract the largest possible value from the given number while appending the corresponding Roman numeral

Example

using System;
using System.Collections.Generic;

class Program {
    static string ConvertToRomanIterative(int number) {
        // Define Roman numeral mappings in descending order
        Dictionary<int, string> romanMap = new Dictionary<int, string> {
            {1000, "M"}, {900, "CM"}, {500, "D"}, {400, "CD"},
            {100, "C"}, {90, "XC"}, {50, "L"}, {40, "XL"},
            {10, "X"}, {9, "IX"}, {5, "V"}, {4, "IV"}, {1, "I"}
        };

        string result = "";

        foreach(var item in romanMap) {
            while (number >= item.Key) {
                result += item.Value; // Append Roman numeral
                number -= item.Key;   // Reduce the number
            }
        }
        return result;
    }

    static void Main() {
        int number = 1994;
        string romanNumeral = ConvertToRomanIterative(number);
        Console.WriteLine($"The Roman numeral for {number} is: {romanNumeral}");
        
        // Test with another example
        number = 58;
        romanNumeral = ConvertToRomanIterative(number);
        Console.WriteLine($"The Roman numeral for {number} is: {romanNumeral}");
    }
}

The output of the above code is

The Roman numeral for 1994 is: MCMXCIV
The Roman numeral for 58 is: LVIII

Using StringBuilder for Efficiency

For better performance with string concatenation, we can use StringBuilder instead of regular string concatenation. This approach is more efficient for larger numbers

Example

using System;
using System.Collections.Generic;
using System.Text;

class Program {
    static string ConvertToRomanUsingStringBuilder(int number) {
        Dictionary<int, string> romanMap = new Dictionary<int, string> {
            {1000, "M"}, {900, "CM"}, {500, "D"}, {400, "CD"},
            {100, "C"}, {90, "XC"}, {50, "L"}, {40, "XL"},
            {10, "X"}, {9, "IX"}, {5, "V"}, {4, "IV"}, {1, "I"}
        };

        StringBuilder result = new StringBuilder();

        foreach(var item in romanMap) {
            while (number >= item.Key) {
                result.Append(item.Value);
                number -= item.Key;
            }
        }

        return result.ToString();
    }

    static void Main() {
        int number = 3999; // Maximum standard Roman numeral
        string romanNumeral = ConvertToRomanUsingStringBuilder(number);
        Console.WriteLine($"The Roman numeral for {number} is: {romanNumeral}");
    }
}

The output of the above code is

The Roman numeral for 3999 is: MMMCMXCIX

Using a Recursive Approach

We can also solve this problem recursively by finding the largest Roman numeral value that fits into the number, then recursively converting the remainder

Example

using System;
using System.Collections.Generic;

class Program {
    static Dictionary<int, string> romanMap = new Dictionary<int, string> {
        {1000, "M"}, {900, "CM"}, {500, "D"}, {400, "CD"},
        {100, "C"}, {90, "XC"}, {50, "L"}, {40, "XL"},
        {10, "X"}, {9, "IX"}, {5, "V"}, {4, "IV"}, {1, "I"}
    };

    static string ConvertToRomanRecursive(int number) {
        if (number == 0) return "";

        foreach(var item in romanMap) {
            if (number >= item.Key) {
                return item.Value + ConvertToRomanRecursive(number - item.Key);
            }
        }
        return "";
    }

    static void Main() {
        int number = 2749;
        string romanNumeral = ConvertToRomanRecursive(number);
        Console.WriteLine($"The Roman numeral for {number} is: {romanNumeral}");
    }
}

The output of the above code is

The Roman numeral for 2749 is: MMDCCXLIX

Comparison

Common Use Cases

• Educational Tools: Converting numbers to Roman numerals for learning purposes and mathematical applications.

• Historical Representations: Used in clocks, book chapters, movie credits, and architectural inscriptions for aesthetic or traditional reasons.

• Game Development: Roman numerals in scoreboards, levels, or ranks to provide a classical gaming experience.

• Document Formatting: Numbering sections, appendices, or footnotes in formal documents and publications.

Conclusion

Converting numbers to Roman numerals in C# can be efficiently accomplished using iterative, StringBuilder-based, or recursive approaches. The iterative method with a dictionary mapping is the most straightforward, while StringBuilder offers better performance for frequent operations. All approaches have O(1) time complexity since Roman numerals have a fixed set of symbols.