Given a Romal numeral, the task is to find its corresponding decimal value.
Example :
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.
SYMBOL VALUE I 1 IV 4 V 5 IX 9 X 10 XL 40 L 50 XC 90 C 100 CD 400 D 500 CM 900 M 1000
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 ), "" ;
// This code is contributed by ajit ?> |
Output:
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!