#!/usr/bin/perl
    
use strict;
use warnings;
     
my @heap;

sub heapify;
sub heapify {
    my $idx = shift;

    my $min = $idx;
    for my $try (2 * $idx + 1, 2 * $idx + 2) {
        $min = $try if $try < @heap && $heap [$try] < $heap [$min]
    }
    return if $min == $idx;
        
    @heap [$idx, $min] = @heap [$min, $idx];
    heapify $min;
}
 
sub extract_min {
    return unless @heap;
    my $min = $heap [0];
    my $tmp = pop @heap;
    if (@heap) {
        $heap [0] = $tmp;
        heapify 0;
    }
    return $min;
}
     
#
# First argument the number of smallest elements to be returned.
# Then the list to find the elements in.
#
sub smallest {
    my $k = shift;
    @heap = @_;
    for (my $i = int (@heap / 2); $i --;) {
        heapify $i;
    }
    my @result;
    push @result => extract_min while @heap && $k --;
    @result;
}

__END__
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The running time of this is O (N + k log N), where N is the size of the set, and k the number of elements to be returned.

Abigail