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. @end @complexity

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

sift down After removing the root, the last value moves to the root and swaps with the smaller child until order is restored.

C# DSA Implementation

basic.cs

using System;
using System.Collections.Generic;
using System.Linq;
class Program {
    static string ListString(IEnumerable<int> values) => "[" + string.Join(", ", values) + "]";
    static void HeapInsert(List<int> heap, int value) {
        heap.Add(value);
        int child = heap.Count - 1;
        while (child > 0) {
            int parent = (child - 1) / 2;
            if (heap[parent] <= heap[child]) break;
            (heap[parent], heap[child]) = (heap[child], heap[parent]);
            child = parent;
        }
    }
    static int HeapPop(List<int> heap) {
        int smallest = heap[0];
        heap[0] = heap[^1];
        heap.RemoveAt(heap.Count - 1);
        int parent = 0;
        while (true) {
            int left = parent * 2 + 1, right = left + 1;
            if (left >= heap.Count) break;
            int child = left;
            if (right < heap.Count && heap[right] < heap[left]) child = right;
            if (heap[parent] <= heap[child]) break;
            (heap[parent], heap[child]) = (heap[child], heap[parent]);
            parent = child;
        }
        return smallest;
    }
    static void Main() { var heap = new List<int> {1, 4, 2, 9, 6, 7}; int popped = HeapPop(heap); Console.WriteLine($"{popped} -> {ListString(heap)}"); }
}

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