How do you solve Roman to Integer on LeetCode?

Roman to Integer (LeetCode #13) 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(n) space complexity. Key insight: The key observation is that Roman numerals follow a specific pattern where smaller values before larger values indicate subtraction. Recognizing this pattern allows for efficient conversion.

What is the brute force solution for Roman to Integer?

The brute force approach for Roman to Integer is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves iterating through the Roman numeral string and converting each character to its corresponding integer value. We then need to handle special cases where a smaller numeral precedes a larger one, indicating subtraction. The optimal Optimal Solution (Hash Map) approach improves this to O(n).

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

Roman to Integer 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 Roman to Integer?

When you first see this problem, mention that you will consider both the straightforward and optimal approaches to ensure clarity. Communicate your approach clearly, explaining how you will handle the special subtraction cases and the use of a hash map. Mention edge cases such as the smallest and largest Roman numerals, and ensure you validate that the input is a valid Roman numeral.

What are common mistakes when solving Roman to Integer?

Students often forget to handle the subtraction cases correctly, leading to incorrect totals. Another common mistake is to not account for the order of processing the Roman numerals, which can lead to miscalculations.

#13

Roman to Integer

Easy

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(n)

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Intuition

Time O(n)Space O(n)

The optimal approach uses a hash map to store the values of Roman numerals and iterates through the string in a single pass. By checking the current numeral against the next one, we can efficiently decide whether to add or subtract its value.

⚙️

Algorithm

4 steps

1Step 1: Create a mapping of Roman numeral characters to their integer values using a hash map.
2Step 2: Initialize a variable to hold the total value.
3Step 3: Iterate through the string from the end to the beginning.
4Step 4: For each character, check if the current value is less than the previous value. If it is, subtract it from the total; otherwise, add it.

solution.py15 lines

1# Full working Python code with comments
2
3def roman_to_integer(s: str) -> int:
4    roman_map = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
5    total = 0
6    prev_value = 0
7    for char in reversed(s):
8        value = roman_map[char]
9        if value < prev_value:
10            total -= value  # Subtract if current value is less than previous
11        else:
12            total += value  # Add otherwise
13        prev_value = value
14    return total
15

ℹ

Complexity note: The time complexity is O(n) because we iterate through the string once. The space complexity is O(n) due to the hash map storing the Roman numeral values.

1The key observation is that Roman numerals follow a specific pattern where smaller values before larger values indicate subtraction. Recognizing this pattern allows for efficient conversion.
2Another important insight is that using a hash map for value lookups reduces the time complexity significantly, making the solution optimal.

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