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 40Input: 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;
}
Output:
Integer form of Roman Numeral is 1904Complexity 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 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 1904Time complexity - O(N)
Auxiliary Space - O(1)
Please refer complete article on
Converting Roman Numerals to Decimal lying between 1 to 3999for more details!
