PHP Program to Convert Roman Numerals To Decimal Lying Between 1 to 3999

Given a Romal numeral, the task is to find its corresponding decimal value.

Examples

Input: IX
Output: 9
IX is a Roman symbol which represents 9 

Input: XL
Output: 40
XL is a Roman symbol which represents 40

Input: MCMIV
Output: 1904
M is a thousand, CM is nine hundred and IV is four

Roman numerals are based on the following symbols.

Approach: A number in Roman Numerals is a string of these symbols written in descending order(e.g. M's first, followed by D's, etc.). However, in a few specific cases, to avoid four characters being repeated in succession(such as IIII or XXXX), subtractive notation is often used as follows: 

• I placed before V or X indicates one less, so four is IV (one less than 5) and 9 is IX (one less than 10).
• X placed before L or C indicates ten less, so forty is XL (10 less than 50) and 90 is XC (ten less than a hundred).
• C placed before D or M indicates a hundred less, so four hundred is CD (a hundred less than five hundred) and nine hundred is CM (a hundred less than a thousand).

Algorithm to convert Roman Numerals to Integer Number:  

• Split the Roman Numeral string into Roman Symbols (character).
• Convert each symbol of Roman Numerals into the value it represents.
• Take symbol one by one from starting from index 0: 
  
  • If current value of symbol is greater than or equal to the value of next symbol, then add this value to the running total.
  • else subtract this value by adding the value of next symbol to the running total.

Following is the implementation of the above algorithm: 

<?php
// PHP Program to convert Roman
// Numerals to Numbers

// This function returns
// value of a Roman symbol
function value($r) {
    if ($r == "I") {
        return 1;
    }
    if ($r == "V") {
        return 5;
    }
    if ($r == "X") {
        return 10;
    }
    if ($r == "L") {
        return 50;
    }
    if ($r == "C") {
        return 100;
    }
    if ($r == "D") {
        return 500;
    }
    if ($r == "M") {
        return 1000;
    }

    return -1;
}

// Returns decimal value
// of roman numeral
function romanToDecimal(&$str) {
  
    // Initialize result
    $res = 0;

    // Traverse given input
    for ($i = 0; $i < strlen($str); $i++) {
      
        // Getting value of
        // symbol s[i]
        $s1 = value($str[$i]);

        if ($i + 1 < strlen($str)) {
          
            // Getting value of
            // symbol s[i+1]
            $s2 = value($str[$i + 1]);

            // Comparing both values
            if ($s1 >= $s2) {
              
                // Value of current symbol
                // is greater or equal to
                // the next symbol
                $res = $res + $s1;
            } else {
                $res = $res + $s2 - $s1;

                // Value of current symbol is
                // less than the next symbol
                $i++;
            }
        } else {
            $res = $res + $s1;
            $i++;
        }
    }
    return $res;
}

// Driver Code

// Considering inputs
// given are valid
$str = "MCMIV";
echo "Integer form of Roman Numeral is " 
  	. romanToDecimal($str), "";

?>

Integer form of Roman Numeral is 1904

Complexity Analysis

• Time Complexity: O(n), where n is the length of the string. Only one traversal of the string is required.
• Space Complexity: O(1). As no extra space is required.

Please refer complete article on Converting Roman Numerals to Decimal lying between 1 to 3999 for more details!