The solution below is functional.
 romanMapInt is a helper function that has a switch statement that maps each single Roman numeral to its int value;
I → 1
V → 5
X → 10
L → 50
C → 100
D → 500
M → 1000
Let curr = current numeral, and prev = previous numeral for the purpose of this explanation.
 romanToInt iterates through each character in String s. Notice that Roman numerals are always in the order of greatest to least (curr <= prev), except in the case of 4, 40, 400, etc. For these exceptional numbers, a smaller numeral comes before a larger one to symbolize subtraction.
We can pretty much extrapolate this observation into the following rule:

if curr is less than or equal to prev, add up as usual. Roman numerals can be viewed as a sum of smaller units

...except for 4, 40, 400, etc. where curr is greater than prev, which warrants subtraction of prev from curr
I came up with a simple algorithm to properly subtract the right amount when 4, 40, 400 occur. This is by no means the one correct answer; there are definitely other ways to go about it. This method was just the clearest for me.
class Solution {
public int romanToInt(String s) {
length = s.length();
int prev = 0;
int sum = 0;
for (int i=0; i<length; i++) {
int curr = romanMapInt(s.charAt(i));
if ( curr < prev ) {
sum += curr;
}
else { //4, 40, 400
sum += curr;
sum = 2 * prev;
}
prev = curr;
}
}
public int romanMapInt(char c) {
int num = 0;
switch(c){
case 'I':
num = 1;
break;
case 'V':
num = 5;
break;
case 'X':
num = 10;
break;
case 'L':
num = 50;
break;
case 'C':
num = 100;
break;
case 'D':
num = 500;
break;
case 'M':
num = 1000;
break;
default:
num = 0;
break;
}
return num;
}
}