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. @end @complexity

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

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

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)}")

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