Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.

 

Symbol                Value

I             1
V             5
X             10
L             50
C             100
D             500
M             1000

 

For example, 2 is written as II in Roman numeral, just two one’s added together. 12 is written as XII, which is simply X + II. The number 27 is written as XXVII, which is XX + V + II.

Roman numerals are usually written largest to smallest from left to right. However, the numeral for four is not IIII. Instead, the number four is written as IV. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as IX. There are six instances where subtraction is used:

• I can be placed before V (5) and X (10) to make 4 and 9.
• X can be placed before L (50) and C (100) to make 40 and 90.
• C can be placed before D (500) and M (1000) to make 400 and 900.

Given a roman numeral, convert it to an integer.

 

Example 1:

Input:

 s = "III"

Output:

 3

Example 2:

Input:

 s = "IV"

Output:

 4

Example 3:

Input:

 s = "IX"

Output:

 9

Example 4:

Input:

 s = "LVIII"

Output:

 58

Explanation:

 L = 50, V= 5, III = 3.

Example 5:

Input:

 s = "MCMXCIV"

Output:

 1994

Explanation:

 M = 1000, CM = 900, XC = 90 and IV = 4.

 

Constraints:

• 1 <= s.length <= 15
• s contains only the characters ('I', 'V', 'X', 'L', 'C', 'D', 'M').
• It is guaranteed that s is a valid roman numeral in the range [1, 3999].

This problem was taken from Leetcode Roman To Integer

 

Solution 1: Left to right pass

/**
 * @param {string} s
 * @return {number}
 */
var romanToInt = function(s) {
    var len = s.length;
    var i = 0;
    var map = {
        'I': 1,
        'V': 5,
        'X': 10,
        'L': 50,
        'C': 100,
        'D': 500,
        'M': 1000
    }
    var sum = 0;
    while(i < len) {
        var currentVal = map[ s[i] ];
        var nextVal = map[ s[i + 1] ];
        if( currentVal < nextVal) {
            sum += nextVal - currentVal;
            i ++;            
        }
        else {
            sum += currentVal;
        }
        i ++;
    }
    return sum;
};

Solution 2: Left to right (or right to left) pass improved

/**
 * @param {string} s
 * @return {number}
 */
var romanToInt = function(s) {
    var len = s.length;
    var i = 0;
    var map = {
        '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
    }
    var sum = 0;
    while(i < len) {
        var currentVal = map[ s[i] ];
        var nextVal = map[ s[i + 1] ];
        if( currentVal < nextVal) {
            var sumbol = s[i] + s[i+1];
            sum += map[sumbol];
            i ++;            
        }
        else {
            sum += currentVal;
        }
        i ++;
    }
    return sum;
};

Solution3: Right to left pass

In the “subtraction” cases, such as XC, we’ve been updating our running sum as follows:

sum += value(C) - value(X)

However, notice that this is mathematically equivalent to the following:

sum += value(C)
sum -= value(X)

Utilizing this means that we can process one symbol each time we go around the main loop. We still need to determine whether or not our current symbol should be added or subtracted by looking at the neighbour though.

This way we could start from the most right symbol an initialize the sym with it, since every most right symbol will always be added to the sum.

 

/**
 * @param {string} s
 * @return {number}
 */
var romanToInt = function(s) {
    var len = s.length;
    var i = len - 1;
    var map = {
        'I': 1,
        'V': 5,
        'X': 10,
        'L': 50,
        'C': 100,
        'D': 500,
        'M': 1000
    }
    var sum = map[ s[i] ];
    i --;
    while(i > -1) {
        var currentVal = map[ s[i] ];
        var prevVal = map[ s[i + 1] ];
        if( currentVal < prevVal) {
            sum -= currentVal;          
        }
        else {
            sum += currentVal;
        }
        i --;
    }
    return sum;
};