08-heaps

Min-Heap Insert (Sift Up)

Insert one value into a min-heap and restore the parent-child order by sifting upward.

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

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(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.

Array state [2, 4, 7, 9, 6, 1] as a heap-shaped tree.2i04i17parent9i36i41new

Step 2 - Swap with 7

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

After the first sift-up swap: [2, 4, 1, 9, 6, 7].2parent4i11child9i36i47i5

Step 3 - Swap with 2

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

Final heap after insert: [1, 4, 2, 9, 6, 7].1root4i12i29i36i47i5

Output

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

Implementation notes

  • Kotlin stores the heap in val heap = mutableListOf(2, 4, 7, 9, 6), a MutableList<Int> whose binding is stable but whose elements mutate in place.
  • heapInsert(heap: MutableList<Int>, value: Int) mutates the caller-owned list and returns no value.
  • Insertion appends with heap.add(value), then initializes mutable var child = heap.lastIndex to the new element's index.
  • Parent indexes use val parent = (child - 1) / 2; the while (child > 0) guard prevents subtracting from zero before that calculation.
  • This is a min-heap: if (heap[parent] <= heap[child]) break stops when the parent is already no larger than the child.
  • Swaps use an explicit temporary variable: val tmp = heap[parent]; heap[parent] = heap[child]; heap[child] = tmp, then child = parent continues sifting upward.
  • The trace shows [2, 4, 7, 9, 6], append to [2, 4, 7, 9, 6, 1], swap with parent 7 to [2, 4, 1, 9, 6, 7], then swap with parent 2 to [1, 4, 2, 9, 6, 7].
  • println(listString(heap)) formats the mutated heap as [1, 4, 2, 9, 6, 7].