提取最小元素后的最小堆问题

def extract_min(heap):
    if len(heap) == 0:
        return None
    if len(heap) == 1:
        return heap.pop()
    
    # 移除根节点并保存最小值
    min_value = heap[0]
    # 将最后一个元素移到根节点位置
    heap[0] = heap.pop()
    # 从根节点开始向下调整堆
    heapify_down(heap, 0)
    return min_value

def heapify_down(heap, index):
    left_child_index = 2 * index + 1
    right_child_index = 2 * index + 2
    smallest = index
    
    # 找到最小的子节点
    if left_child_index < len(heap) and heap[left_child_index] < heap[smallest]:
        smallest = left_child_index
    if right_child_index < len(heap) and heap[right_child_index] < heap[smallest]:
        smallest = right_child_index
    
    # 如果最小子节点不是当前节点，交换并继续向下调整
    if smallest != index:
        heap[index], heap[smallest] = heap[smallest], heap[index]
        heapify_down(heap, smallest)

# 示例堆
heap = [3, 5, 8, 9, 10, 12, 15]
print("原始堆:", heap)
min_value = extract_min(heap)
print("提取的最小值:", min_value)
print("调整后的堆:", heap)