Given a Roman 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:
Java
// 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 roman 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)); }} |
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 –
Java
// 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)
Please refer complete article on Converting Roman Numerals to Decimal lying between 1 to 3999 for more details!
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