C++ Program For 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++
// 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; } |
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++
// C++ Program to convert Roman // Numerals to Numbers #include <bits/stdc++.h> using namespace std; // This function returns value // of a Roman symbol int 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 Code int main() { // Considering inputs given are valid string str = "MCMIV"; cout << "Integer form of Roman Numeral is " << romanToDecimal(str) << endl; return 0; } |
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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