string-comparison algorithm for user defined dictionary

Question

In my project the user input is translated to a string in the form of [x,x,x,x,x,x,x,x,x,x] where x is a number between 1 and 8 and stored to a library of this type of strings. Later I have to compare the user new input with every string in that library.

So I'm trying to find the similarity between two strings of the mention format. I tried the Levenhstein distance algorithm but it does not suit my needs. For the strings [1,8,7,6,5,4,3,2,0,0] and [1,7,6,5,4,3,2,0,0,0], Levenhstein finds distance of 7 while in my prospective the distance is only one. Levenhstein only edits each character but does not shift the characters.

Can someone suggest another spell-check or string-compare algorithm with the criteria I mentioned before?

Levenshtein algorithm I used:

public static int getLevenshteinDistance(String s, String t)
{
   if (s == null || t == null)
   {
      throw new IllegalArgumentException("Strings must not be null");
   }
   int d[][]; // matrix
   int n; // length of s
   int m; // length of t
   int i; // iterates through s
   int j; // iterates through t
   char s_i; // ith character of s
   char t_j; // jth character of t
   int cost; // cost

   // Step 1
   n = s.length();
   m = t.length();
   if (n == 0)
   {
      return m;
   }
   if (m == 0)
   {
      return n;
   }
   d = new int[n + 1][m + 1];

   // Step 2
   for (i = 0; i <= n; i++)
   {
      d[i][0] = i;
   }

   for (j = 0; j <= m; j++)
   {
      d[0][j] = j;
   }

   // Step 3
   for (i = 1; i <= n; i++)
   {
      s_i = s.charAt(i - 1);

      // Step 4
      for (j = 1; j <= m; j++)
      {
         t_j = t.charAt(j - 1);

         // Step 5
         if (s_i == t_j)
         {
            cost = 0;
         }
         else
         {
            cost = 1;
         }

         // Step 6
         d[i][j] = min(d[i - 1][j] + 1, d[i][j - 1] + 1, d[i - 1][j - 1] + cost);
      }
   }

   // Step 7
   return d[n][m];
}