Detailed distance between words

Question

How would I go about displaying detailed distance between words. For example, the output of the program could be:

Words are "car" and "cure":
Replace "a" with "u".
Add "e".

The Levenshtein distance does not fulfill my needs (I think).

Answer 1

Try the following. The algorithm is roughly following Wikipedia (Levenshtein distance). The language used below is ruby

Use as an example, the case of changing s into t as follows:

s = 'Sunday'
t = 'Saturday'

First, s and t are turned into arrays, and an empty string is inserted at the beginning. m will eventually be the matrix used in the argorithm.

s = ['', *s.split('')]
t = ['', *t.split('')]
m = Array.new(s.length){[]}

m here, however, is different from the matrix given if the algorithm in wikipedia for the fact that each cell includes not only the Levenshtein distance, but also the (non-)operation (starting, doing nothing, deletion, insertion, or substitution) that was used to get to that cell from an adjacent (left, up, or upper-left) cell. It may also include a string describing the parameters of the operation. That is, the format of each cell is:

[Levenshtein distance, operation(, string)]

Here is the main routine. It fills in the cells of m following the algorithm:

s.each_with_index{|a, i| t.each_with_index{|b, j|
    m[i][j] =
    if i.zero?
        [j, "started"]
    elsif j.zero?
        [i, "started"]
    elsif a == b
        [m[i-1][j-1][0], "did nothing"]
    else
        del, ins, subs = m[i-1][j][0], m[i][j-1][0], m[i-1][j-1][0]
        case [del, ins, subs].min
        when del
            [del+1, "deleted", "'#{a}' at position #{i-1}"]
        when ins
            [ins+1, "inserted", "'#{b}' at position #{j-1}"]
        when subs
            [subs+1, "substituted", "'#{a}' at position #{i-1} with '#{b}'"]
        end
    end
}}

Now, we set i, j to the bottom-right corner of m and follow the steps backwards as we unshift the contents of the cell into an array called steps, until we reach the start.

i, j = s.length-1, t.length-1
steps = []
loop do
    case m[i][j][1]
    when "started"
        break
    when "did nothing", "substituted"
        steps.unshift(m[i-=1][j-=1])
    when "deleted"
        steps.unshift(m[i-=1][j])
    when "inserted"
        steps.unshift(m[i][j-=1])
    end
end

Then we print the operation and the string of each step unless that is a non-operation.

steps.each do |d, op, str=''|
    puts "#{op} #{str}" unless op == "did nothing" or op == "started"
end

With this particular example, it will output:

inserted 'a' at position 1
inserted 't' at position 2
substituted 'n' at position 2 with 'r'