Integer To Roman Leetcode Problem 12 [Python Solution]

Welcome to another exciting LeetCode problem-solving session!

In this blog post, we're going to tackle the Integer To Roman problem, which is Problem 12 on LeetCode.

This problem falls under the category of Math & Geometry and is of medium difficulty.

Before we dive into the solution, let's understand the problem statement.

Problem Overview

Roman numerals are represented by seven different symbols: I, V, X, L, C, D, and M, with corresponding values of 1, 5, 10, 50, 100, 500, and 1000. Roman numerals are usually written from largest to smallest from left to right.

However, there are some special cases where subtraction is used.

For example, "IV" represents 4 because I is placed before V, and "IX" represents 9 because I is placed before X.

The same logic applies to "XL," "XC," "CD," and "CM."

Your task is to convert an integer into its Roman numeral representation.

Example 1:

Input: num = 3
Output: "III"
Explanation: 3 is represented as three ones.

Example 2:

Input: num = 58
Output: "LVIII"
Explanation: L = 50, V = 5, III = 3.

Example 3:

Input: num = 1994
Output: "MCMXCIV"
Explanation: M = 1000, CM = 900, XC = 90, and IV = 4.

Constraints:

• 1 <= num <= 3999

Now that we have a clear understanding of the problem, let's proceed to the solution.

Efficient Python Code Solution

Here's a Python solution to convert an integer to its Roman numeral representation:

def intToRoman(self, num: int) -> str:
    symList = [
        ["I", 1],
        ["IV", 4],
        ["V", 5],
        ["IX", 9],
        ["X", 10],
        ["XL", 40],
        ["L", 50],
        ["XC", 90],
        ["C", 100],
        ["CD", 400],
        ["D", 500],
        ["CM", 900],
        ["M", 1000],
    ]
    res = ""
    for sym, val in reversed(symList):
        if num // val:
            count = num // val
            res += sym * count
            num = num % val
    return res

This code provides an efficient solution for converting an integer to a Roman numeral.

Let's break down how it works:

1. We start by defining a list called symList, which contains pairs of Roman numerals and their corresponding integer values.

This list includes special cases for subtraction, such as IV (4) and IX (9).

1. We initialize an empty string res to store the Roman numeral representation of the input number.

2. We iterate through the symList in reverse order (from largest values to smallest values) using a for loop.

This ensures that we build the Roman numeral representation from left to right, following the rules of Roman numerals.

1. Inside the loop, we check if the current value (val) can be divided evenly into the input number (num).

If the division result is greater than 0, it means that the current Roman numeral should be included in the representation.

1. We calculate the number of times the Roman numeral should be added by dividing num by val and store it in the count variable.

2. We concatenate the Roman numeral (sym) to the result string count times, using Python's string multiplication.

3. Finally, we update the num by taking the remainder of the division (num % val).

This ensures that we move on to the next set of Roman numerals.

1. The loop continues until we've processed all the Roman numeral symbols, and the result string contains the Roman numeral representation of the input number.

By following this approach, we can efficiently convert any integer in the range of 1 to 3999 into its corresponding Roman numeral.

Time and Space Complexity

It's essential to consider the time and space complexity of the solution.

Time Complexity: The time complexity of this solution is O(1).

Since there is a finite set of Roman numeral symbols and a fixed number of iterations through the symList, the time complexity remains constant.

Space Complexity: The space complexity is also O(1).

The memory used to store the symList, res, and other variables is not dependent on the input size but remains constant.

Reasoning Behind Our Approach

The reasoning behind this approach lies in the systematic representation of Roman numerals.

By breaking down the problem into specific cases and iteratively constructing the Roman numeral representation, we ensure that the solution is both correct and efficient.

We take advantage of the rules of Roman numerals, where specific symbols can be placed before others to indicate subtraction.

This allows us to create an elegant and concise Python code solution.

In summary, we've successfully tackled the Integer To Roman problem by leveraging a well-defined approach and adhering to the rules of Roman numerals.

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Conclusion

In this blog post, we explored the Integer To Roman problem, which required us to convert an integer into its Roman numeral representation.

We provided an efficient Python code solution that follows the rules of Roman numerals, including special cases for subtraction.

By understanding the problem, breaking it down, and systematically constructing the Roman numerals, we've achieved a correct and efficient solution.

The time and space complexity of our solution remain constant, making it a practical approach for converting integers to Roman numerals.

If you'd like to further explore this problem or try it out on LeetCode, you can find the original question here.

We hope this guide has been helpful, and we encourage you to comment, ask questions, make suggestions, and share this content with others.

Happy coding!