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.

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 = [2, 4, 7, 9, 6]
heap_insert(heap, 1)
print(list_string(heap))

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