Efficient Roman Numeral Converter in C++

This article explores the creation of a Roman numeral converter in C++. We’ll delve into the conversion process, focusing on transforming decimal numbers into their Roman numeral counterparts. A clear understanding of the underlying logic is crucial for developing efficient and accurate code.

Table of Contents

• Converting Decimal to Roman Numerals
• C++ Implementation
• Error Handling and Efficiency
• Conclusion

Converting Decimal to Roman Numerals

The Roman numeral system utilizes combinations of letters to represent numbers. Each letter has a specific numerical value:

• I = 1
• V = 5
• X = 10
• L = 50
• C = 100
• D = 500
• M = 1000

Conversion involves iterating through these values, strategically adding or subtracting based on numeral position and adjacent values. For instance, IV (4) is V (5) – I (1), and IX (9) is X (10) – I (1). This subtractive principle is key to efficient representation.

C++ Implementation

The following C++ function efficiently converts decimal numbers to Roman numerals:

#include <iostream>
#include <map>
#include <string>

std::string decimalToRoman(int num) {
    if (num <= 0 || num > 3999) return "Invalid Input";

    std::map<int, std::string> romanMap = {
        {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"}
    };

    std::string result = "";
    for (auto const& [value, symbol] : romanMap) {
        while (num >= value) {
            result += symbol;
            num -= value;
        }
    }
    return result;
}

int main() {
    int decimalNum;
    std::cout << "Enter a decimal number (1-3999): ";
    std::cin >> decimalNum;
    std::string romanNum = decimalToRoman(decimalNum);
    std::cout << "The Roman numeral equivalent is: " << romanNum << std::endl;
    return 0;
}

This code leverages a map for efficient symbol lookup and a while loop to handle repeated numerals. The subtractive cases (like 4 and 9) are explicitly defined in the map for optimal performance.

Error Handling and Efficiency

The provided code includes basic error handling for inputs outside the range of 1 to 3999. For a more robust solution, additional checks could be added. The use of a map significantly enhances efficiency by providing O(1) lookup time for Roman numeral symbols. The iterative approach avoids unnecessary computations.

Conclusion

This article presented a clear and efficient method for converting decimal numbers to Roman numerals in C++. The use of a map improves both readability and performance. This approach is easily adaptable to handle larger numbers or integrate into more complex applications. Always remember thorough error handling for a production-ready solution.