Min-Heap Insert (Sift Up)

Insert one value into a min-heap and restore the parent-child order by sifting upward.

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(log n)
Space: O(1) extra @end

sift up A new value starts at the end of the array and swaps with its parent while it is smaller.

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 = (2, 4, 7, 9, 6);
heap_insert(\@heap, 1);
print list_string(@heap) . "\n";

@end @output [1, 4, 2, 9, 6, 7] @end