PHP Program for Converting Roman Numerals to Decimal Lying Between 1 to 3999

Roman numerals are characters used in a numeric notation system based on the ancient Roman system. In this tutorial, we'll convert Roman numeral strings to decimal values in the range 1 to 3999.

Roman Numeral System

Roman numerals follow descending order but use subtractive notation to avoid four consecutive characters. Here are the main symbols

Algorithm

The conversion follows these rules

• If current symbol value ? next symbol value, add current value
• If current symbol value
• Process the string from left to right

Example

Let's implement the conversion function ?

<?php
function romanValue($ch) {
    $val = -1;
    if ($ch == 'I')
        $val = 1;
    else if ($ch == 'V')
        $val = 5;
    else if ($ch == 'X')
        $val = 10;
    else if ($ch == 'L')
        $val = 50;
    else if ($ch == 'C')
        $val = 100;
    else if ($ch == 'D')
        $val = 500;
    else if ($ch == 'M')
        $val = 1000; 
    return $val;
}

function convertRomanToDecimal($str) {
    $decValue = 0;
    $n = strlen($str);
    
    for ($i = 0; $i < $n; $i++) {
        $current = romanValue($str[$i]); 
        
        if ($i + 1 < $n) {
            $next = romanValue($str[$i + 1]); 
            
            if ($current >= $next) {
                $decValue += $current;
            } else {
                $decValue += $next - $current; 
                $i++; 
            }
        } else {
            $decValue += $current; 
        }
    }
    
    return $decValue;
}

// Test examples
$examples = ["DCCCLXXIV", "CMXCIX", "I"];

foreach ($examples as $roman) {
    $decimal = convertRomanToDecimal($roman);
    echo "Roman: $roman = Decimal: $decimal<br>";
}
?>

Roman: DCCCLXXIV = Decimal: 874
Roman: CMXCIX = Decimal: 999
Roman: I = Decimal: 1

How It Works

• DCCCLXXIV: D(500) + C(100) + C(100) + C(100) + L(50) + X(10) + X(10) + IV(4) = 874
• CMXCIX: CM(900) + XC(90) + IX(9) = 999
• I: I(1) = 1

Time and Space Complexity

The algorithm has O(N) time complexity where N is the string length, and O(1) space complexity as no extra storage is used.

Conclusion

This PHP implementation efficiently converts Roman numerals to decimal values using a single-pass algorithm that handles subtractive notation correctly for the range 1-3999.