FuzzyQuery中计算edit distance的算法函数

FuzzyQuery使用中有一个计算edit distance的函数，在类FuzzyTermEnum中，如下：

 

 /******************************
   * Compute Levenshtein distance
   ******************************/
  
  /**
   * <p>Similarity returns a number that is 1.0f or less (including negative numbers)
   * based on how similar the Term is compared to a target term.  It returns
   * exactly 0.0f when
   * <pre>
   *    editDistance &gt; maximumEditDistance</pre>
   * Otherwise it returns:
   * <pre>
   *    1 - (editDistance / length)</pre>
   * where length is the length of the shortest term (text or target) including a
   * prefix that are identical and editDistance is the Levenshtein distance for
   * the two words.</p>
   *
   * <p>Embedded within this algorithm is a fail-fast Levenshtein distance
   * algorithm.  The fail-fast algorithm differs from the standard Levenshtein
   * distance algorithm in that it is aborted if it is discovered that the
   * minimum distance between the words is greater than some threshold.
   *
   * <p>To calculate the maximum distance threshold we use the following formula:
   * <pre>
   *     (1 - minimumSimilarity) * length</pre>
   * where length is the shortest term including any prefix that is not part of the
   * similarity comparison.  This formula was derived by solving for what maximum value
   * of distance returns false for the following statements:
   * <pre>
   *   similarity = 1 - ((float)distance / (float) (prefixLength + Math.min(textlen, targetlen)));
   *   return (similarity > minimumSimilarity);</pre>
   * where distance is the Levenshtein distance for the two words.
   * </p>
   * <p>Levenshtein distance (also known as edit distance) is a measure of similarity
   * between two strings where the distance is measured as the number of character
   * deletions, insertions or substitutions required to transform one string to
   * the other string.
   * @param target the target word or phrase
   * @return the similarity,  0.0 or less indicates that it matches less than the required
   * threshold and 1.0 indicates that the text and target are identical
   */
  private float similarity(final String target) {
    final int m = target.length();
    final int n = text.length;
    if (n == 0)  {
      //we don't have anything to compare.  That means if we just add
      //the letters for m we get the new word
      return prefix.length() == 0 ? 0.0f : 1.0f - ((float) m / prefix.length());
    }
    if (m == 0) {
      return prefix.length() == 0 ? 0.0f : 1.0f - ((float) n / prefix.length());
    }

    final int maxDistance = calculateMaxDistance(m);

    if (maxDistance < Math.abs(m-n)) {
      //just adding the characters of m to n or vice-versa results in
      //too many edits
      //for example "pre" length is 3 and "prefixes" length is 8.  We can see that
      //given this optimal circumstance, the edit distance cannot be less than 5.
      //which is 8-3 or more precisely Math.abs(3-8).
      //if our maximum edit distance is 4, then we can discard this word
      //without looking at it.
      return 0.0f;
    }

    // init matrix d
    for (int i = 0; i<=n; ++i) {
      p[i] = i;
    }

    // start computing edit distance
    for (int j = 1; j<=m; ++j) { // iterates through target
      int bestPossibleEditDistance = m;
      final char t_j = target.charAt(j-1); // jth character of t
      d[0] = j;

      for (int i=1; i<=n; ++i) { // iterates through text
        // minimum of cell to the left+1, to the top+1, diagonally left and up +(0|1)
        if (t_j != text[i-1]) {
          d[i] = Math.min(Math.min(d[i-1], p[i]),  p[i-1]) + 1;
		} else {
          d[i] = Math.min(Math.min(d[i-1]+1, p[i]+1),  p[i-1]);
		}
        bestPossibleEditDistance = Math.min(bestPossibleEditDistance, d[i]);
      }

      //After calculating row i, the best possible edit distance
      //can be found by found by finding the smallest value in a given column.
      //If the bestPossibleEditDistance is greater than the max distance, abort.

      if (j > maxDistance && bestPossibleEditDistance > maxDistance) {  //equal is okay, but not greater
        //the closest the target can be to the text is just too far away.
        //this target is leaving the party early.
        return 0.0f;
      }

      // copy current distance counts to 'previous row' distance counts: swap p and d
      int _d[] = p;
      p = d;
      d = _d;
    }