"Edit Distance" algorithm

Question

I have a piece of code that calculates the edit distance between words and works, but it's apparently not fast enough.

ClosestWords.java:

import java.util.LinkedList;
import java.util.List;

public class ClosestWords {
  LinkedList<String> closestWords = null;

  int closestDistance = -1;

  public int dynamicEditDistance(char[] str1, char[] str2){
        int temp[][] = new int[str1.length+1][str2.length+1];

        for(int i=0; i < temp[0].length; i++){
            temp[0][i] = i;
        }

        for(int i=0; i < temp.length; i++){
            temp[i][0] = i;
        }

        for(int i=1;i <=str1.length; i++){
            for(int j=1; j <= str2.length; j++){
                if(str1[i-1] == str2[j-1]){
                    temp[i][j] = temp[i-1][j-1];
                }else{
                    temp[i][j] = 1 + Math.min(temp[i-1][j-1], Math.min(temp[i-1][j], temp[i][j-1]));
                }
            }
        }
        return temp[str1.length][str2.length];

    }

  public ClosestWords(String w, List<String> wordList) {
    for (String s : wordList) {
      int dist = dynamicEditDistance(w.toCharArray(), s.toCharArray());
      if (dist < closestDistance || closestDistance == -1) {
        closestDistance = dist;
        closestWords = new LinkedList<String>();
        closestWords.add(s);
      }
      else if (dist == closestDistance)
        closestWords.add(s);
    }
  }

  int getMinDistance() {
    return closestDistance;
  }

  List<String> getClosestWords() {
    return closestWords;
  }
}

Main.java:

import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.LinkedList;
import java.util.List;

public class Main {

  public static List<String> readWordList(BufferedReader input) throws IOException {
    LinkedList<String> list = new LinkedList<String>();
    while (true) {
      String s = input.readLine();
      if (s.equals("#"))
        break;
      list.add(s);
    }
    return list;
  }

  public static void main(String args[]) throws IOException {
    BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in, "UTF-8"));
    List<String> wordList = readWordList(stdin);
    String word;
    while ((word = stdin.readLine()) != null) {
      ClosestWords closestWords = new ClosestWords(word, wordList);
      System.out.print(word + " (" + closestWords.getMinDistance() + ")");
      for (String w : closestWords.getClosestWords())
        System.out.print(" " + w);
      System.out.println();
    }
  }
}

Example input:

skål
skålar
skålen
skålens
skålform
#
kål
k
b
sklfrm
skala

Example Output:

kål (1) skål
k (3) skål
b (4) skål
sklfrm (2) skålform
skala (2) skål skålar

The upper part of the input are all the "correct" words and the lower part of the input (below the '#') are the words that need to be corrected. The output lines are of the form:

misspeltWord (minEditDistance) 
listOfPossibleCorrectWordsThatShareTheSameEditDistance

Is there a way to make this code more efficient? I am running the code through a sort of "speed test" and it keeps failing on the last part of the test.

Answer 1

Preliminaries: there's strategy, and there's tactics.
A somewhat common procedure to tackle performance problems is to look at "inner" loops first - not entirely wrong, but the golden rule is
measure.
(And, when turning to others for support, provide measurement results and a test data generator or test data.)

Some statements regarding edit distance:
• difference in length gives a lower bound on insertions+deletions
• accumulated differences in frequency gives a lower bound on 2*replacements+insertions+deletions

---

Review proper using m = len(str1) and n = len(str2):

• Document your code. In the code.
• design
  • I don't like heavyweight constructors
   From the preparation possible, I'd prefer a constructor taking a set of words and
  • a "query function" with a word as a parameter (String rather than char[]) -
   too bad returning a multipart result gets verbose, ugly or both in Java
• program against interfaces, not implementations
  List<String> closestWords;
• dynamicEditDistance()
  • I can guess what's dynamic about it, but that's an implementation detail; such does not belong in a method name: editDistance()
  • does not use any instance member: make it static
  • with "the usual" cost model you don't need a full m×n array
  • If your edit cost is symmetric (cost(insertion) == cost(deletion) && cost(replace(a, b)) == cost(replace(b, a))), you don't need previous row(s) and previous column(s).
  • you iterate the first index in the outer loop and the second one in the inner:
    That's the sequence I'd arrange initialisation
    (I'd even use j in the 2nd loop)
• work currently done in ClosestWords():
  • code the way you think about the procedure/solution
    - I'd think w doesn't change, let's get the chars exactly once
     (a nifty language system might be doing this for you)
  • prefer List.clear() over instantiation
  • (today,) I'd prefer redundantly checking for minimum distance over repeating the add():

          closestWords = new LinkedList<>();
          closestDistance = Integer.MAX_VALUE;
          char[] chars = w.toCharArray();
          for (String s : wordList) {
            int dist = editDistance(chars, s.toCharArray());
            if (dist < closestDistance) {
              closestDistance = dist;
              closestWords.clear();
            }
            if (dist == closestDistance)
              closestWords.add(s);
          }

A "slightly" weirder approach is to handle words from the word list in order of length, first descending from same length, then above and increasing; terminating both when "more extremal length words" can't possibly have a smaller edit distance.
Trying to avoid duplicating the code now extracted as handleDistance() "in line" got out of hand - not pleased, still.
Don't do like I do (not documenting tally (, words) & init()),
do like I say (better than handleDistance() & query(), still)

    final Comparator<String> tally = new Comparator<String>() { @Override
            public int compare(String l, String r) {
                if (l.equals(r))
                    return 0;
                final int ll = l.length(), rl = r.length();
                return ll < rl ? -1
                    : rl < ll ? 1
                      : l.compareTo(r);
            }
        };
    String[] words;
    void init(Collection<String> allWords) {
        words = allWords.toArray(NOSTRINGS);
        Arrays.sort(words, tally);
    }
    /** handles the distance between one pair of <code>String</code>s
     *  updating <code>closestDistance</code> and <code>closestWords</code>
     * @param chars chars of the query <code>String</code>
     * @param s <code>String</code> from <code>words</code>
     */
    void handleDistance(final char[] chars, String s) {
        // System.out.println(">>>" + s + '<');
        final int dist = editDistance(chars, s.toCharArray());
        if (dist < closestDistance) {
            closestDistance = dist;
            closestWords.clear();
        }
        if (dist == closestDistance)
            closestWords.add(s);
    }

    /** queries <code>words</code> for lowest edit distance to <code>w</code>
     *  updating <code>closestDistance</code> and <code>closestWords</code>
     * @param w <code>String</code> to find closest words to
     * @return closest words
     */
    public Collection<String> query(String w) {
        final char[] chars = w.toCharArray();
        int sameLength = Arrays.binarySearch(words, w, tally);
        if (0 <= sameLength) {
            closestDistance = 0;
            return closestWords = Collections.singletonList(words[sameLength]);
        }
        closestDistance = Integer.MAX_VALUE;
        sameLength = -sameLength; // insert index + 1
        for (int i = sameLength ; 0 <= --i ; ) {
            final String s = words[i];
            if (closestDistance <= chars.length - s.length())
                break;
            handleDistance(chars, s);
        }
        for (int i = sameLength ; ++i < words.length ; ) {
            final String s = words[i];
            if (closestDistance <= s.length() - chars.length)
                break;
            handleDistance(chars, s);
        }
        return closestWords;
    }