From: Daniel Martin <martin@...>
Date: 2007-05-18T14:39:55+09:00
Subject: Re: Damerau-Levenshtein_distance

Jeremy <jwells@servalsystems.co.uk> writes:

> I wrote the method below by copying the algorithm from
> http://en.wikipedia.org/wiki/Damerau-Levenshtein_distance (and matrix
> is a really simple 2d array implementation). But the problem is that
> it slows wat down as the string size gets bigger. At string length of
> about 150 it takes 1s, at 500 10s. Is there any way to recode this to
> get better performance without rewriting it in C, and would rewrting
> it in C even help or is this just a slow algorithm?

Well, the algorithm itself is O(n*m), where n and m are the size of
the strings involved, so on large strings it's going to get slow.

I was able to shave about 40% off the time for your method, and fix a
bug.

The bug was caused because the wikipedia article indexes the strings
starting from 1, but indexes the array starting form 0.  In ruby both
start at 0, of course.  To fix this, I added a fake element at the
start of both strings.

Anyway, here's my slightly faster version:

    def self.distance(string1, string2)
        string1 = string1.unpack('C*')
        string2 = string2.unpack('C*')
        s1n = string1.length
        s2n = string2.length
        string1.unshift -1
        string2.unshift -1
        m = Array.new(s1n+1){Array.new(s2n+1,0)}
        cost = 0
        a = nil; b = nil
        (0..s1n).each {|i| m[i][0] = i}
        (1..s2n).each {|j| m[0][j] = j}
        (1..s1n).each do |i|
            (1..s2n).each do |j|
                cost = string1[i] == string2[j] ? 0 : 1
                
                a = m[i-1][j] + 1
                a = b if ((b = m[i][j-1]+1) < a)
                a = b if ((b = m[i-1][j-1]+cost) < a)
                
                if(i > 1 && j > 1 && 
                   string1[i] == string2[j-1] &&
                   string1[i-1] == string2[j]) then
                    a = b if ((b = m[i-2][j-2] + 1) < a)
                end
                m[i][j] = a
            end
        end
        m[s1n][s2n]
    end


-- 
s=%q(  Daniel Martin -- martin@snowplow.org
       puts "s=%q(#{s})",s.to_a.last       )
       puts "s=%q(#{s})",s.to_a.last