When tackling coding challenges like LeetCode’s “Roman to Integer” problem (LeetCode 13), it’s essential to not only solve the problem but also understand the process behind it. In this post, we will walk through a complete LeetCode 13 solution with clear explanations. The goal is to convert a Roman numeral into an integer, using Python.
Roman Numerals: What You Need to Know
Roman numerals are symbols used in the ancient Roman numbering system. The basic symbols and their values are:
- I = 1
- V = 5
- X = 10
- L = 50
- C = 100
- D = 500
- M = 1000
These symbols can be combined to form different numbers. For example, “II” equals 2, “XII” equals 12, and “XXVII” equals 27. The trickier part is that sometimes Roman numerals are not just added together; smaller numerals placed before larger ones indicate subtraction. For instance, “IV” equals 4 (5 – 1) and “IX” equals 9 (10 – 1).
In this problem, you are given a Roman numeral, and your task is to convert it into an integer. Let’s dive into the logic behind the LeetCode 13 solution.
Understanding the Problem: The Roman to Integer Conversion
The problem asks you to convert a string representing a Roman numeral into its corresponding integer. The Roman numeral can be as short as a single character like “I” (which is 1) or as long as 15 characters. You don’t have to worry about invalid inputs because it’s guaranteed that all inputs are valid Roman numerals ranging from 1 to 3999.
To solve this problem efficiently, we need to go through the Roman numeral from left to right, deciding when to add or subtract based on the position of each symbol. If a smaller numeral comes before a larger one (like “IV”), it signals subtraction. Otherwise, we add the values directly.
High-Level Approach to the LeetCode 13 Solution
To break it down simply, we can store the Roman numerals and their corresponding integer values in a Python dictionary. As we scan the Roman numeral string, we compare each symbol with the one following it. If the current symbol is smaller, we subtract its value. Otherwise, we add its value. At the end, we return the total sum as the integer representation of the Roman numeral.
Python Code for Roman to Integer Conversion
Here is the Python implementation of the LeetCode 13 solution:
def romanToInt(s: str) -> int:
# Dictionary of Roman numeral values
roman_values = {
'I': 1, 'V': 5, 'X': 10, 'L': 50,
'C': 100, 'D': 500, 'M': 1000
}
total = 0
n = len(s)
# Iterate through each character, comparing with the next character
for i in range(n - 1):
current_value = roman_values[s[i]]
next_value = roman_values[s[i + 1]]
# If current numeral is less than the next, we subtract it
if current_value < next_value:
total -= current_value
else:
total += current_value
# Always add the value of the last Roman numeral
total += roman_values[s[-1]]
return totalThis Python function starts by initializing a dictionary of Roman numeral values. It then iterates over the string, comparing each character with the next one. If the current symbol is smaller than the next, we subtract its value. Otherwise, we add it. Finally, we handle the last symbol by simply adding its value to the total.
Why This Approach Works
The key to this LeetCode 13 solution is understanding the subtraction rule in Roman numerals. By comparing each Roman numeral to the next one, we can decide when to subtract and when to add. This allows us to handle all valid Roman numerals, including tricky cases like “IV” (4) or “MCMXCIV” (1994).
This approach is efficient because it only requires a single pass through the string. For each character in the string, we perform a constant-time lookup in the dictionary, making the overall time complexity O(n), where n is the length of the input string. Since the length of the input is at most 15, this solution runs very efficiently.
Handling Edge Cases
In this problem, edge cases include short Roman numerals like “I” (which equals 1) or numerals involving subtraction, like “IX” (which equals 9). The code handles these cases seamlessly by checking whether the current symbol is smaller than the next one. This means that whether the numeral involves adding or subtracting, the logic remains consistent.
Time and Space Complexity
The time complexity of our solution is O(n), where n is the length of the Roman numeral string. We process each character exactly once. The space complexity is O(1) because the dictionary storing Roman numeral values is fixed in size and does not grow with the input.
Conclusion
The Roman to Integer problem on LeetCode (LeetCode 13) is a classic example of how understanding simple rules like addition and subtraction in Roman numerals can lead to an efficient algorithm. Using a Python dictionary to store numeral values, and scanning the input string while applying the Roman numeral rules, results in an elegant and efficient solution. This LeetCode 13 solution is both simple to understand and highly efficient, making it a perfect example for coders looking to strengthen their problem-solving skills.
By mastering this problem, you can confidently approach similar string-based problems or tasks involving conversions between different numerical representations.
Happy coding!
Looking for more LeetCode solutions? Stay tuned for upcoming guides on tackling other LeetCode challenges in Python. Whether you’re preparing for technical interviews or aiming to improve your coding skills, exploring a variety of problems will enhance your understanding and proficiency.
You can find this problem on LeedCode, click here.
