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:
C++
// Program to convert Roman // Numerals to Numbers #include <bits/stdc++.h> using namespace std; // This function returns value // of a Roman symbol int value( char 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 numaral int romanToDecimal(string& str) { // Initialize result int res = 0; // Traverse given input for ( int i = 0; i < str.length(); i++) { // Getting value of symbol s[i] int s1 = value(str[i]); if (i + 1 < str.length()) { // Getting value of symbol s[i+1] int 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 { // Value of current symbol is // less than the next symbol res = res + s2 - s1; i++; } } else { res = res + s1; } } return res; } // Driver Code int main() { // Considering inputs given are valid string str = "MCMIV" ; cout << "Integer form of Roman Numeral is " << romanToDecimal(str) << endl; return 0; } |
Java
// Program to convert Roman // Numerals to Numbers import java.util.*; public class RomanToNumber { // This function returns // value of a Roman symbol int value( char 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 ; } // Finds decimal value of a // given romal numeral int romanToDecimal(String str) { // Initialize result int res = 0 ; for ( int i = 0 ; i < str.length(); i++) { // Getting value of symbol s[i] int s1 = value(str.charAt(i)); // Getting value of symbol s[i+1] if (i + 1 < str.length()) { int s2 = value(str.charAt(i + 1 )); // Comparing both values if (s1 >= s2) { // Value of current symbol // is greater or equalto // the next symbol res = res + s1; } else { // Value of current symbol is // less than the next symbol res = res + s2 - s1; i++; } } else { res = res + s1; } } return res; } // Driver Code public static void main(String args[]) { RomanToNumber ob = new RomanToNumber(); // Considering inputs given are valid String str = "MCMIV" ; System.out.println( "Integer form of Roman Numeral" + " is " + ob.romanToDecimal(str)); } } |
Python
# Python program to convert Roman Numerals # to Numbers # This function returns value of each Roman symbol def 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 def romanToDecimal( str ): res = 0 i = 0 while (i < len ( str )): # Getting value of symbol s[i] s1 = value( str [i]) if (i + 1 < len ( 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 i = i + 1 else : # Value of current symbol is greater # or equal to the next symbol res = res + s2 - s1 i = i + 2 else : res = res + s1 i = i + 1 return res # Driver code print ( "Integer form of Roman Numeral is" ), print (romanToDecimal( "MCMIV" )) |
C#
// C# Program to convert Roman // Numerals to Numbers using System; class GFG { // This function returns value // of a Roman symbol public virtual int value( char 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; } // Finds decimal value of a // given romal numeral public virtual int romanToDecimal( string str) { // Initialize result int res = 0; for ( int i = 0; i < str.Length; i++) { // Getting value of symbol s[i] int s1 = value(str[i]); // Getting value of symbol s[i+1] if (i + 1 < str.Length) { int s2 = value(str[i + 1]); // Comparing both values if (s1 >= s2) { // Value of current symbol is greater // or equalto the next symbol res = res + s1; } else { res = res + s2 - s1; i++; // Value of current symbol is // less than the next symbol } } else { res = res + s1; i++; } } return res; } // Driver Code public static void Main( string [] args) { GFG ob = new GFG(); // Considering inputs given are valid string str = "MCMIV" ; Console.WriteLine( "Integer form of Roman Numeral" + " is " + ob.romanToDecimal(str)); } } // This code is contributed by Shrikant13 |
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 ; $i ++; // Value of current symbol is // less than the next symbol } } 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 ), "\n" ; // This code is contributed by ajit ?> |
Python3
def romanToInt(rom): value = { 'M' : 1000 , 'D' : 500 , 'C' : 100 , 'L' : 50 , 'X' : 10 , 'V' : 5 , 'I' : 1 } # Initialize previous character and answer p = 0 ans = 0 # Traverse through all characters n = len (rom) for i in range (n - 1 , - 1 , - 1 ): # If greater than or equal to previous, # add to answer if value[rom[i]] > = p: ans + = value[rom[i]] # If smaller than previous else : ans - = value[rom[i]] # Update previous p = value[rom[i]] print (ans) romanToInt( 'MCMIV' ) |
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.
References: https://en.wikipedia.org/wiki/Roman_numerals
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