Min-Heap Pop (Sift Down)

Remove the minimum value, move the last item to the root, and sift downward.

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.

Complexity

Time: O(log n)
Space: O(1) extra

sift down After removing the root, the last value moves to the root and swaps with the smaller child until order is restored.

Visual walkthrough

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 = (1, 4, 2, 9, 6, 7);
my $popped = heap_pop(\@heap);
print "$popped -> " . list_string(@heap) . "\n";

After popping the minimum, the last value moves to the root and sifts down by swapping with the smaller child.

Step 1 - Replace root

The saved minimum is 1; the last value 7 moves to the root before sifting down.

Step 2 - Swap with the smaller child

7 swaps with 2, producing the final heap [2, 4, 7, 9, 6].

Implementation notes

my @heap = (1, 4, 2, 9, 6, 7) stores the min-heap in a Perl array with the @ sigil.
heap_pop(\@heap) passes an array reference, so the helper mutates the original heap.
Inside heap_pop, my ($heap) = @_ stores that reference in the scalar $heap.
my $smallest = $heap->[0] saves the root value 1; Perl array references use $heap->[index] for element access.
$heap->[0] = pop @$heap removes the last array element, 7, and writes it into the root slot.
Perl heap indexing here is zero-based: for parent index p, the left child is p * 2 + 1 and the right child is left + 1.
Sift-down starts at my $parent = 0 and runs in while (1).
last if $left >= scalar @$heap stops when the current parent has no child.
The code starts with the left child, then chooses the right child only when $right < scalar @$heap && $heap->[$right] < $heap->[$left].
This is a min-heap: last if $heap->[$parent] <= $heap->[$child] stops when the parent is no larger than the smaller child.
Swaps use Perl list assignment: ($heap->[$parent], $heap->[$child]) = ($heap->[$child], $heap->[$parent]).
return $smallest gives the caller the popped value, 1.

Sift-down replay

start heap:          [1, 4, 2, 9, 6, 7]
save root:           popped = 1
move last to root:   [7, 4, 2, 9, 6]
children of index 0: left=4, right=2, choose 2
swap 7 with 2:       [2, 4, 7, 9, 6]
stop: index 2 has no children

list_string(@heap) joins the final heap with ", ", and print "$popped -> " . list_string(@heap) . "\n" outputs 1 -> [2, 4, 7, 9, 6].

Output

1 -> [2, 4, 7, 9, 6]