# 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";
  }
} 
##</code><code>##

___INPUT(set of triplets)____
b c a
a c d
d e b
##</code><code>##

b c
a c
d e 
##</code><code>##

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.
##</code><code>##

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 ...)
##</code><code>##

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