Roman to Integer

Ever wondered how to turn Roman numerals like XIV or MCMXCIV into plain numbers? It’s a popular question in coding interviews and problem-solving platforms. And if you're looking for the easiest and fastest way to solve it, hashing is your best friend.

In this guide, we’ll walk you through how to solve the Roman to Integer problem step by step using a hashing algorithm. We’ll keep things simple, explain every part, and make sure you really understand how it works. Along the way, we’ll touch on important ideas like string hashing, string manipulation, integer conversion, and even numerical representation — but without overcomplicating anything.

Let’s get started.

What Are Roman Numerals?

Roman numerals are symbols like I, V, X, L, C, D, and M that were used in ancient Rome to write numbers. Even today, we see them on clocks, book chapters, or old buildings.

Here’s a quick cheat sheet:

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

But there’s a twist.

Sometimes, a smaller value comes before a bigger one, like:

• IV = 4 (5 - 1)
• IX = 9 (10 - 1)

So it’s not just about adding values. You have to follow the rules of the numeral system. That’s where many people get confused — but don’t worry, we’re going to make it easy.

What’s the Problem We’re Solving?

We need to write a function that takes a Roman numeral string and returns the correct number. Here’s what it looks like:

Example:

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Input: "MCMXCIV"
Output: 1994

This challenge tests how well you can handle numeric data processing and how smart your algorithm implementation is. Let’s solve it using a technique that keeps things simple — hashing.

Why Use Hashing for Roman to Integer Conversion?

Instead of checking every Roman symbol with a bunch of if-else statements, we’ll use a simple idea: map every symbol to its value using a hash table (or dictionary).

This is where hashing algorithms shine. With them, we can quickly find the value of any character in the string without looping through a bunch of options. It’s perfect for string manipulation problems like this.

How to Convert Roman to Integer Using Hashing – Step by Step

Let’s go through the process together.

1. Create a Map of Roman Symbols

We start by creating a dictionary that stores the value for each Roman numeral. This is the core of our string hashing logic.

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roman_map = {
    'I': 1,
    'V': 5,
    'X': 10,
    'L': 50,
    'C': 100,
    'D': 500,
    'M': 1000
}

2. Loop Through the String from Right to Left

We process the Roman numeral from the end. That makes it easier to handle the subtraction rule.

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total = 0
prev_value = 0

3. Add or Subtract Based on Current and Previous Values

For each character:

• If the current value is smaller than the previous one, subtract it.
• Otherwise, add it.

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for char in reversed(roman_string):
    current_value = roman_map[char]
    if current_value < prev_value:
        total -= current_value
    else:
        total += current_value
        prev_value = current_value

This logic keeps your code clean and fast — a great example of smart algorithm implementation.

The Final Code

Here’s the full solution:

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def roman_to_integer(roman_string):
    roman_map = {
        'I': 1, 'V': 5, 'X': 10,
        'L': 50, 'C': 100, 'D': 500, 'M': 1000
    }

    total = 0
    prev_value = 0

    for char in reversed(roman_string):
        current_value = roman_map[char]
        if current_value < prev_value:
            total -= current_value
        else:
            total += current_value
            prev_value = current_value

    return total

Try running this function with different Roman numerals and see how well it works.

How Efficient Is This?

Let’s talk about performance.

• Time Complexity: O(n) – You loop through the string once.
• Space Complexity: O(1) – The map has a fixed number of items.

This is a fast and efficient solution, which is great for interviews and large inputs. Thanks to hashing algorithms and simple string manipulation, it performs well and is easy to understand.

Conclusion

And that’s it! You just learned how to solve the Roman to Integer problem using hashing — the easiest and most efficient way.

We covered:

• What Roman numerals are
• How to build a hash map
• How to process the string
• A working Python function
• Real-world uses like numerical representation and data encoding

This problem may look tricky at first, but once you understand the pattern and use hashing algorithms, it becomes super easy. So go ahead and try it yourself. You’ve got this!