How do you convert integers to Roman numerals?

Discover the method to convert integers into Roman numerals, an essential skill for those interested in historical numeral systems or enhancing their problem-solving abilities in mathematics. This guide explains the conversion process in detail, from the basics of Roman numeral symbols to practical conversion techniques. Perfect for educators, students, and enthusiasts, learn how to accurately transform modern numbers into their ancient, symbolic forms with ease.

Problem Statement
Convert a given integer into its equivalent Roman numeral. Roman numerals use combinations of the letters I, V, X, L, C, D, and M.

Examples

• Input: 3
  Output: III
  Explanation: 3 is represented as III in Roman numerals.

• Input: 58
  Output: LVIII
  Explanation: 58 combines L (50) + V (5) + III (3).

Approaches to Convert Integers to Roman Numerals

1. Direct Mapping Approach

• Method: Use a list of thresholds and corresponding Roman numerals to construct the numeral from the largest value downward.

• Time Complexity: The time complexity of this code is considered O(n^2),
• Space Complexity: Constant, utilizing a fixed amount of space for the mappings.

2. Optimized Mapping Approach

• Method: This method enhances readability and efficiency by structuring quick access through division and multiplication.

• Time Complexity: The time complexity of this code is considered O(n), where n is the input number.
• Space Complexity: Constant, as the size of the map does not change.

Application

Understanding and implementing the conversion from integers to Roman numerals provides practical insights into ancient numeral systems, offering a unique perspective on historical calculation methods. This knowledge is especially relevant for those studying history, classical studies, or looking to improve their understanding of numeral systems in a broader context.

Conclusion

The conversion of integers to Roman numerals is an instructive problem that combines basic programming skills with historical knowledge, useful for those interested in history, mathematics, or coding fundamentals.