Levenshtein distance/Alignment

The Levenshtein distance algorithm returns the number of atomic operations (insertion, deletion or edition) that must be performed on a string in order to obtain an other one, but it does not say anything about the actual operations used or their order.

Levenshtein distance/Alignment is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

An alignment is a notation used to describe the operations used to turn a string into an other. At some point in the strings, the minus character ('-') is placed in order to signify that a character must be added at this very place. For instance, an alignment between the words 'place' and 'palace' is:

P-LACE
PALACE

For this task, write a function that shows the alignment of two strings for the corresponding levenshtein distance. As an example, use the words "rosettacode" and "raisethysword".

You can either implement an algorithm, or use a dedicated library (thus showing us how it is named in your language).

Perl

<lang perl>use List::Util qw(min);

sub levenshtein_distance_alignment {

   my @s = ('^', split //, shift);
   my @t = ('^', split //, shift);

   my @d;
   $d[$_][0] = $_ for 0 .. @s-1;
   $d[0][$_] = $_ for 0 .. @t-1;

   my (@AS, @AT);
   $AS[$_][0] = join , @s[1 .. $_] for 0 .. @s-1;
   $AS[0][$_] = '-' x $_ for 0 .. @t-1;
   $AT[0][$_] = join , @t[1 .. $_] for 0 .. @t-1;
   $AT[$_][0] = '-' x $_ for 0 .. @s-1;

   for my $i (1 .. @s-1) {
       for my $j (1 .. @t-1) {
           if ($s[$i] eq $t[$j]) {
               $AS[$i][$j] = $AS[$i-1][$j-1] . $s[$i];
               $AT[$i][$j] = $AT[$i-1][$j-1] . $t[$j];
               $d[$i][$j] = $d[$i-1][$j-1];
               next;
           }
           $d[$i][$j] = 1 + (
               my $min = min $d[$i-1][$j], $d[$i][$j-1], $d[$i-1][$j-1]
           );
           if ($d[$i-1][$j] == $min) {
               $AS[$i][$j] = $AS[$i-1][$j] . $s[$i];
               $AT[$i][$j] = $AT[$i-1][$j] . '-';
           }
           elsif ($d[$i][$j-1] == $min) {
               $AS[$i][$j] = $AS[$i][$j-1] . '-';
               $AT[$i][$j] = $AT[$i][$j-1] . $t[$j];
           }
           else {
               $AS[$i][$j] = $AS[$i-1][$j-1] . $s[$i];
               $AT[$i][$j] = $AT[$i-1][$j-1] . $t[$j];
           }
       }
   }
   return $AS[-1][-1], $AT[-1][-1];

}

print join "\n", levenshtein_distance_alignment "rosettacode", "raisethysword"; </lang>

Output:

ro-settac-o-de
raisethysword-

Perl 6

Translation of: Perl

<lang Perl 6>sub align ( Str $σ, Str $t ) {

   my @s = *, $σ.comb;
   my @t = *, $t.comb;
    
   my @d;
   @d[$_][ 0] = $_ for ^@s;
   @d[ 0][$_] = $_ for ^@t;

   my %A;
   %A[$_][ 0] = @s[1..$_].join for ^@s;
   %A[ 0][$_] = '-' x $_ for ^@t;
   %A<t>[ 0][$_] = @t[1..$_].join for ^@t;
   %A<t>[$_][ 0] = '-' x $_ for ^@s;
    
   for 1..@s.end X 1..@t.end -> $i, $j {

if @s[$i] eq @t[$j] { # No operation required when eq %A[$i][$j] = %A[$i-1][$j-1] ~ @s[$i]; %A<t>[$i][$j] = %A<t>[$i-1][$j-1] ~ @t[$j]; @d[$i][$j] = @d[$i-1][$j-1]; next; } @d[$i][$j] = 1 + my $min = min @d[$i-1][$j], @d[$i][$j-1], @d[$i-1][$j-1]; if @d[$i-1][$j] == $min { # Deletion %A[$i][$j] = %A[$i-1][$j] ~ @s[$i]; %A<t>[$i][$j] = %A<t>[$i-1][$j] ~ '-'; } elsif @d[$i][$j-1] == $min { # Insertion %A[$i][$j] = %A[$i][$j-1] ~ '-'; %A<t>[$i][$j] = %A<t>[$i][$j-1] ~ @t[$j]; } else { # Substitution %A[$i][$j] = %A[$i-1][$j-1] ~ @s[$i]; %A<t>[$i][$j] = %A<t>[$i-1][$j-1] ~ @t[$j]; }

   }
    
   return map *[*-1][*-1], %A;

}

.say for align |<rosettacode raisethysword>; </lang>

Output:

ro-settac-o-de
raisethysword-