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.

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(1, 4, 2, 9, 6, 7); val popped = heapPop(heap); println("$popped -> ${listString(heap)}") }

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