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

Python DSA Implementation

basic.py

def list_string(values):
    return "[" + ", ".join(str(v) for v in values) + "]"

def heap_insert(heap, value):
    heap.append(value)
    child = len(heap) - 1
    while child > 0:
        parent = (child - 1) // 2
        if heap[parent] <= heap[child]:
            break
        heap[parent], heap[child] = heap[child], heap[parent]
        child = parent

def heap_pop(heap):
    smallest = heap[0]
    heap[0] = heap.pop()
    parent = 0
    while True:
        left = parent * 2 + 1
        right = left + 1
        if left >= len(heap):
            break
        child = left
        if right < len(heap) and heap[right] < heap[left]:
            child = right
        if heap[parent] <= heap[child]:
            break
        heap[parent], heap[child] = heap[child], heap[parent]
        parent = child
    return smallest
heap = [1, 4, 2, 9, 6, 7]
popped = heap_pop(heap)
print(f"{popped} -> {list_string(heap)}")

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].

Output

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

Implementation notes

Python stores the min-heap in one mutable list. heap_pop saves smallest = heap[0], removes the last slot with heap.pop(), and assigns that last value back to heap[0] before sifting down.
Child indexes are computed from the current parent with left = parent * 2 + 1 and right = left + 1. The loop stops when left is outside the list or when heap[parent] <= heap[child].
When both children exist, right < len(heap) and heap[right] < heap[left] selects the smaller child for this min-heap. Swaps use Python tuple assignment to mutate list slots in place without building a new heap list.
The function returns the saved minimum value, while the replay shows the list changing from [7, 4, 2, 9, 6] after root replacement to [2, 4, 7, 9, 6] after the sift-down swap. Python manages the heap list while it is referenced, and any temporary values while they exist.