Understanding Roman Numerals: Converting Roman to Integer

Roman numerals are a fascinating number system that has been used for centuries. They consist of various symbols that represent different values. In this blog, we will explore how to convert Roman numerals into integers using a systematic approach. This process, while seemingly simple, involves understanding the rules governing the numeral system.

What are Roman Numerals?

Roman numerals are a combination of letters from the Latin alphabet. The primary symbols include:

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

These symbols can be combined to form other numbers. For example, II represents 2, while IV represents 4. Understanding how these symbols interact is crucial for converting them into integers.

Rules for Writing Roman Numerals

There are specific rules that dictate how Roman numerals are written:

Symbols are generally written from largest to smallest from left to right.
If a smaller number appears before a larger number, it is subtracted (e.g., IV = 4).
If a smaller number appears after a larger number, it is added (e.g., VI = 6).

These rules are essential to remember when converting from Roman numerals to integers.

Steps to Convert Roman to Integer

The process of converting Roman numerals to integers can be broken down into a few straightforward steps:

Start from the last character of the Roman numeral string.
Compare the current symbol with the previous one.
If the current value is greater than or equal to the previous value, add it to the total.
If the current value is less than the previous value, subtract it from the total.
Repeat until all symbols have been processed.

Let’s look at a practical example to clarify this method.

Example: Converting “MCMXCIV”

Consider the Roman numeral “MCMXCIV”. Here’s how to convert it step by step:

M = 1000
C = 100
M = 1000
X = 10
C = 100
I = 1
V = 5

Working from right to left:

V (5) is added.
I (1) is added.
C (100) is added.
X (10) is added.
M (1000) is added.
C (100) is subtracted from M (1000), resulting in 900.

The final total for “MCMXCIV” is 1994.

Implementing the Solution in Java

Now that we understand the conversion process, let’s look at how to implement this in Java. Below is a sample code snippet that demonstrates this logic:

public class RomanToInteger {
    public int romanToInt(String s) {
        int total = 0;
        int prevValue = 0;

        for (int i = s.length() - 1; i >= 0; i--) {
            int currentValue = getValue(s.charAt(i));
            if (currentValue < prevValue) {
                total -= currentValue;
            } else {
                total += currentValue;
            }
            prevValue = currentValue;
        }
        return total;
    }

    private int getValue(char c) {
        switch (c) {
            case 'I': return 1;
            case 'V': return 5;
            case 'X': return 10;
            case 'L': return 50;
            case 'C': return 100;
            case 'D': return 500;
            case 'M': return 1000;
            default: return 0;
        }
    }
}

This code defines a method to convert a Roman numeral string into an integer. It uses a helper method to map Roman numeral characters to their integer values.

Complexity Analysis

When analyzing the complexity of this algorithm, we can consider both time and space complexity:

Time Complexity: O(n), where n is the length of the input string. We traverse the string once.
Space Complexity: O(1), as we are using a fixed amount of space for variables.

Conclusion

Converting Roman numerals to integers is a valuable skill that can enhance your programming knowledge. By understanding the rules and implementing the conversion method, you can efficiently tackle problems involving Roman numerals.

For additional coding challenges and insights into data structures, check out the Tree Data Structure and Graph Data Structure playlists on YouTube.

Roman to Integer