Integer to Roman

Integer to Roman

1. What is this problem about?

The Integer to Roman interview question asks you to convert a standard decimal integer (base 10) into its Roman numeral representation. Roman numerals use symbols like I, V, X, L, C, D, and M. The logic involves both additive rules (e.g., II is 2) and subtractive rules (e.g., IV is 4, IX is 9). You need to handle values from 1 to 3999.

2. Why is this asked in interviews?

Companies like Meta, Amazon, and Apple ask the Integer to Roman coding problem to test a candidate's ability to handle mapping and rule-based logic. It evaluates whether you can organize your data structures (like arrays or maps) to simplify complex conditional logic. It’s a great test of clean code and Math interview pattern proficiency.

3. Algorithmic pattern used

This problem follows the Greedy Subtraction pattern.

1. Predefined Lists: Create two parallel arrays or a list of pairs containing all Roman symbols and their corresponding values, including the subtractive cases (e.g., 1000: M, 900: CM, 500: D, 400: CD...).
2. Iterate: Start from the largest value (1000).
3. Subtract: While the current integer is greater than or equal to the current value, append the symbol to the result and subtract the value from the integer.
4. Repeat: Move to the next smaller symbol and value.

4. Example explanation

$n = 1994$

1. Largest value $\leq 1994$ is 1000 (M). result = "M", $n = 994$.
2. Largest value $\leq 994$ is 900 (CM). result = "MCM", $n = 94$.
3. Largest value $\leq 94$ is 90 (XC). result = "MCMXC", $n = 4$.
4. Largest value $\leq 4$ is 4 (IV). result = "MCMXCIV", $n = 0$. Result: "MCMXCIV".

5. Common mistakes candidates make

• Ignoring Subtractive cases: Writing separate, complex if statements for 4, 9, 40, 90, 400, and 900 instead of including them in the main lookup list.
• Wrong Order: Iterating from smallest to largest, which makes the greedy approach much harder to manage.
• Inefficient Concatenation: Using string + inside a loop in Java/C# instead of a StringBuilder.

6. Interview preparation tip

Always include the special subtractive cases (IV, IX, XL, XC, CD, CM) directly in your mapping. This turns a problem full of "edge cases" into a simple, elegant greedy loop. This is a foundational String interview pattern.