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.

Kotlin DSA Implementation

basic.kt

fun listString(values: List<Int>) = values.joinToString(", ", "[", "]")
fun heapInsert(heap: MutableList<Int>, value: Int) {
    heap.add(value)
    var child = heap.lastIndex
    while (child > 0) {
        val parent = (child - 1) / 2
        if (heap[parent] <= heap[child]) break
        val tmp = heap[parent]; heap[parent] = heap[child]; heap[child] = tmp
        child = parent
    }
}
fun heapPop(heap: MutableList<Int>): Int {
    val smallest = heap[0]
    heap[0] = heap.removeAt(heap.lastIndex)
    var parent = 0
    while (true) {
        val left = parent * 2 + 1
        val right = left + 1
        if (left >= heap.size) break
        var child = left
        if (right < heap.size && heap[right] < heap[left]) child = right
        if (heap[parent] <= heap[child]) break
        val tmp = heap[parent]; heap[parent] = heap[child]; heap[child] = tmp
        parent = child
    }
    return smallest
}
fun main() { val heap = mutableListOf(2, 4, 7, 9, 6); heapInsert(heap, 1); println(listString(heap)) }

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