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.
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
<lang Perl 6>sub levenshtein_distance_alignment ( 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 { %A{$_}[*-1][*-1] },;
}
.say for levenshtein_distance_alignment |<rosettacode raisethysword>; </lang>
- Output:
ro-settac-o-de raisethysword-