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.

Complexity

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

sift up A new value starts at the end of the array and swaps with its parent while it is smaller.

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(2, 4, 7, 9, 6); heapInsert(heap, 1); println(listString(heap)) }
}

The heap is still an array, but the tree view makes parent-child swaps visible. The labels use the pinned replay states from the lesson.

Step 1 - Append 1

The new value 1 starts at index 5 and compares with its parent value 7.

Step 2 - Swap with 7

Because 1 is smaller than 7, those array slots swap.

Step 3 - Swap with 2

1 is also smaller than 2, so it moves to the root and the heap order is restored.

Implementation notes

The heap is a scala.collection.mutable.ArrayBuffer[Int], so insertion uses heap += value to append into the same mutable collection.
This is a min-heap: the loop stops when heap(parent) <= heap(child).
After appending, var child = heap.length - 1 tracks the new slot, and each parent is computed with (child - 1) / 2.
The sift-up loop runs while child > 0; reaching index 0 means the value has become the root.
Swaps are explicit slot updates with val tmp = heap(parent), then writes to heap(parent) and heap(child).
The trace starts from [2, 4, 7, 9, 6], appends 1, swaps it with 7, then swaps it with 2.
main prints listString(heap), which uses mkString("[", ", ", "]"), so the final replayed output is [1, 4, 2, 9, 6, 7].

Output

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