['A','B','C'],
['A','B','D']

##</code><code>##

A  A
B  B
C
   D

##</code><code>##

['A','B','C'],
['A','D','C'],
['A','B','C']

##</code><code>##

A       A       A
B       B
C       C
                D
                C

##</code><code>##

A       A       A
B       B
                D
C       C       C

##</code><code>##

#!/usr/bin/perl -w

use strict;
#use Data::Dumper;

my $hash;
#$hash->{'Vector1'} = ['A','B','D','H','J'];
#$hash->{'Vector2'} = ['A','B','C','D'];
#$hash->{'Vector4'} = ['H','K'];

$hash->{'Vector3'} = ['A','B','C'];
$hash->{'Vector4'} = ['A','D','C'];
$hash->{'Vector5'} = ['A','B','C'];



#print Dumper($hash);

my $count_total = scalar (keys %{$hash});
my @keys = keys %{$hash};
my $aligned;
my $minimum;

my $key_count=0;
for (0 .. $#keys) {
  my $test = shift(@keys);
  push(@keys,$test);

  #
  # push first into results matrix
  # to start with
  #

  my @result;
  foreach (@{$hash->{$keys[0]}}) {
    push(@result,[$_]);
  }

  #
  # compare
  #

  my $count_processed=0;
  my @vector;
  foreach (keys %{$hash}) {
    if (($count_processed+2)>$count_total) {
      last;
    }
    @vector = @{$hash->{$keys[$count_processed+1]}};
    my $i=0;
    while ($i <= $#vector) {
      my $entry = $vector[$i];
      if (defined(${$result[$i]}[0])) {
	# print "1)Is ";
	# print $entry;
	# print " in ";
	# print join(',',@{$result[$i]});
	# print " ?";
	if (grep $_ eq $entry,@{$result[$i]}) {
	  #   print " => yes\n";
	  push(@{$result[$i]},$entry);
	} else {
	  #   print " => no\n";
	  splice(@vector,$i,0,'');
	  my @space;
	  for (0 .. ($count_processed-$#{$result[$i]})) {
	    push(@space,'');
	  }
	  push(@{$result[$i]},@space);
	}
	;
      } else {
	# print "undefined => shift\n";
	my @space;
	for (0 .. $count_processed) {
	  push(@space,'');
	}
	push(@{$result[$i]},@space,$entry);
      }
      $i++;
    }

    #
    # the latest column might have missing ''s at the end. This needs to be
    # filled up
    #

    my $p=0;
    foreach (@result) {
      if ($#{$result[$p]} < $#{$result[0]} ) {
	push(@{$result[$p]},'');
      }
      $p++;
    }
    $count_processed++;
  }

  #
  # count the number of holes
  #

  my $n=0;
  foreach (@result) {
    foreach (@$_) {
      # print "$_ \t";
      if ($_ eq '') {
	$n++;
      }
    }
  }
#  print "\n";
 
  if($key_count == 0){
    $minimum = $n;
    $aligned = {
		'matrix' => [@result],
		'n'      => $n
	       };
  }else{
    if($n < $minimum){
      $minimum = $n;
      $aligned = {
		  'matrix' => [@result],
		  'n'      => $n
		 };

    }
  }
  $key_count++;
}
  
print "minimal configuration ($aligned->{'n'} holes):\n";
foreach (@{$aligned->{'matrix'}}) {
  foreach (@$_) {
    print "$_ \t";
  }
  print "\n";
}