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.

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)) }
}

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