Master Roman to Integer Conversion with Python | Leetcode 13 Solution

Table of Contents

1. Introduction
2. Understanding Roman Numerals
3. Converting Roman Numerals to Integers
4. Algorithm Explanation
5. Implementing the Code
6. Step-by-Step Example
7. Time and Space Complexity Analysis
8. Pros and Cons of the Algorithm
9. Conclusion

Converting Roman Numerals to Integers: A Step-by-Step Guide

Roman numerals have been used for centuries and are still encountered in various fields, such as mathematics, history, and even pop culture. In this article, we will discuss how to convert Roman numerals to integers, providing an in-depth explanation of the algorithm involved and its implementation in Python.

1. Introduction

Roman numerals are a numeral system that originated in ancient Rome. Unlike the decimal system we use today, Roman numerals are based on a combination of specific letters to represent different values. Understanding how to convert Roman numerals to integers can be useful in various scenarios, such as solving mathematical problems, historical research, or even deciphering old inscriptions.

2. Understanding Roman Numerals

Before diving into the conversion process, it's essential to understand how Roman numerals are represented. Roman numerals are composed of seven basic symbols:

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

These symbols can be combined in various ways to create different numbers. For example, II represents 2, VIII represents 8, and XIV represents 14.

3. Converting Roman Numerals to Integers

The goal of our algorithm is to convert a given Roman numeral into its corresponding integer value. To achieve this, we'll iterate over the Roman numeral from left to right, comparing each symbol's value with the next one. If the current symbol's value is less than the next symbol, we subtract it from the total. Otherwise, we add it to the total.

4. Algorithm Explanation

The algorithm for converting Roman numerals to integers can be summarized in the following steps:

1. Create a dictionary to store the values corresponding to each Roman numeral symbol.
2. Initialize two variables: previous and total. Set them both to 0.
3. Iterate over the Roman numeral string from left to right.
4. Compare the value of the current symbol with the previous symbol.
5. If the current symbol's value is greater than the previous symbol's value, subtract the previous symbol's value twice from the total.
6. Otherwise, add the current symbol's value to the total.
7. Update the previous variable to hold the current symbol's value.
8. After iterating through all the symbols, return the total.

5. Implementing the Code

Now, let's implement the algorithm in Python. We'll define a function called "roman_to_integer" that takes a Roman numeral string as input and returns its corresponding integer value.

def roman_to_integer(roman_numeral):
    values = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000}
    previous = 0
    total = 0

    for symbol in roman_numeral:
        current = values[symbol]
        if current > previous:
            total -= 2 * previous
        total += current
        previous = current

    return total

6. Step-by-Step Example

To better understand how the algorithm works, let's walk through an example. Suppose we want to convert the Roman numeral "XLIX" to an integer.

• The Roman numeral "XLIX" represents the number 49.
• We initialize the previous and total variables to 0.
• We iterate through the symbols of the Roman numeral from left to right.
  • The first symbol is 'X'. Its value is 10, which is greater than 0. We subtract 2 * 0 (previous) from the total, resulting in 0. Then we add 10 to the total, making it 10. We update the previous variable to 10.
  • The second symbol is 'L'. Its value is 50, which is greater than 10. We subtract 2 * 10 (previous) from the total, resulting in -10. Then we add 50 to the total, making it 40. We update the previous variable to 50.
  • The third symbol is 'I'. Its value is 1, which is not greater than 50. We simply add 1 to the total, making it 41. We update the previous variable to 1.
  • The fourth symbol is 'X'. Its value is 10, which is not greater than 1. We simply add 10 to the total, making it 51. We update the previous variable to 10.
• After iterating through all the symbols, we return the total, which is 49.

Thus, the Roman numeral "XLIX" is correctly converted to the integer 49 using our algorithm.

7. Time and Space Complexity Analysis

The time complexity of our algorithm is O(n), where n is the length of the input Roman numeral string. This is because we iterate through each symbol once to calculate the total.

The space complexity is O(1) since we use a constant amount of additional space to store the values and variables required for the algorithm.

8. Pros and Cons of the Algorithm

Pros:

• The algorithm provides an efficient way to convert Roman numerals to integers.
• It handles various combinations of symbols correctly, considering their specific value rules.

Cons:

• The algorithm assumes that the input Roman numeral is valid and follows the rules of Roman numeral representation.
• If an invalid Roman numeral is provided, the algorithm may still produce a result without indicating the error.

9. Conclusion

Converting Roman numerals to integers is an interesting problem with practical applications in different fields. In this article, we have explored the algorithm for converting Roman numerals to integers, explained its implementation in Python, and provided a step-by-step example. By understanding and using this algorithm, you can easily convert Roman numerals to their corresponding integer values and solve a variety of problems.