LeetCode 12 Solution presents one of the most interesting challenges by requiring the conversion of integers into Roman numerals. While the Roman numeral system may seem ancient, it offers a fascinating way to sharpen your algorithmic skills through its unique rules for converting numbers. The problem asks us to take an integer and convert it into its corresponding Roman numeral using a combination of symbols and subtractive notation.
In this blog post, we’ll dive into a comprehensive solution to the LeetCode 12 problem, breaking down the conversion process step-by-step.
Roman Numerals and Their Symbols
The Roman numeral system is based on combinations of letters, each representing a specific value. The core Roman symbols are:
- M = 1000, D = 500, C = 100, L = 50, X = 10, V = 5, and I = 1.
However, there are additional rules to keep in mind, especially when handling numbers that involve subtractive notation. For instance, 4 is represented as “IV” (1 less than 5), and 9 is represented as “IX” (1 less than 10). This system ensures that numbers are expressed in their most concise form.
Problem Breakdown: Integer to Roman
The challenge here is to convert a given integer between 1 and 3999 into its corresponding Roman numeral. The conversion follows a greedy approach, where we repeatedly subtract the largest possible Roman symbol from the number and append it to the result. This continues until the number is reduced to zero.
For example, consider the number 1994. We can break it down as follows:
- The largest symbol that fits is M (1000), so we subtract 1000 and append “M”.
- Now, the number is 994. The largest fitting symbol is CM (900), so we subtract 900 and append “CM”.
- The remaining number is 94, so we use XC (90), subtract 90, and append “XC”.
- Finally, we handle 4 by appending IV (4).
Thus, 1994 is converted to the Roman numeral MCMXCIV.
Algorithmic Approach: LeetCode 12 Solution
To solve the LeetCode 12 problem, we use a simple yet effective greedy algorithm. We first create a mapping of all Roman numeral symbols paired with their corresponding integer values. By iterating through this list in descending order of value, we can continuously subtract the largest possible value from the input number while building the Roman numeral string.
Let’s dive into the code:
def intToRoman(num: int) -> str:
roman_map = [
(1000, 'M'), (900, 'CM'), (500, 'D'), (400, 'CD'),
(100, 'C'), (90, 'XC'), (50, 'L'), (40, 'XL'),
(10, 'X'), (9, 'IX'), (5, 'V'), (4, 'IV'), (1, 'I')
]
roman = []
for value, symbol in roman_map:
while num >= value:
roman.append(symbol)
num -= value
return ''.join(roman)The solution begins by defining a list of tuples, where each tuple contains a Roman numeral and its corresponding integer value, arranged in descending order. We then loop over this list, and for each symbol, we repeatedly subtract its value from the input number and append the symbol to our result string. This process continues until we exhaust the input number, ensuring that we handle all cases, including numbers requiring subtractive notation like 4, 9, 40, and 90.
Understanding Edge Cases
The problem has some interesting edge cases that highlight the flexibility of this approach. Consider the smallest input, num = 1. The algorithm will append “I” since it’s the smallest possible Roman numeral. For larger numbers like 3999, which is the upper limit of the problem constraints, the algorithm handles the input smoothly using symbols like “MMM”, “CM”, “XC”, and “IX” to form the result “MMMCMXCIX”.
Another example is num = 58, where the algorithm first appends “L” (50), followed by “VIII” (8) to produce the final result “LVIII”. The beauty of this approach lies in how subtractive notation is naturally incorporated by our Roman numeral mapping, simplifying the solution.
Time and Space Complexity
The time complexity of this solution is O(1) due to the fixed range of Roman numeral symbols and values. Regardless of the input number, the algorithm performs a constant amount of work for each symbol, making this approach highly efficient. Similarly, the space complexity is O(1) since the space required for the output string is bounded by the constraints of the problem.
Conclusion: Mastering LeetCode 12
In this LeetCode 12 Solution, we explored how to convert an integer into a Roman numeral using a greedy algorithm that makes use of predefined Roman symbol mappings. This approach efficiently handles all edge cases, including subtractive notation, and runs in constant time. By breaking the number down step-by-step and appending the corresponding symbols, we ensure a clear and concise result.
With this solution, you’re well-equipped to master this problem. You can also apply similar strategies to other number conversion tasks in your algorithmic journey. Whether you’re a coding enthusiast or preparing for technical interviews, this problem offers a solid foundation. It helps you understand how old systems like Roman numerals can be converted into efficient algorithms.
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.
