Convert Roman numeral to an integer

We will implement a simple algorithm to convert the Roman numeral to an integer in Javascript.

Example

Input:
'IV'
'XXIX'
'XVII'

Output:
4
29
17

Implementation

• We will create an array with sequence of roman letters and an object which will store the value of the respective roman letters.
• Then we will loop through each letter of the given roman numerals in reverse order.
• With each iteration we will check if the current letters sequence is greater or less than its previous letters.
• If it is less then we will add the value else we will subtract the value.
• Everything will be written in ES6.

let romanToInteger = (roman) => {
     //sequence of roman letters
     let arr = ['I','V','X','L','C','D','M'];
    
     //value of the respective roman letters
     let values = {
         I: 1,
         V: 5,
	 X: 10,
	 L: 50,
	 C: 100,
	 D: 500,
	 M: 1000
     };
     
     let sum = 0;
   
     //keep track of the previous index
     let prevIndex = 0;

     for(let i = roman.length - 1; i >= 0; i--){
        //if the current letter is having greater index than previous letter then add values
	if(arr.indexOf(roman[i]) >= prevIndex){
	   sum = sum + values[roman[i]]; 
	}else{
        //if the current letter is having lesser index than previous letter then sub values
	   sum = sum - values[roman[i]];
	}
        
        //store the index of the previous roman letters
	prevIndex = arr.indexOf(roman[i]);
     }

   return sum;
}

Input: 
console.log(romanToInteger('I'));
console.log(romanToInteger('VI'));
console.log(romanToInteger('XVI'));
console.log(romanToInteger('XXIX'));

Output:
1
6
16
29

How it works

/*How it works
'IV'

'I' is less than 'V' in the sequence ['I','V','X','L','C','D','M'], so we will subtract the value so 5 - 1 = 4;

'XIV' we are looping in reverse direction 'VIX' like this

sum = 'V' = 5;
As I sequence is less than V we will subtract it
sum = sum - 'I' = 5 - 1 = 4;
As X sequence is greater than V so we will add it
sum = sum +  'X' = 4 + 10 = 14
*/

Time complexity: O(n).

Space complexity: O(1).

Time and Space complexity

• We are iterating each letter of the given string, so Time complexity is O(n) where n is the length of the string.
• We are using constant space, so Space complexity is O(1).