Levenshtein Distance Algorithm: Java Implementation

by Chas Emerick

Mr. Gilleland,

As you may know, the Apache Jakarta Commons project had appropriated 
your sample implementation of the Levenshtein Distance algorithm for 
its commons-lang Java library.  While attempting to use it with two 
very large strings, I encountered an OutOfMemoryError, due to the fact 
that a matrix is created with the dimensions of the two strings' 
lengths.  I know you created the implementation to go with your 
(excellent) illustration of the algorithm, so this matrix approach 
translates that illustration and tutorial perfectly.

However, as I said, the matrix approach doesn't lend itself to getting 
the edit distance of two large strings.  For this purpose, I modified 
your implementation to use two single-dimensional arrays; this is 
clearly more memory-friendly (although it probably results in some very 
slight performance degradation when comparing smaller strings).

I've submitted the modification to the maintainers of the commons-lang 
project, and I've appended the relevant method below.

Thanks!

Chas Emerick  

public static int getLevenshteinDistance (String s, String t) {
  if (s == null || t == null) {
    throw new IllegalArgumentException("Strings must not be null");
  }
		
  /*
    The difference between this impl. and the previous is that, rather 
     than creating and retaining a matrix of size s.length()+1 by t.length()+1, 
     we maintain two single-dimensional arrays of length s.length()+1.  The first, d,
     is the 'current working' distance array that maintains the newest distance cost
     counts as we iterate through the characters of String s.  Each time we increment
     the index of String t we are comparing, d is copied to p, the second int[].  Doing so
     allows us to retain the previous cost counts as required by the algorithm (taking 
     the minimum of the cost count to the left, up one, and diagonally up and to the left
     of the current cost count being calculated).  (Note that the arrays aren't really 
     copied anymore, just switched...this is clearly much better than cloning an array 
     or doing a System.arraycopy() each time  through the outer loop.)

     Effectively, the difference between the two implementations is this one does not 
     cause an out of memory condition when calculating the LD over two very large strings.  		
  */		
		
  int n = s.length(); // length of s
  int m = t.length(); // length of t
		
  if (n == 0) {
    return m;
  } else if (m == 0) {
    return n;
  }

  int p[] = new int[n+1]; //'previous' cost array, horizontally
  int d[] = new int[n+1]; // cost array, horizontally
  int _d[]; //placeholder to assist in swapping p and d

  // indexes into strings s and t
  int i; // iterates through s
  int j; // iterates through t

  char t_j; // jth character of t

  int cost; // cost

  for (i = 0; i<=n; i++) {
     p[i] = i;
  }
		
  for (j = 1; j<=m; j++) {
     t_j = t.charAt(j-1);
     d[0] = j;
		
     for (i=1; i<=n; i++) {
        cost = s.charAt(i-1)==t_j ? 0 : 1;
        // minimum of cell to the left+1, to the top+1, diagonally left and up +cost				
        d[i] = Math.min(Math.min(d[i-1]+1, p[i]+1),  p[i-1]+cost);  
     }

     // copy current distance counts to 'previous row' distance counts
     _d = p;
     p = d;
     d = _d;
  } 
		
  // our last action in the above loop was to switch d and p, so p now 
  // actually has the most recent cost counts
  return p[n];
}