Leetcode: Roman digit to integer
Run time is linear, and memory usage is constant (and small), so I don't think you're going to see much improvement in either.  

You might be able to make some slight improvements by using pointers in unsafe mode (see https://stackoverflow.com/questions/13179554/is-it-faster-to-access-char-in-string-via-operator-or-faster-to-access-char-i), but unless you're processing a very large number of strings this is probably not necessary.  As always, profile before and after making any optimizations!

Stylistically, there are a few improvements that could be made:


Declare your variables in separate statements.
HighestValue should be highestValue.
In CharacterValue, you don't need to break when you're returning anyway.
It would be clearer to remove the blank line between the inner if and else.
You don't need the outer if/else for the length of the string; the code inside the main case would handle a length-1 string fine.
The way the logic works, the first item doesn't have to be handled as a special case, so this could be rewritten as a for loop, which would make it (for many people) easier to read.


And one functional one - your code doesn't currently handle the string being null or empty; it should either return 0 or throw an appropriate exception in that case, depending on whether you consider that to be valid input.

So for example:

    public static int RomanToInt(string s)
    {
        if (string.IsNullOrEmpty(s))
        {
            return 0;
        }

        int highestValue = 0;
        int number = 0;

        for(int currentIndex = s.Length - 1; currentIndex &gt;= 0; currentIndex--)
        {
            int currentValue = CharacterValue(s[currentIndex]);

            if (currentValue &gt;= highestValue)
            {
                number += currentValue;
                highestValue = currentValue;
            }
            else
            {
                number -= currentValue;
            }
        }

        return number;
    }

    private static int CharacterValue(char c)
    {
        switch (c)
        {
            case 'I': return 1;
            case 'V': return 5;
            case 'X': return 10;
            case 'L': return 50;
            case 'C': return 100;
            case 'D': return 500;
            case 'M': return 1000;
            default:  return 0;
        }
    }