How do you solve Integer to Roman on LeetCode?

Integer to Roman (LeetCode #12) can be solved using Brute Force or Optimal Solution (Hash Map). The optimal approach is Optimal Solution (Hash Map) with O(n) time complexity and O(1) space complexity. Key insight: Recognizing the patterns in Roman numeral representation, especially the subtractive combinations (like IV, IX) helps streamline the conversion process.

What is the brute force solution for Integer to Roman?

The brute force approach for Integer to Roman is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves repeatedly subtracting the largest possible Roman numeral value from the integer until we reach zero. This method is straightforward but inefficient, as it may require multiple iterations for each numeral. The optimal Optimal Solution (Hash Map) approach improves this to O(n).

What algorithm or data structure is used to solve Integer to Roman?

Integer to Roman uses the following concepts: Hash Table, Math, String. The recommended patterns to study are: Hash Map, Array, Two Pointers.

What are the interview tips for Integer to Roman?

When you first see this problem, clarify the rules of Roman numeral representation to ensure you understand the requirements. Communicate your approach clearly, explaining how you plan to handle both the standard and subtractive cases. Mention edge cases such as the smallest and largest values (1 and 3999) to show that you're considering the full range of inputs.

What are common mistakes when solving Integer to Roman?

Students often forget to handle the subtractive cases correctly, leading to incorrect outputs. Some may also attempt to build the numeral string in a non-optimized way, leading to unnecessary complexity.

#12

Integer to Roman

Medium

Hash TableMathStringHash MapArrayTwo Pointers

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution (Hash Map)★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

Using a hash map (or a list of tuples) allows us to efficiently map the integer values to their corresponding Roman numeral symbols. This approach is more efficient than brute force as it directly checks and subtracts the largest possible values in a single pass.

⚙️

Algorithm

3 steps

1Step 1: Create a list of tuples containing Roman numeral symbols and their corresponding integer values, sorted from largest to smallest.
2Step 2: Initialize an empty string to build the Roman numeral result.
3Step 3: Use a loop to iterate through the list, subtracting the value from the number and appending the corresponding symbol to the result until the number is reduced to zero.

solution.py27 lines

1# Full working Python code with comments
2
3def int_to_roman(num):
4    roman_numerals = [
5        (1000, 'M'),
6        (900, 'CM'),
7        (500, 'D'),
8        (400, 'CD'),
9        (100, 'C'),
10        (90, 'XC'),
11        (50, 'L'),
12        (40, 'XL'),
13        (10, 'X'),
14        (9, 'IX'),
15        (5, 'V'),
16        (4, 'IV'),
17        (1, 'I')
18    ]
19    result = ''
20    for value, symbol in roman_numerals:
21        while num >= value:
22            result += symbol
23            num -= value
24    return result
25
26# Example usage
27print(int_to_roman(1994))  # Output: MCMXCIV

ℹ

Complexity note: The time complexity is O(n) because we iterate through the list of Roman numeral values at most once for each numeral. The space complexity is O(1) since we only use a fixed amount of space for the result string.

1Recognizing the patterns in Roman numeral representation, especially the subtractive combinations (like IV, IX) helps streamline the conversion process.
2Understanding that we can efficiently use a sorted list of numeral values allows for a more systematic approach to building the final Roman numeral string.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.