# this will be part perl part pseudo code:
@groups;
$distinct_flag; # a flag to see if we have a distinct value in an array
while (($key, $value) = each(%list)){
# where key is name and group is value
# so here we want to run through our groups array and see if our value is in it:
foreach $group (@groups)
if ($value ne $group)
{
   $distinct_flag = "true";
}
else 
{ distinct_flag = "false"; }
} # end foreach
if {distinct_flag = "true" }
push (@groups, $value}
} #endwhile

#!/usr/bin/perl -w
 
use strict;
 
 
my %INV_LIST;
while (<>) {
        my($old_key, @old_val) = split(/:*\s+/);
 
        foreach my $new_key(@old_val) {
                $INV_LIST{$new_key} .= " ".$old_key;
        }
}       
 
foreach my $key (sort(keys(%INV_LIST))) {
        print $key.":".$INV_LIST{$key}."\n";
}

### Data splited and store in hash format
map($hash{$_}.="$1 ", (split / /, $2)) while (<DATA>=~ m{(.*?): ([^\n]+)}gs);
 
### print the hashes data 
print "$_: $hash{$_}\n" for sort keys %hash;
 
__DATA__
name1: group1
name2: group4
name3: group1 group2
name4: group4