# perl code.pl data
# ___data____
#b c a
#a c d
#d e b
#This program read the triplets from file named "data" and returns the
#supertree.
#### NOTE ::: SuperTree part hasnt been incorporated yet.
use strict;
use warnings;
use Data::Dumper;
use Graph;
use Data::Dump qw/ pp /;
####READ IN THE INPUT DATA ########
my @triplets; # Get all the triplets
while (<>) {
push @triplets, [ split ];
}
#Make a deep copy of @triplets
my @triplet_deep_copy = map { [@$_] } @triplets;
#####AUXILIARY GRAPH G(L) #######
# In order to generate the G(L) first of all extract first two columns of @triplets into another matrix
my @auxiliary_edges=@triplets;
splice(@$_, 2, 1)
foreach @auxiliary_edges;
print "----EDGE LIST TO BUILD AUXILIARY GRAPH-----\n";
print Dumper \@auxiliary_edges;
##### CONNECTED COMPONENTS ##########
my $auxiliary_graph = Graph->new( undirected => 1 );
my @from;
my @to;
for (my $p = 0; $p <= 2; $p++) {
$from[$p]=$triplets[$p][0];
}
for (my $q = 0; $q <= 2; $q++) {
$to[$q]=$triplets[$q][1];
}
for (my $r = 0; $r <= 2; $r++) {
$auxiliary_graph->add_edge($from[$r], $to[$r]);
}
my @subgraphs = $auxiliary_graph->connected_components; # Subgraphs
my $V = $auxiliary_graph->vertices; # Number of taxa
my $connected_components=scalar @subgraphs; #Get the number of connected components
###### FINDING THE TRIPLETS WHICH ARE SUBSET(OR INDUCED BY) OF EACH OF THE CONNECTED COMPONENTS######
Main(@auxiliary_edges);
exit(0);
sub induced {
my $trip = shift;
my @matches;
for my $QT ( @_ ) {
for my $triplet ( @$trip ) {
my %seen; # my %Pie;
undef @seen{@$QT};
delete @seen{@$triplet};
if ( keys( %seen ) <= ( @$QT - @$triplet ) ) {
push @matches, $triplet;
}
} ## end for my $triplet ( @$trip )
} ## end for my $QT ( @_ )
return @matches;
}## end sub induced
sub Main {
my $tree = Graph->new( undirected => 1 );
my $dad='u';
$tree->add_vertex($dad);
for my $one (@subgraphs) {
my @matches = induced( \@triplet_deep_copy, $one );
print "\nTriplet induced by subgraph ", pp( $one => { MATCHES => \@matches } ), "\n\n";
}
}
##```
##
___INPUT(set of triplets)____
b c a
a c d
d e b
##
```

```
##
b c
a c
d e
##
```

```
##
TreeConstruct(S)
1. Let L be the set of species appear in S. Build G(L)
2. Let C1 , C2 , . . . , Cq be the set of connected components in G(L)
3. If q >1, then
• For i = 1, 2, . . . , q, let Si be the set of triplets in S labeled by the set
of leaves in Ci .
• Let Ti = TreeConstruct(Si )
• Let T be a tree formed by connecting all Ti with the same parent node.
Return T.
4. If q=1 and C1 contains exactly one leaf, return the leaf; else return fail.
##
```

```
##
1. Initially we have q=2 (a-c-b & d-e). So introduce an internal vertex (u) and make these connected components child of u.
u=> a-c-b;
d-e;
2. Select component 1 = a-c-b. Check all lines from INPUT which are a subset of this component1.First line of INPUT i.e. "b c a" is a subset of component1.
3."b c a" now becomes the INPUT for the program and it is recursed again with this INPUT(Now for input "b c a" the auxiliary graph will be "b-c" & "a",i.e. two connected components,thus q=2 ...)
##
```

```
##
u => u => d
=> e
=> u => a
=> u => b
=> c
```