Min-Heap Insert (Sift Up)

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

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

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(2, 4, 7, 9, 6)); heapInsert(heap, 1); System.out.println(listString(heap)); }
}

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