Need better solution for combination of numbers - linux

Question

I have file with following entries:
1,2
2,3
4,5
1,3
1,4
5,6
...
This tells the ids: first column matches with second column. Now I want to find all id groups that are having all combinations only. i.e. the following needs to be output:
1,2,3
4,5
1,4
5,6
I tried to write a perl script for the solution:
while(<STDIN>) {
if(m/^(\d+),(\d+)/) {
$dub{$1}{$2} = 1;
$dub{$2}{$1} = 1;
$hs{$1} = 1;
$hs{$2} = 1;
}
}
$i=0;
foreach $a (keys %dub) {
$grp[$i]{$a} = 1;
foreach $b (keys %{$dub{$a}}) {
$grp[$i]{$b} = 1;
foreach $c (keys %hs) {
if($c == $a || $c == $b) { next; }
$flag = 1;
foreach $d (keys %{$grp[$i]}) {
if(!$dub{$d}{$c}) {
$flag = 0;
last;
}
}
$grp[$i]{$c} = 1 if($flag);
}
$i++;
}
}
for($i=0; $i<=$#grp; $i++) {
print join(",", (keys %{$grp[$i]}))."\n";
}
But this takes hell lot of time for execution.
Is there a better solution, algorithm or performance tune for above script?
Any solution in LAMP is appreciated.
Thanks
EDIT:
Think of this way:
(1,2) is defined as "1 and 2 are similar"
(2,3) is defined as "2 and 3 are similar"
(1,4) is defined as "1 and 4 are similar"
(1,3) is defined as "1 and 3 are similar"
From these similarities I conclude that group (1,2,3) are similar to each other but not group (1,2,3,4).
In order to form group (1,2,3,4) there should be other entries in data as (2,4) and (3,4).
Finally I wanted to find all groups in given set of co-ordinates.

Answer 1

From my understanding, {1,2,3} are in the same group because all point to each other ({1,2}, {2,3},{1,3} exist). So, we can reduce this problem to finding cliques in an undirected graph, which is NP-Complete problem. So, every solution will be quite inefficient on big data.

Answer 2

This works for me:
use Data::Dump;
my #results;
my ($last_a, $last_b) = (0,0);
while(<DATA>) {
chomp;
my ($a, $b) = split /,/;
if( $last_b == $a ) {
my $last_item = $results[$#results];
push #$last_item, $b;
}
else {
push #results, [$a, $b];
}
($last_a, $last_b) = ($a, $b);
}
dd #results; # ([1, 2, 3], [4, 5], [1, 3], [1, 4], [5, 6])
__DATA__
1,2
2,3
4,5
1,3
1,4
5,6

Answer 3

You haven't really described the algorithm that we're supposed to used. I can't really understand why your input generates "1,2,3" and "1,4" rather than just "1,2,3,4".
But is this what you want?
#!/usr/bin/perl
use strict;
use warnings;
use 5.010;
my %data;
while (<DATA>) {
chomp;
my ($k, $v) = split /,/;
push #{ $data{$k} }, $v;
}
foreach (sort keys %data) {
say "$_,", join ',', #{ $data{$_ } };
}
__DATA__
1,2
2,3
4,5
1,3
1,4
5,6