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.

Java DSA Implementation

Basic.java

import java.util.*;
class Basic {
    static String listString(List<Integer> values) { return values.toString(); }
    static void heapInsert(List<Integer> heap, int value) {
        heap.add(value);
        int child = heap.size() - 1;
        while (child > 0) {
            int parent = (child - 1) / 2;
            if (heap.get(parent) <= heap.get(child)) break;
            Collections.swap(heap, parent, child);
            child = parent;
        }
    }
    static int heapPop(List<Integer> heap) {
        int smallest = heap.get(0);
        heap.set(0, heap.remove(heap.size() - 1));
        int parent = 0;
        while (true) {
            int left = parent * 2 + 1;
            int right = left + 1;
            if (left >= heap.size()) break;
            int child = left;
            if (right < heap.size() && heap.get(right) < heap.get(left)) child = right;
            if (heap.get(parent) <= heap.get(child)) break;
            Collections.swap(heap, parent, child);
            parent = child;
        }
        return smallest;
    }
    public static void main(String[] args) { List<Integer> heap = new ArrayList<>(Arrays.asList(1, 4, 2, 9, 6, 7)); int popped = heapPop(heap); System.out.println(popped + " -> " + listString(heap)); }
}

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