Top-K with a Heap

Keep only the largest k values by maintaining a small min-heap.

Algorithm

@steps

Store the heap in an array.
Compare parent and child indexes instead of building explicit tree nodes.
Swap only when the heap order is violated.
Print the deterministic final heap state for replay comparison. @end @complexity

Time: O(n log k)
Space: O(k) @end

bounded heap For top-k largest values, a min-heap of size k keeps the current cutoff at the root.

Perl DSA Implementation

basic.pl

use strict;
use warnings;
sub list_string { return "[" . join(", ", @_) . "]"; }
sub heap_insert {
    my ($heap, $value) = @_;
    push @$heap, $value;
    my $child = scalar(@$heap) - 1;
    while ($child > 0) {
        my $parent = int(($child - 1) / 2);
        last if $heap->[$parent] <= $heap->[$child];
        ($heap->[$parent], $heap->[$child]) = ($heap->[$child], $heap->[$parent]);
        $child = $parent;
    }
}
sub heap_pop {
    my ($heap) = @_;
    my $smallest = $heap->[0];
    $heap->[0] = pop @$heap;
    my $parent = 0;
    while (1) {
        my $left = $parent * 2 + 1; my $right = $left + 1;
        last if $left >= scalar @$heap;
        my $child = $left;
        $child = $right if $right < scalar @$heap && $heap->[$right] < $heap->[$left];
        last if $heap->[$parent] <= $heap->[$child];
        ($heap->[$parent], $heap->[$child]) = ($heap->[$child], $heap->[$parent]);
        $parent = $child;
    }
    return $smallest;
}
my @heap;
for my $value (5, 1, 9, 3, 7, 2) { heap_insert(\@heap, $value); heap_pop(\@heap) if scalar(@heap) > 3; }
@heap = sort { $b <=> $a } @heap;
print list_string(@heap) . "\n";

@end @output [9, 7, 5] @end