Roman Number to Integer Example in JAVA, PHP, JS, PYTHON
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
// 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 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
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”;
?>
Output
Integer form of Roman Numeral is 1904
JS
<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 roman 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
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”))
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.