Custom Sort String: Modified BubbleSort

Problem is here (#416th in my solved list): https://leetcode.com/problems/custom-sort-string/

S and T are strings composed of lowercase letters. In S, no letter occurs more than once.

S was sorted in some custom order previously. We want to permute the characters of T so that they match the order that Swas sorted. More specifically, if x occurs before y in S, then x should occur before y in the returned string.

Return any permutation of T (as a string) that satisfies this property.

Example :
Input: 
S = "cba"
T = "abcd"
Output: "cbad"
Explanation: 
"a", "b", "c" appear in S, so the order of "a", "b", "c" should be "c", "b", and "a". 
Since "d" does not appear in S, it can be at any position in T. "dcba", "cdba", "cbda" are also valid outputs.

Note:

• S has length at most 26, and no character is repeated in S.
• T has length at most 200.
• S and T consist of lowercase letters only.

Here is the approach I used: the heart of the solution will be a modified BubbleSort (BubbleSort should work fine here given the small input size). First add all the elements of S to a hash table to indicate the position of each letter. Next, copy the letters in T to a StringBuilder (since you'll need to manipulate it) but do it in a way that you copy to the front the letters that appear in S, and to the back the letters that do not appear in S. Do not worry about the order of letters at this point, just split these two sets (set 1: in S. Set 2: not in S). Then perform a standard BubbleSort but when comparing the elements, reference the hash table to see which one is larger. That's about it. Code is below, cheers, ACC.

public class Solution
{
    public string CustomSortString(string S, string T)
    {
        Hashtable order = new Hashtable();

        for (int i = 0; i < S.Length; i++)
        {
            order.Add(S[i], S.Length - i);
        }

        StringBuilder sb = new StringBuilder(T);

        int left = 0;
        int right = T.Length - 1;
        for (int i = 0; i < T.Length; i++)
        {
            if (order.ContainsKey(T[i]))
            {
                sb[left++] = T[i];
            }
            else
            {
                sb[right--] = T[i];
            }
        }

        bool sorted = false;
        while (!sorted)
        {
            sorted = true;
            for (int i = 0; i < T.Length - 1; i++)
            {
                if (order.ContainsKey(sb[i]) && order.ContainsKey(sb[i + 1]) && (int)order[sb[i]] < (int)order[sb[i + 1]])
                {
                    char temp = sb[i];
                    sb[i] = sb[i + 1];
                    sb[i + 1] = temp;
                    sorted = false;
                }
            }
        }

        return sb.ToString();
    }
}