static int leven(S s, S t) {
  // degenerate cases
  if (s.equals(t)) return 0;
  int ls = s.length(), lt = t.length();
  if (ls == 0) return lt;
  if (lt == 0) return ls;

  // create two work vectors of integer distances
  int[] v0 = new int[lt + 1];
  int[] v1 = new int[lt + 1];

  // initialize v0 (the previous row of distances)
  // this row is A[0][i]: edit distance for an empty s
  // the distance is just the number of characters to delete from t
  for (int i = 0; i < v0.length; i++)
      v0[i] = i;

  for (int i = 0; i < ls; i++)
  {
      // calculate v1 (current row distances) from the previous row v0

      // first element of v1 is A[i+1][0]
      //   edit distance is delete (i+1) chars from s to match empty t
      v1[0] = i + 1;

      // use formula to fill in the rest of the row
      for (int j = 0; j < lt; j++)
      {
          int cost = s.charAt(i) == t.charAt(j) ? 0 : 1;
          v1[j + 1] = Math.min(Math.min(v1[j] + 1, v0[j + 1] + 1), v0[j] + cost);
      }

      // swap arrays
      int[] v = v1; v1 = v0; v0 = v;
  }

  return v0[lt];
}

from Wikipedia, translated to JavaX