LeetCode #12: Integer to Roman

🏛️ What Are Roman Numerals?

Roman numerals use letters to represent values:

The key: represent numbers by combining symbols, using subtractive notation for 4, 9, 40, etc.

The Problem

Given an integer between 1 and 3999, convert it to a Roman numeral string.

Examples

✅ Algorithm: Greedy Matching

We use a greedy approach: always use the largest possible symbol first.

1. Create a list of values and their Roman symbols (including subtractive cases)
2. Sort them in descending order
3. While the number > 0, subtract the largest possible value and append its symbol
4. Repeat until the number is 0

Solution (JavaScript)

function intToRoman(num) {
  const values = [
    1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1
  ];
  const symbols = [
    "M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I"
  ];

  let result = "";

  for (let i = 0; i < values.length; i++) {
    const value = values[i];
    const symbol = symbols[i];

    while (num >= value) {
      result += symbol;
      num -= value;
    }
  }

  return result;
}

🧠 Why Greedy Works

Because Roman numerals are designed with decreasing values, we can always safely use the largest symbol possible.

Example: For 1994:

• Use M (1000) → 994 left
• Use CM (900) → 94 left
• Use XC (90) → 4 left
• Use IV (4) → 0 left

Result: MCMXCIV

🎮 Try It: Roman Numeral Builder

Watch how each symbol is added step by step.