How to turn Roman numerals into numbers in C?

Converting Roman numerals to their integer (decimal) equivalents in C involves systematically parsing the input string, mapping each Roman character to its numerical value, and applying a specific algorithm to correctly handle both additive and subtractive notations.

Understanding Roman Numeral Values

Roman numerals are represented by seven different symbols, each with a fixed integer value.

Roman Symbol	Integer Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

While most symbols are simply added together (e.g., VI = 5 + 1 = 6, LX = 50 + 10 = 60), a crucial rule is subtractive notation. If a symbol of smaller value appears before a symbol of larger value, it is subtracted from the larger value. Common subtractive pairs include:

• IV (4): 5 - 1
• IX (9): 10 - 1
• XL (40): 50 - 10
• XC (90): 100 - 10
• CD (400): 500 - 100
• CM (900): 1000 - 100

This rule is key to developing an accurate conversion algorithm. For a comprehensive guide on Roman numerals, refer to Wikipedia's Roman Numerals page.

The Core Conversion Algorithm

The most common and effective algorithm to convert a Roman numeral string to an integer proceeds by iterating through the string, typically from left to right, comparing adjacent character values.

Here are the steps for the algorithm:

1. Initialize total_value to 0. This variable will store the final integer result.
2. Iterate through the Roman numeral string from the first character up to, but not including, the last character.
   • For each character current_char at index i, get its integer value, current_value.
   • Get the integer value of the next_char at index i+1, next_value.
   • Compare current_value with next_value:
     • If current_value < next_value (e.g., 'I' followed by 'V'), it's a subtractive case. Subtract current_value from total_value.
     • Otherwise (current_value >= next_value), it's an additive case. Add current_value to total_value.
3. Process the last character: After the loop finishes, the last character's value needs to be added to total_value because it never had a "next" character to compare against.
4. Return total_value.

This algorithm ensures that subtractive pairs are handled correctly, as the smaller preceding value is subtracted rather than added.

C Program Implementation Steps

To implement this conversion in C, you'll generally follow these steps:

1. Take a Roman number as input. This typically involves using scanf() or fgets() to read the Roman numeral string from the user.
2. Define the value of each Roman digit. A helper function is ideal for this. Using a switch statement within this function is a clean way to map each Roman character ('I', 'V', 'X', etc.) to its corresponding integer value.
3. Access each digit of a Roman number and compute the value. This involves iterating through the input string, character by character, and applying the core conversion algorithm described above. Inside the loop, you'll call your helper function to get the integer value of each character.
4. Print the computed value. Display the final integer result to the user.

Example C Code for Roman to Integer Conversion

Here's a complete C program demonstrating how to convert a Roman numeral string into its decimal equivalent:

#include <stdio.h> // For input/output functions like printf, scanf
#include <string.h> // For string manipulation functions like strlen

// Helper function to get the integer value of a single Roman character
int romanCharToInt(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 -1; // Indicate an invalid Roman character
    }
}

// Function to convert an entire Roman numeral string to an integer
int romanToInt(char *s) {
    int total_value = 0;
    int len = strlen(s);

    if (len == 0) {
        return 0; // Empty string, no value
    }

    for (int i = 0; i < len; i++) {
        int current_value = romanCharToInt(s[i]);

        // Check for invalid characters
        if (current_value == -1) {
            printf("Error: Invalid Roman numeral character '%c' found.\n", s[i]);
            return -1; // Or some other error indicator
        }

        // Look at the next character if not the last one
        if (i + 1 < len) {
            int next_value = romanCharToInt(s[i+1]);

            // If current value is less than next value, it's a subtractive case
            if (current_value < next_value) {
                total_value -= current_value;
            } else {
                total_value += current_value;
            }
        } else {
            // Last character, always add its value
            total_value += current_value;
        }
    }
    return total_value;
}

int main() {
    char roman_numeral[20]; // Assuming Roman numerals won't exceed 19 characters + null terminator

    printf("Enter a Roman numeral: ");
    if (scanf("%19s", roman_numeral) != 1) { // %19s to prevent buffer overflow
        printf("Error reading input.\n");
        return 1;
    }

    // Convert input to uppercase for consistent processing
    for (int i = 0; roman_numeral[i]; i++) {
        if (roman_numeral[i] >= 'a' && roman_numeral[i] <= 'z') {
            roman_numeral[i] = roman_numeral[i] - 32; // Convert to uppercase
        }
    }

    int result = romanToInt(roman_numeral);

    if (result != -1) { // Check if an error occurred during conversion
        printf("The integer equivalent of %s is: %d\n", roman_numeral, result);
    } else {
        printf("Failed to convert Roman numeral '%s' due to invalid characters.\n", roman_numeral);
    }

    return 0;
}

Helper Function romanCharToInt

The romanCharToInt function is a simple yet crucial component. It takes a single character and returns its corresponding integer value. The switch statement makes this mapping clear and efficient. Returning -1 is a common way to signal an invalid Roman character, which can be used for basic error checking.

Main Conversion Function romanToInt

This is where the core algorithm lives.

• It iterates through the Roman numeral string.
• Inside the loop, it fetches the values of the current_char and, if available, next_char.
• The if (current_value < next_value) condition is vital for handling subtractive cases (e.g., 'IV', 'IX'). If true, current_value is subtracted from the running total_value.
• Otherwise, current_value is added.
• The special handling for the last character (the else block when i + 1 == len) ensures its value is always added, as there's no subsequent character to form a subtractive pair.

Handling Invalid Input

The provided example includes a basic check for invalid Roman characters within the romanCharToInt function and the main romanToInt function. If romanCharToInt returns -1, it indicates an unrecognized character, prompting an error message. For robust applications, you might want more sophisticated validation, such as checking for valid sequence rules (e.g., 'IIX' is invalid). The input is also converted to uppercase to allow for case-insensitive input.

Practical Considerations

• Maximum Value: Standard Roman numerals typically represent numbers up to 3999 (MMMCMXCIX). This code will work correctly within this range.
• Error Reporting: For professional applications, returning an enum or using errno for error reporting instead of just -1 might be preferred, especially if -1 could be a valid output for some other conversion logic.
• Input Buffer Size: Always be mindful of buffer overflows when reading user input into fixed-size character arrays (char roman_numeral[20]). Using %19s in scanf (reserving one byte for the null terminator) is a good practice.