Converting Roman Numerals to Decimal lying between 1 to 3999
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 symbolint 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 numaralint 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 Codeint 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 Numbersimport 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 symboldef 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 -1def 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 codeprint("Integer form of Roman Numeral is"),print(romanToDecimal("MCMIV")) |
C#
// C# Program to convert Roman// Numerals to Numbersusing 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 symbolfunction 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 numeralfunction 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') |
Javascript
<script>// Program to convert Roman// Numerals to Numberspublic // 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; } // Finds decimal value of a // given romal numeral function romanToDecimal( str) { // Initialize result var res = 0; for (i = 0; i < str.length; i++) { // Getting value of symbol s[i] var s1 = value(str.charAt(i)); // Getting value of symbol s[i+1] if (i + 1 < str.length) { var 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 // Considering inputs given are valid var str = "MCMIV"; document.write("Integer form of Roman Numeral" + " is " + romanToDecimal(str));// This code contributed by umadevi9616</script> |
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.
Another solution –
C++
// Program to convert Roman// Numerals to Numbers#include <bits/stdc++.h>using namespace std;// This function returns value// of a Roman symbolint romanToDecimal(string& str){ map<char, int> m; m.insert({ 'I', 1 }); m.insert({ 'V', 5 }); m.insert({ 'X', 10 }); m.insert({ 'L', 50 }); m.insert({ 'C', 100 }); m.insert({ 'D', 500 }); m.insert({ 'M', 1000 }); int sum = 0; for (int i = 0; i < str.length(); i++) { /*If present value is less than next value, subtract present from next value and add the resultant to the sum variable.*/ if (m[str[i]] < m[str[i + 1]]) { sum+=m[str[i+1]]-m[str[i]]; i++; continue; } sum += m[str[i]]; } return sum;}// Driver Codeint 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 Numbersimport java.util.Map;import java.util.HashMap;class GFG{ private static final Map<Character, Integer> roman = new HashMap<Character, Integer>(){{ put('I', 1); put('V', 5); put('X', 10); put('L', 50); put('C', 100); put('D', 500); put('M', 1000);}};// This function returns value// of a Roman symbolprivate static int romanToInt(String s){ int sum = 0; int n = s.length(); for(int i = 0; i < n; i++) { // If present value is less than next value, // subtract present from next value and add the // resultant to the sum variable. if (i != n - 1 && roman.get(s.charAt(i)) < roman.get(s.charAt(i + 1))) { sum += roman.get(s.charAt(i + 1)) - roman.get(s.charAt(i)); i++; } else { sum += roman.get(s.charAt(i)); } } return sum;}// Driver Codepublic static void main(String[] args){ // Considering inputs given are valid String input = "MCMIV"; System.out.print("Integer form of Roman Numeral is " + romanToInt(input));}}// This code is contributed by rahuldevgarg |
Output
Integer form of Roman Numeral is 1904
Time complexity – O(N)
Auxiliary Space – O(1)
Another Solution: Shorter code using python
Python3
def romanToInt(s): translations = { "I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000 } number = 0 s = s.replace("IV", "IIII").replace("IX", "VIIII") s = s.replace("XL", "XXXX").replace("XC", "LXXXX") s = s.replace("CD", "CCCC").replace("CM", "DCCCC") for char in s: number += translations[char] print(number) romanToInt('MCMIV') |
Output
1904
Time complexity – O(N)
Auxiliary Space – O(1)
References: https://en.wikipedia.org/wiki/Roman_numerals
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