Roman To Integer Leetcode Problem 13 [Python Solution]

Welcome to another coding adventure!

Today, we're going to tackle the Roman to Integer problem, which is a relatively easy problem from LeetCode.

However, don't let its simplicity fool you; it's an excellent exercise in problem-solving and algorithmic thinking.

In this blog post, we'll walk you through the problem statement, constraints, and various approaches to solve it efficiently in Python.

Problem Name: Roman to Integer
Difficulty: Easy
Category: Math & Geometry
Companies: Google
Keyword: Roman to Integer LeetCode

If you want to check out the problem directly on LeetCode, here's the question link.

Problem Overview

Roman numerals are represented by seven different symbols: I, V, X, L, C, D, and M.

Each of these symbols has a specific numerical value associated with it.

Here's a quick reference:

I – 1
V – 5
X – 10
L – 50
C – 100
D – 500
M – 1000

For instance, the number 2 is written as "II" in Roman numerals, simply two ones added together.

Similarly, 12 is written as "XII," which is X (10) + II (2).

The number 27 is written as "XXVII," representing XX (20) + V (5) + II (2).

Roman numerals are typically written from largest to smallest, from left to right.

However, there's a special case when a smaller numeral appears before a larger one, which indicates subtraction.

For example:

IV represents 4 because it's I (1) placed before V (5), subtracting 1 from 5.
IX represents 9 because it's I (1) before X (10), subtracting 1 from 10.
XL represents 40 because it's X (10) before L (50), subtracting 10 from 50.
XC represents 90 because it's X (10) before C (100), subtracting 10 from 100.
CD represents 400 because it's C (100) before D (500), subtracting 100 from 500.
CM represents 900 because it's C (100) before M (1000), subtracting 100 from 1000. Given a Roman numeral, your task is to convert it to an integer.

Example 1:

Input: s = "III"
Output: 3
Explanation: "III" in Roman numerals is equivalent to 3.

Example 2:

Input: s = "LVIII"
Output: 58
Explanation: "LVIII" in Roman numerals is equivalent to 50 (L) + 5 (V) + 3 (III) = 58.

Example 3:

Input: s = "MCMXCIV"
Output: 1994
Explanation: "MCMXCIV" in Roman numerals is equivalent to 1000 (M) + 900 (CM) + 90 (XC) + 4 (IV) = 1994.

Constraints:

1 <= s.length <= 15
s contains only the characters ('I', 'V', 'X', 'L', 'C', 'D', 'M').
It is guaranteed that s is a valid Roman numeral in the range [1, 3999].

Now that we have a clear understanding of the problem, let's explore the constraints, edge cases, and solutions.

Understanding Roman to Integer Constraints

The constraints provided in the problem statement help us understand the limits and expectations for the input data:

String Length (1 <= s.length <= 15): The length of the input Roman numeral string can range from 1 to 15 characters.

This is a reasonable constraint and doesn't pose any significant challenges for our algorithm's efficiency.

Valid Characters: The string s contains only the characters 'I', 'V', 'X', 'L', 'C', 'D', and 'M'.

This constraint ensures that we don't need to handle unexpected characters in the input.

Valid Range (1 to 3999): The problem guarantees that s is a valid Roman numeral in the range [1, 3999].

This means we won't receive invalid inputs, such as zero or negative values.

With these constraints in mind, we can move on to solving the problem using both a brute-force approach and a more efficient approach.

Brute-force Approach

Let's start with a straightforward, brute-force approach to solving this problem.

In this approach, we'll iterate through the input string s, check each character, and apply the rules of Roman numerals to calculate the corresponding integer value.

Pseudo Code:

Initialize a result variable to 0
Iterate through the characters in the input string `s`:
    If the current character is 'I' and the next character is 'V' or 'X':
        Subtract 1 from the result
    Else if the current character is 'X' and the next character is 'L' or 'C':
        Subtract 10 from the result
    Else if the current character is 'C' and the next character is 'D' or 'M':
        Subtract 100 from the result
    Else:
        Add the value of the current character to the result
Return the result

This brute-force approach compares each character to its adjacent character to decide whether to add or subtract its value, following the Roman numeral rules.

It's a straightforward solution, but not the most efficient.

Efficient Approach with Hash Map

While the brute-force approach works, it's not the most efficient way to solve the problem.

We can improve the efficiency of our solution by using a hash map to store the values associated with each Roman numeral symbol.

With the hash map, we can instantly access the values, making the solution more efficient.

Here's the efficient Python solution:

View on GitHub ➹

def romanToInt(s: str) -&gt; int:
    # Create a hash map to store the values of Roman numerals.

roman = {
        &quot;I&quot;: 1, &quot;V&quot;: 5, &quot;X&quot;: 10, &quot;L&quot;: 50,
        &quot;C&quot;: 100, &quot;D&quot;: 500, &quot;M&quot;: 1000
    }

    # Initialize the result variable to 0. res = 0

    # Iterate through the input string `s`.

for i in range(len(s)):
        # Check if the next character is larger, indicating subtraction.

if i + 1 &lt; len(s) and roman[s[i]] &lt; roman[s[i + 1]]:
            res -= roman[s[i]]
        else:
            res += roman[s[i]]

    # Return the final result.

return res

In this efficient approach, we create a hash map that stores the values of Roman numerals.

We then iterate through the input string, comparing each character with the next character to decide whether to add or subtract its value based on the rules we discussed earlier.

By using a hash map, we avoid the need for multiple conditional statements

, making the code more concise and efficient.

Time and Space Complexity

Time Complexity

The time complexity of this efficient solution is O(n), where n is the length of the input string s.

We iterate through the string once, performing constant-time operations for each character.

Space Complexity

The space complexity is O(1) because the size of the input and the hash map remains constant, regardless of the length of the input string.

Reasoning Behind Our Efficient Approach

The efficient approach is based on the understanding that Roman numerals are typically written from left to right, in decreasing order from largest to smallest.

However, there are exceptions when a smaller numeral appears before a larger one, indicating subtraction.

We use a hash map to store the values of Roman numerals to make value retrieval fast and straightforward.

By iterating through the input string, we can compare each character with the next character to determine whether we need to add or subtract its value based on the Roman numeral rules.

This approach simplifies the code, makes it more efficient, and ensures the correct conversion of Roman numerals to integers.

Conclusion

In this blog post, we've explored the Roman to Integer problem on LeetCode, which involves converting Roman numerals to their integer equivalents.

We discussed the problem statement, constraints, and provided both a brute-force and an efficient approach to solving it.

The efficient solution uses a hash map to store the values of Roman numerals, simplifying the code and improving its efficiency.

Remember, even easy problems can be excellent opportunities to practice problem-solving skills and enhance your understanding of fundamental concepts.

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Now it's your turn!

Try solving the Roman to Integer problem on LeetCode, and feel free to comment, ask questions, make suggestions, or share your own solutions.

Happy coding!

Question Link