08-heaps

Min-Heap Pop (Sift Down)

Remove the minimum value, move the last item to the root, and sift downward.

Algorithm

Steps

  1. Store the heap in an array.
  2. Compare parent and child indexes instead of building explicit tree nodes.
  3. Swap only when the heap order is violated.
  4. 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

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)}") }

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.

Replacement state [7, 4, 2, 9, 6] with removed value 1.1removed7root4left2smaller9i36i4

Step 2 - Swap with the smaller child

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

Final heap after pop and one sift-down swap.2root4i17i29i36i4

Output

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

Implementation notes

  • Kotlin stores the heap in val heap = mutableListOf(1, 4, 2, 9, 6, 7), a MutableList<Int> whose binding is stable while its elements are mutated in place.
  • heapPop(heap: MutableList<Int>): Int copies val smallest = heap[0] and returns that removed minimum after the sift-down.
  • Root replacement uses heap[0] = heap.removeAt(heap.lastIndex): removeAt removes and returns the last element, then that value is written into index 0. The checked call uses a six-element heap; this compact helper does not handle an empty or singleton heap separately.
  • Sift-down starts with mutable var parent = 0; child indexes are left = parent * 2 + 1 and right = left + 1.
  • if (left >= heap.size) break stops at a leaf. var child = left is replaced by right only when right < heap.size && heap[right] < heap[left].
  • This is a min-heap: if (heap[parent] <= heap[child]) break stops when the parent is already no larger than the smaller child.
  • Swaps use an explicit temporary variable: val tmp = heap[parent]; heap[parent] = heap[child]; heap[child] = tmp, then parent = child continues downward.
  • The trace shows [1, 4, 2, 9, 6, 7], removes 1 and moves 7 to the root as [7, 4, 2, 9, 6], then swaps with smaller child 2 to [2, 4, 7, 9, 6].
  • println("$popped -> ${listString(heap)}") prints 1 -> [2, 4, 7, 9, 6].