#!/usr/bin/env perl

use strict;
use warnings;

use constant {
    CHILD_ID => 0,
    CAT_NAME => 1,
};

my $VAR1 = {
    986172 => { cat_parent_id => '', cat_name => 'Category1' },
    986178 => { cat_parent_id => '986177', cat_name => 'Category4' },
    986177 => { cat_parent_id => '986176', cat_name => 'Category3' },
    986176 => { cat_name => 'Category2', cat_parent_id => '986172' }
};

my $wanted_string = get_wanted_string($VAR1);
print "$wanted_string\n";

sub get_wanted_string {
    my ($data) = @_;
    my (%family, @cats);

    for my $child_id (keys %$data) {
        my ($parent_id, $cat_name)
            = @{$data->{$child_id}}{qw{cat_parent_id cat_name}};
        $family{$parent_id} = [$child_id, $cat_name];
    }

    return join ',', @{recurse_family(\%family, \@cats)};
}

sub recurse_family {
    my ($family, $cats, $parent) = @_;
    $parent = '' unless defined $parent;
    return $cats unless exists $family->{$parent};
    push @$cats, $family->{$parent}[CAT_NAME];
    recurse_family($family, $cats, $family->{$parent}[CHILD_ID]);
}