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.

Complexity

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

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

Visual walkthrough

Scala DSA Implementation

basic.scala

import scala.collection.mutable.ArrayBuffer
object Main {
  def listString(values: Seq[Int]): String = values.mkString("[", ", ", "]")
  def heapInsert(heap: ArrayBuffer[Int], value: Int): Unit = {
    heap += value
    var child = heap.length - 1
    while (child > 0) {
      val parent = (child - 1) / 2
      if (heap(parent) <= heap(child)) return
      val tmp = heap(parent); heap(parent) = heap(child); heap(child) = tmp
      child = parent
    }
  }
  def heapPop(heap: ArrayBuffer[Int]): Int = {
    val smallest = heap(0)
    heap(0) = heap.remove(heap.length - 1)
    var parent = 0
    var done = false
    while (!done) {
      val left = parent * 2 + 1
      val right = left + 1
      if (left >= heap.length) done = true
      else {
        var child = left
        if (right < heap.length && heap(right) < heap(left)) child = right
        if (heap(parent) <= heap(child)) done = true
        else { val tmp = heap(parent); heap(parent) = heap(child); heap(child) = tmp; parent = child }
      }
    }
    smallest
  }
  def main(args: Array[String]): Unit = { val heap = ArrayBuffer(1, 4, 2, 9, 6, 7); val popped = heapPop(heap); println(s"$popped -> ${listString(heap)}") }
}

After popping the minimum, the last value moves to the root and sifts down by swapping with the smaller child.

Step 1 - Replace root

The saved minimum is 1; the last value 7 moves to the root before sifting down.

Step 2 - Swap with the smaller child

7 swaps with 2, producing the final heap [2, 4, 7, 9, 6].

Implementation notes

The heap is a Scala mutable ArrayBuffer[Int], and heapPop mutates that same buffer while returning the removed minimum.
This source is a min-heap: parent values must stay <= child values.
val smallest = heap(0) saves the root result before the structure changes.
heap(0) = heap.remove(heap.length - 1) removes the last slot and writes that returned value into the root position.
Sift-down starts with var parent = 0; each loop computes left = parent * 2 + 1 and right = left + 1.
If there is no left child, done = true; otherwise var child = left, with the right child selected only when it exists and is smaller.
The swap uses an explicit val tmp and slot writes, then updates parent = child to continue downward.
The trace starts from [1, 4, 2, 9, 6, 7], removes 1, moves 7 to the root, then swaps 7 with smaller child 2.
main prints the returned value and remaining heap as 1 -> [2, 4, 7, 9, 6].

Output

1 -> [2, 4, 7, 9, 6]