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

Dart DSA Implementation

basic.dart

String listString(List<int> values) => "[${values.join(", ")}]";
void heapInsert(List<int> heap, int value) {
  heap.add(value);
  var child = heap.length - 1;
  while (child > 0) {
    final parent = (child - 1) ~/ 2;
    if (heap[parent] <= heap[child]) break;
    final tmp = heap[parent]; heap[parent] = heap[child]; heap[child] = tmp;
    child = parent;
  }
}
int heapPop(List<int> heap) {
  final smallest = heap[0];
  heap[0] = heap.removeLast();
  var parent = 0;
  while (true) {
    final left = parent * 2 + 1;
    final right = left + 1;
    if (left >= heap.length) break;
    var child = left;
    if (right < heap.length && heap[right] < heap[left]) child = right;
    if (heap[parent] <= heap[child]) break;
    final tmp = heap[parent]; heap[parent] = heap[child]; heap[child] = tmp;
    parent = child;
  }
  return smallest;
}
void main() { final heap = [1, 4, 2, 9, 6, 7]; final popped = heapPop(heap); print('$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].

Output

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