Integer to Roman Number

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.

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.

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.

O(1)

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