**π‘ Problem Formulation:** Converting Roman numerals to integers is a common programming challenge that involves translating the ancient number system used in Roman times to the Arabic numbers we use today. For instance, converting the Roman numeral “XIV” should result in the integer 14. This article discusses five methods to achieve this conversion in Python.

## Method 1: Sequential Subtraction

The Sequential Subtraction method involves traversing the Roman numeral from left to right and subtracting the value of a letter if it’s less than the value that follows it, or adding it otherwise. This method simulates how Roman numerals are typically constructed and calculated by hand.

Here’s an example:

def roman_to_int(s): values = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000} total = 0 prev_value = 0 for char in reversed(s): if values[char] < prev_value: total -= values[char] else: total += values[char] prev_value = values[char] return total print(roman_to_int("XIV"))

Output: 14

This code defines a function `roman_to_int()`

that converts a Roman numeral into an integer by iterating over each character in reverse. It uses a dictionary for the Roman numeral mappings and adds or subtracts values based on the previous character’s value.

## Method 2: Lookahead Comparison

The Lookahead Comparison method optimizes the sequential method by comparing the current Roman numeral value with the next one during iteration. It adds or subtracts the value without needing to reverse the input string.

Here’s an example:

def roman_to_int(s): values = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000} total, prev_value = 0, 0 for char in s: curr_value = values[char] total += curr_value if prev_value < curr_value: total -= 2 * prev_value prev_value = curr_value return total print(roman_to_int("MCMXCIV"))

Output: 1994

This snippet enhances efficiency by avoiding string reversal. The `roman_to_int()`

function adds each numeral’s value to the total and adjusts the total if it finds a smaller value followed by a larger one.

## Method 3: Patterns and Groups

In the Patterns and Groups method, Roman numerals are matched to their equivalent values using regular expressions, which identify the standard numeral patterns.

Here’s an example:

import re def roman_to_int(s): roman_pattern = re.compile(r'(CM|CD|XC|XL|IX|IV|M|D|C|L|X|V|I)') values = {'M': 1000, 'CM': 900, 'D': 500, 'CD': 400, 'C': 100, 'XC': 90, 'L': 50, 'XL': 40, 'X': 10, 'IX': 9, 'V': 5, 'IV': 4, 'I': 1} total = 0 for roman_numeral in roman_pattern.findall(s): total += values[roman_numeral] return total print(roman_to_int("LVIII"))

Output: 58

The `roman_to_int()`

function defined here uses Python’s regular expression library to find and sum the values of all the numeral patterns in the string, building up the total as it goes.

## Method 4: Mapping Prefixes

This method involves creating a mapping for not just single Roman numerals but also for the prefixes that subtract value (e.g., IV, IX, XL). This reduces the comparison needed during iteration.

Here’s an example:

def roman_to_int(s): values = {'IV': 4, 'IX': 9, 'XL': 40, 'XC': 90, 'CD': 400, 'CM': 900, 'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000} total = i = 0 while i < len(s): if i+1 < len(s) and s[i:i+2] in values: total += values[s[i:i+2]] i += 2 else: total += values[s[i]] i += 1 return total print(roman_to_int("CDXLIII"))

Output: 443

This `roman_to_int()`

function takes advantage of prefixes representing subtraction to minimize operations, allowing the function to jump forward in the string when these patterns are identified.

## Bonus One-Liner Method 5: Using reduce

This one-liner solution uses the Python’s `functools.reduce()`

function, which is useful for performing cumulative operations on a sequence of data in a concise manner.

Here’s an example:

from functools import reduce def roman_to_int(s): values = {'I': 1, 'V': 5, 'X': 10, 'L': 50, 'C': 100, 'D': 500, 'M': 1000} return reduce(lambda total, p: total + values[p[1]] - 2 * values[p[0]] if values[p[0]] < values[p[1]] else total + values[p[1]], zip(s, s[1:] + 'I'), 0) print(roman_to_int("III"))

Output: 3

This code snippet cleverly combines `zip()`

and `reduce()`

to construct pairs of numerals to be processed, applying the necessary addition or subtraction in one compact expression.

## Summary/Discussion

**Method 1:**Sequential Subtraction. Simple and follows the traditional approach. Can be slower due to the need to reverse the string.**Method 2:**Lookahead Comparison. More efficient as it removes the need for string reversal. A slight increase in complexity over the sequential method.**Method 3:**Patterns and Groups. Leveraging regular expressions provides a clean and efficient approach. However, constructing and understanding regular expressions can be complex for some users.**Method 4:**Mapping Prefixes. Efficient and clever use of subtraction prefixes for faster computation. Requires an initialisation of a more complex mapping.**Method 5:**Using reduce. Extremely concise and showcases functional programming prowess. It’s less readable and not advised for new Python users or for those unfamiliar with`reduce()`

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Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.