Integer to Roman

LeetCode 12 | Difficulty: Medium

Medium

Problem Description

Seven different symbols represent Roman numerals with the following values:

        Symbol
        Value
    


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

Roman numerals are formed by appending the conversions of decimal place values from highest to lowest. Converting a decimal place value into a Roman numeral has the following rules:

- If the value does not start with 4 or 9, select the symbol of the maximal value that can be subtracted from the input, append that symbol to the result, subtract its value, and convert the remainder to a Roman numeral.

- If the value starts with 4 or 9 use the **subtractive form** representing one symbol subtracted from the following symbol, for example, 4 is 1 (`I`) less than 5 (`V`): `IV` and 9 is 1 (`I`) less than 10 (`X`): `IX`. Only the following subtractive forms are used: 4 (`IV`), 9 (`IX`), 40 (`XL`), 90 (`XC`), 400 (`CD`) and 900 (`CM`).

- Only powers of 10 (`I`, `X`, `C`, `M`) can be appended consecutively at most 3 times to represent multiples of 10. You cannot append 5 (`V`), 50 (`L`), or 500 (`D`) multiple times. If you need to append a symbol 4 times use the **subtractive form**.

Given an integer, convert it to a Roman numeral.

Example 1:

Input: num = 3749

Output: "MMMDCCXLIX"

Explanation:

3000 = MMM as 1000 (M) + 1000 (M) + 1000 (M)
 700 = DCC as 500 (D) + 100 (C) + 100 (C)
  40 = XL as 10 (X) less of 50 (L)
   9 = IX as 1 (I) less of 10 (X)
Note: 49 is not 1 (I) less of 50 (L) because the conversion is based on decimal places

Example 2:

Input: num = 58

Output: "LVIII"

Explanation:

50 = L
 8 = VIII

Example 3:

Input: num = 1994

Output: "MCMXCIV"

Explanation:

1000 = M
 900 = CM
  90 = XC
   4 = IV

Constraints:

- `1 <= num <= 3999`

Topics: Hash Table, Math, String

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Approach

Hash Map

Use a hash map for O(1) average lookups. Store seen values, frequencies, or indices. The key question: what should I store as key, and what as value?

When to use

Need fast lookups, counting frequencies, finding complements/pairs.

Mathematical

Look for mathematical patterns or formulas. Consider: modular arithmetic, GCD/LCM, prime factorization, combinatorics, or geometric properties.

When to use

Problems with clear mathematical structure, counting, number properties.

String Processing

Consider character frequency counts, two-pointer approaches, or building strings efficiently. For pattern matching, think about KMP or rolling hash. For palindromes, expand from center or use DP.

When to use

Anagram detection, palindrome checking, string transformation, pattern matching.

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Solutions

Solution 1: C# (Best: 159 ms)

Metric	Value
Runtime	159 ms
Memory	N/A
Date	2017-07-18

Solution

public class Solution {
    public string IntToRoman(int num) {
    int[] values = { 1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1 };
    string[] romans = { "M", "CM", "D", "CD", "C", "XC", "L", "XL", "X", "IX", "V", "IV", "I" };
    StringBuilder sb = new StringBuilder();
    int i=0;
    while (num > 0)
    {
        while (num >= values[i])
        {
            num -= values[i];
            sb.Append(romans[i]);           
        }
        i++;
    }
    
    return sb.ToString();
    }
}

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Complexity Analysis

Approach	Time	Space
Hash Map	$O(n)$	$O(n)$

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Interview Tips

Key Points

• Discuss the brute force approach first, then optimize. Explain your thought process.
• Hash map gives O(1) lookup — think about what to use as key vs value.