00112233222000

##</code><code>##

(3,1), (5,2), (7,3), (9,2), (12,0)

##</code><code>##

my @intervals = ([3,11], [5,8], [7,11]);
for (@intervals) {
    my ($start,$end) = @$_;
    $delta{$start}++;
    $delta{$end+1}--;
}

my $total = 0;
my @points;
for (sort { $a <=> $b } keys %delta) {
    next if $delta{$_} == 0; ## update: added this line
    $total += $delta{$_};
    push @points, [$_, $total];
}