**Advent Calendar 2021**

### | **Day 1** | **Day 2** | **Day 3** |

The gift is presented by **Dave Jacoby**. Today he is talking about his solution to **“The Weekly Challenge - 096”**. This is re-produced for **Advent Calendar 2021** from the original **post** by `Dave Jacoby`

.

## Task #2: Edit Distance

Write a script to find out the minimum operations required to convert `$S1`

into `$S2`

. The operations can be insert, remove or replace a character.

This is an easy challenge to go halfway on. If we simply want the number of changes it would take, that’s **Levenshtein Distance**. We even have **Text::Levenshtein** in CPAN if you don’t want to go to the trouble of copying it from Wikipedia or the like.

But **no**, we can’t just leave it at that, because the examples show **which** changes are made! This forced me to `read and understand(!)`

what’s going on with Levenshtein Distance. I mean, `really!?!?`

So, let’s take a much simpler example than those given in the challenge. `test`

to `text`

. We first create an empty 2-dimensional array, with the size of each axis equalling the length of each of the words, plus 1. We start here:

```
t e s t
[0,1,2,3,4]
t [1, , , , ]
e [2, , , , ]
x [3, , , , ]
t [4, , , , ]
```

We start at `[1,1]`

, where we check if the first letter of `test`

is the same as the first letter of `text`

, which it is, and so, the value in `[1,1]`

is the same as in `[0,0]`

, which is zero.

```
t e s t
[0,1,2,3,4]
t [1,0, , , ]
e [2, , , , ]
x [3, , , , ]
t [4, , , , ]
```

So we step on to `[1,2]`

, where we see if `e`

in `test`

is the same as `t`

in `text`

. Clearly, no. So we get the values of `[0,1],[0,2]`

and `[1,1]`

, which are `0, 1, 2`

. We take the lowest, `0`

, add `1`

and set `[1,2]`

to `1`

.

We go again and again and we end up with.

```
t e s t
[0,1,2,3,4]
t [1,0,1,2,3]
e [2,1,0,1,2]
x [3,2,1,1,2]
t [4,3,2,2,1]
```

And the last one we do, the last column of the last row, is exactly how many changes are necessary.

So, to find out what moves are the right ones, we move backwards, from the last to the first `0`

we find.

## The Code

It’s a bit messy, and very first draft. I was just spitting out the operations as I see them, until I realized that they were coming out backwards. And again, `min`

from **List::Util** because it’s so useful.

```
#!/usr/bin/env perl
use strict;
use warnings;
use feature qw{ say signatures state };
no warnings qw{ experimental };
use List::Util qw{min};
my @input;
push @input, [qw{ kitten sitting }];
push @input, [qw{ sunday monday }];
push @input, [qw{ slight lights }];
push @input, [qw{ fed feed }];
push @input, [qw{ test test }];
push @input, [qw{ test text }];
for my $x (@input) {
edit_distance( $x->@* );
}
# I first found the Levenshtein distance when poking in the center of
# perlbrew. This is how it knows, when you type `perlbrew xeec` to
# suggest you try `perlbrew exec` instead. This gives us the first
# part, the number of changes you'd need to get from S1 to S2. I thought
# about but never implemented it as a kind-of 404 page for endpoints:
# you look like you're looking for "index" but typed "idnex", for example.
# What we don't get from editdist is WHICH changes those would be.
# therefore, it's a half-solution for this problem.
sub edit_distance ( $s1, $s2 ) {
editdist( $s1, $s2 );
}
# let's try to make this a whole solution
sub editdist ( $s1, $s2 ) {
my @s1 = split //, $s1;
my @s2 = split //, $s2;
my @d;
$d[$_][0] = $_ for ( 0 .. @s1 );
$d[0][$_] = $_ for ( 0 .. @s2 );
# this creates a two-dimensional array that starts like this:
# [0,1,2,3,4,5,6]
# [1, , , , , , ]
# [2, , , , , , ]
# [3, , , , , , ]
# [4, , , , , , ]
# [5, , , , , , ]
# which gets filled in iteratively in the nested loops below
for my $i ( 1 .. @s1 ) {
for my $j ( 1 .. @s2 ) {
# Let's understand this. For a particular i and j position
# if the two agree, D[i][j] equals D[-i][-j]
# if they don't however, we find the value above
# the value before and the one above and before, find
# the lowest, and add one.
# this means that $d[-1][-1] would have the total
$d[$i][$j] = (
$s1[ $i - 1 ] eq $s2[ $j - 1 ]
? $d[ $i - 1 ][ $j - 1 ]
: 1 + min(
$d[ $i - 1 ][$j],
$d[$i][ $j - 1 ],
$d[ $i - 1 ][ $j - 1 ]
)
);
}
}
print <<"END";
Input: S1: $s1
S2: $s2
Change Count: $d[-1][-1]
END
my @operations = find_changes( \@d, \@s1, \@s2 );
my $c = 1;
for my $operation ( reverse @operations ) {
say qq{ Operation $c: $operation};
$c++;
}
# returns the last column of the last row, which SHOULD
# be the min changes.
return $d[-1][-1];
}
# d = 2-dimensional array, result of LD
# s1 = array of first input
# s2 = array of second input
# i = current row
# j = current column
sub find_changes ( $d, $s1, $s2, $i = -1, $j = -1 ) {
# -1 means implicit end of array, which gets turned
# into explicit end of array
$i = $i == -1 ? -1 + scalar $d->@* : $i;
$j = $j == -1 ? -1 + scalar $d->[-1]->@* : $j;
# zero means that there are no more changes
return if $d->[$i][$j] == 0;
my $v = $d->[$i][$j];
my $v1 = $d->[ $i - 1 ][ $j - 1 ];
my $v2 = $d->[$i][ $j - 1 ];
my $v3 = $d->[ $i - 1 ][$j];
my @output;
if (0) {
# The impossible situation we never planned for.
# I LIKE to put an if ( false ) statement first,
# so it's easy to just move the elsifs around
# should I decide or discern that I have the order
# wrong.
}
elsif ( $v1 == $v - 1 ) {
my $c1 = $s1->[ $i - 1 ];
my $c2 = $s2->[ $j - 1 ];
push @output, qq{replace '$c1' with '$c2'};
push @output, find_changes( $d, $s1, $s2, $i - 1, $j - 1 );
}
elsif ( $v2 == $v - 1 ) {
my $c1 = $s1->[ $i - 1 ];
my $c2 = $s2->[ $j - 1 ];
if ( $j == scalar $s2->@* ) {
push @output, qq{insert '$c2' at the end};
}
else { push @output, qq{insert '$c2'}; }
push @output, find_changes( $d, $s1, $s2, $i, $j - 1 );
}
elsif ( $v3 == $v - 1 ) {
my $c1 = $s1->[ $i - 1 ];
my $c2 = $s2->[ $j - 1 ];
push @output, qq{remove '$c1' from beginning} if $i == 1;
push @output, qq{remove '$c1'} if $i != 1;
push @output, find_changes( $d, $s1, $s2, $i - 1, $j );
}
elsif ( $v1 == $v ) {
push @output, find_changes( $d, $s1, $s2, $i - 1, $j - 1 );
}
elsif ( $v2 == $v ) {
push @output, find_changes( $d, $s1, $s2, $i, $j - 1 );
}
elsif ( $v3 == $v ) {
push @output, find_changes( $d, $s1, $s2, $i - 1, $j );
}
return @output;
}
# -------------------------------------------------------------------
# straight copy of Wikipedia's "Levenshtein Distance"
sub levenshtein_distance {
my ( $f, $g ) = @_;
my @a = split //, $f;
my @b = split //, $g;
# There is an extra row and column in the matrix. This is the
# distance from the empty string to a substring of the target.
my @d;
$d[$_][0] = $_ for ( 0 .. @a );
$d[0][$_] = $_ for ( 0 .. @b );
for my $i ( 1 .. @a ) {
for my $j ( 1 .. @b ) {
$d[$i][$j] = (
$a[ $i - 1 ] eq $b[ $j - 1 ]
? $d[ $i - 1 ][ $j - 1 ]
: 1 + min(
$d[ $i - 1 ][$j],
$d[$i][ $j - 1 ],
$d[ $i - 1 ][ $j - 1 ]
)
);
}
}
return $d[@a][@b];
}
```

## Output

```
Input: S1: kitten
S2: sitting
Change Count: 3
Operation 1: replace 'k' with 's'
Operation 2: replace 'e' with 'i'
Operation 3: insert 'g' at the end
Input: S1: sunday
S2: monday
Change Count: 2
Operation 1: replace 's' with 'm'
Operation 2: replace 'u' with 'o'
Input: S1: slight
S2: lights
Change Count: 2
Operation 1: remove 's' from beginning
Operation 2: insert 's' at the end
Input: S1: fed
S2: feed
Change Count: 1
Operation 1: insert 'e'
Input: S1: test
S2: test
Change Count: 0
Input: S1: test
S2: text
Change Count: 1
Operation 1: replace 's' with 'x'
```

I think I’m least happy with the inconsistent hackiness with how I specify beginning and end, but eh. Getting to the solution, backtracking from the end of the array, required me to write an in-depth explanation of the problem to my user-group mailing list.

But I’m happy now, and I really loved this one.

If you have any suggestion then please do share with us perlweeklychallenge@yahoo.com.