Levenshtein Distance Formula in CoffeeScript?

Question

I am trying to create or find a CoffeeScript implementation of the Levenshtein Distance formula, aka Edit Distance. Here is what I have so far, any help at all would be much appreciated.

levenshtein = (s1,s2) ->
    n = s1.length
    m = s2.length
    if n < m
        return levenshtein(s2, s1) 
    if not s1 
        return s2.length
    previous_row = [s2.length + 1]
    for c1, i in s1
        current_row = [i + 1]
        for c2, j in s2
            insertions = previous_row[j + 1] + 1
            deletions = current_row[j] + 1
            substitutions = previous_row[j] # is this unnescessary?-> (c1 != c2)
            current_row.push(Math.min(insertions,deletions,substitutions))
        previous_row = current_row
    return previous_row[previous_row.length-1]
#End Levenshetein Function

Btw: I know this code is wrong on many levels, I am happy to receive any and all constructive criticism. Just looking to improve, and figure out this formula!

CodeEdit1: Patched up the errors Trevor pointed out, current code above includes those changes

Update: The question I am asking is - how do we do Levenshtein in CoffeeScript?

Here is the 'steps' for the Levenshtein Distance Algorithm to help you see what I am trying to accomplish.

Steps 1
Set n to be the length of s. Set m to be the length of t. If n = 0, return m and exit. If m = 0, return n and exit. Construct a matrix containing 0..m rows and 0..n columns.

2
Initialize the first row to 0..n. Initialize the first column to 0..m.

3 Examine each character of s (i from 1 to n).

4 Examine each character of t (j from 1 to m).

5 If s[i] equals t[j], the cost is 0. If s[i] doesn't equal t[j], the cost is 1.

6 Set cell d[i,j] of the matrix equal to the minimum of: a. The cell immediately above plus 1: d[i-1,j] + 1. b. The cell immediately to the left plus 1: d[i,j-1] + 1. c. The cell diagonally above and to the left plus the cost: d[i-1,j-1] + cost.

7 After the iteration steps (3, 4, 5, 6) are complete, the distance is found in cell d[n,m].

source:http://www.merriampark.com/ld.htm

Answer 1

This page (linked to from the resource you mentioned) offers a JavaScript implementation of the Levenshtein distance algorithm. Based on both that and the code you posted, here's my CoffeeScript version:

LD = (s, t) ->
  n = s.length
  m = t.length
  return m if n is 0
  return n if m is 0

  d       = []
  d[i]    = [] for i in [0..n]
  d[i][0] = i  for i in [0..n]
  d[0][j] = j  for j in [0..m]

  for c1, i in s
    for c2, j in t
      cost = if c1 is c2 then 0 else 1
      d[i+1][j+1] = Math.min d[i][j+1]+1, d[i+1][j]+1, d[i][j] + cost

  d[n][m]

It seems to hold up to light testing, but let me know if there are any problems.