Every solution I've found uses the following object.
function converter(num) {
var romanKeys =
{M:1000,CM:900,D:500,CD:400,C:100,XC:90,L:50,XL:40,X:10,IX:9,V:5,IV:4,I:1}
When attempting the problem myself, I wasn't too sure which roman numerals were redundant when constructing the object. Procedurally, how do we arrive to this object? e.g How do I know that "VI: 6" is unnecessary but "IV: 4" is?
When a symbol appears after a larger (or equal) symbol it is added Example: VI = V + I = 5 + 1 = 6 Example: LXX = L + X + X = 50 + 10 + 10 = 70
But if the symbol appears before a larger symbol it is subtracted Example: IV = V − I = 5 − 1 = 4 Example: IX = X − I = 10 − 1 = 9
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.
When you are scanning a roman number you are looking from left to right at each symbol and if it appears before a larger symbol, you take them together, do the substraction and add it to the result, then move to the symbol after them. Otherwise you take a single symbol and add its value to the result and move to the next symbol.
For example for XIV:
1) result = 0
2) X < I => result += 10 (result = 10)
3) I < V => result += (5-1) (result = 14)
Note that if you are using that mapping, you only need the combinations where the second symbol is greater than the first one for which the substraction rule applies, as noted above (CM, CD, XC, XL, IX, IV).
Having something like XI in that mapping would give you a wrong result. For XIV you will have XI (11) + V (5) = 16, not X (10) + IV (4) = 14.