use strict;
use warnings;
use Data::Dump qw/pp dd/;

my @paths = find_paths
  (
   [0,0,'start'],
   [3,1,'goal']
  );

pp @paths;



sub find_paths {
    my ($start,$goal)=@_;

    # --- transform to easier coordinates
    ($start,$goal) = map old2new($_), ($start,$goal);

    # --- define closure
    my @results;
    my ($gl,$gr) = @$goal;
    my $pathfinder;

    $pathfinder = sub  {
        my ( $last ) = @_;
        # pp \@_ ;# track recursion path

        my ( $l, $r ) = @$last ;

        if ( $gl == $l and $gr == $r) {
            push @results, [ map new2old($_), reverse @_ ];
            return;
        }

        $pathfinder->( [$l+1,$r   ,"left" ], @_ ) if $l < $gl;

        $pathfinder->( [$l  ,$r+1 ,"right"], @_ ) if $r < $gr;
    };

    # --- init recursion
    $pathfinder->($start);

    return \@results;
}




# --------------------------------------------------
# coordinate transformations


sub old2new {                           # left = level - right
    my ($a_old)=@_;
    my @new = @$a_old;
    $new[0] = $new[0] - $new[1];
    return \@new;
}

sub new2old {                           # level = left + right
    my ($a_new)=@_;
    my @old = @$a_new;
    $old[0] = $old[0] + $old[1];
    return \@old;
}