 # 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:

1. Split the Roman Numeral string into Roman Symbols (character).
2. Convert each symbol of Roman Numerals into the value it represents.
3. Take symbol one by one from starting from index 0:
1. If current value of symbol is greater than or equal to the value of next symbol, then add this value to the running total.
2. 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.