#! perl -sw
use strict;

my @array = (
  [ '03:30', '05:45' ],
  [ '05:45', '09:15' ],
  [ '10:00', '11:35' ],
  [ '10:00', '10:01' ],
  [ '11:00', '15:40' ]
);

sub hhmm2min {
    die "Data error $_[0] not in format HH:MM\n" unless $_[0] =~ m/(\d\d):(\d\d)/;
  return $1*60+$2;
}

sub min2hhmm {
    die "Data error $_[0] > 24:00\n" if $_[0] > 24*60;
  return sprintf "%02d:%02d", int($_[0]/60), $_[0]%60;
}

@array = sort{ 
	$a->[0] <=> $b->[0] 
}map{ 
	[ hhmm2min($_->[0]), hhmm2min($_->[1]) ]
}@array;

my $cur = 0;
my @missing = ();

for my $r( @array ) {
    push @missing, [ min2hhmm($cur), min2hhmm( $r->[0] ) ] if $cur < $r->[0];
    $cur = $r->[1];
}

push @missing, [ min2hhmm($cur), '24:00' ] unless $cur == 24*60;

use Data::Dumper;
print Dumper \@missing;

__END__
P:\test>test
$VAR1 = [
          [
            '00:00',
            '03:30'
          ],
          [
            '09:15',
            '10:00'
          ],
          [
            '10:01',
            '11:00'
          ],
          [
            '15:40',
            '24:00'
          ]
        ];