sorting nodes according to its members - perl

Question

I don't know where to start. I have a long list of nodes comprised of descendant members, for which I want to make a linked tree, a plain text database in the form of child/parent. For example:
N115713
N115713 N96394
N117904 N18574
N140517 N171639 N179536 N208718 N210073 N226737 N4647 N80403
N171639
N171639 N18574
N171639 N208718
N171639 N208718 N210073
N171639 N208718 N210073 N3690
N171639 N208718 N210073 N96585
N171639 N210073
N18574
N18574 N80403
Obviously, "N115713" will go downstream of "N115713 N96394" but I seem unable to turn that recognition into an algorithm. There are several hundred nodes having up to several dozen members. Pointers to get started? I'm using perl.
Thanks!
UPDATE: Well, I have an idea but haven't been able to implement it yet. I'm searching each line in turn for the other lines it's a "member" of then selecting that result which has the next highest number of members as its parent.

Answer 1

Since the main problem here is to check if the input data is consistent and does not have cycles, I recommend using some graph-theoretical module, for example Graph.
If your data allows a child to have multiple parents you have to check if the directed graph produced from your data does not have a cycle.
Otherwise, if your data should be a tree, you have to check that the undirected graph does not have a cycle.
I sketched up a simple script, that implements these checks and outputs child/parent pairs, it is pretty self explanatory:
use strict;use warnings;
use Graph;
my $g=Graph->new(directed=>1);
while(<>) {
chomp;
my #fields=split;
# this assumes that each line starts with a parent and goes down through its descendants
# adjust the logic to your needs
my $parent;
for my $child(#fields) {
$g->add_vertex($child);
if ($parent) {
$g->add_edge($child,$parent);
}
$parent=$child;
}
}
# check if we have a DAG
my #cycle = $g->find_a_cycle();
if (#cycle) {
printf "The directed graph has a cycle: %s\n", join ',', #cycle
}
# check if we have a tree
my $un_g = $g->undirected_copy();
#cycle = $un_g->find_a_cycle();
if (#cycle) {
printf "The undirected graph has a cycle: %s\n", join ',', #cycle
}
print "child,parent\n";
for my $edge(sort { $a->[0] cmp $b->[0] } $g->edges) {
printf "%s,%s\n", $edge->[0], $edge->[1];
}
And the output for your data:
The undirected graph has a cycle: N179536,N171639,N208718
child,parent
N115713,N96394
N117904,N18574
N140517,N171639
N171639,N208718
N171639,N18574
N171639,N179536
N171639,N210073
N179536,N208718
N18574,N80403
N208718,N210073
N210073,N226737
N210073,N96585
N210073,N3690
N226737,N4647
N4647,N80403