//The below function is my implementation for question 2.
//
//:p is the size of the lexicographical order,
//:n is the number of strings in the string array,
//:m is the size of the strings
//
//Run-Time: F(n) = p+n*(m+logn)= O(n*logn) or O(n*m) depending if logn > m or m > logn and noting that p can be at maximum,
//the size of the alphabet, and thus essentially a constant,
//
public static String[] Sort(String[] un_sorted, string order)
{
Dictionary<string, int> priority = new Dictionary<string, int>();
BST string_score = new BST();
//iterate through every charcter in the user-specified lexicographical ordering
//assign a priority to each character corresponding to their index in the string+1
priority.Add(" ", 0);
for (int i = 0; i < order.Length; i++) //O(p)
{
priority.Add(order[i].ToString(), i + 1);
}
for (int i = 0; i < un_sorted.Length; i++) //O(n)
{
string word = un_sorted[i];
if (word != null)
{
double score = -1.0;
if (word.Length > 0)
{
score = 0.0;
//Calculate a score similar to calculting the value of a base N character array
//In this case, our N would be order.Length + 1
for (int j = 0; j < word.Length; j++) //O(m)
{
if (priority.ContainsKey(word[j].ToString()))
score += priority[word[j].ToString()] * (double)Math.Pow(order.Length + 1, order.Length - j);
else
throw new Exception();
}
}
//insert each score with their corresponding string as a key,value pair into a BST. This ensures the strings are sorted based on their score form lowest to greatest,
//when an in-order traveral is performed
string_score.insert(score, word); //O(logn)
}
}
return string_score.inOrderTraversal().ToArray();
}