Min-Heap Insert (Sift Up) - JavaScript DSA

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.

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

JavaScript DSA Implementation

basic.js

function listString(values) { return `[${values.join(", ")}]`; }
function heapInsert(heap, value) {
  heap.push(value);
  let child = heap.length - 1;
  while (child > 0) {
    const parent = Math.floor((child - 1) / 2);
    if (heap[parent] <= heap[child]) break;
    [heap[parent], heap[child]] = [heap[child], heap[parent]];
    child = parent;
  }
}
function heapPop(heap) {
  const smallest = heap[0];
  heap[0] = heap.pop();
  let parent = 0;
  while (true) {
    const left = parent * 2 + 1;
    const right = left + 1;
    if (left >= heap.length) break;
    let child = left;
    if (right < heap.length && heap[right] < heap[left]) child = right;
    if (heap[parent] <= heap[child]) break;
    [heap[parent], heap[child]] = [heap[child], heap[parent]];
    parent = child;
  }
  return smallest;
}
const heap = [2, 4, 7, 9, 6];
heapInsert(heap, 1);
console.log(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.

Step 2 - Swap with 7

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

Step 3 - Swap with 2

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

Output

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

Implementation notes

The heap is a mutable JavaScript Array of Number values using the usual binary-heap index layout, not explicit node objects. This lesson follows the heapInsert path; heapPop is present in basic.js for the paired heap lesson but is not exercised by this replay.
heapInsert(heap, value) appends with heap.push(value), then starts child = heap.length - 1. Each parent index is computed with Math.floor((child - 1) / 2).
The min-heap check uses numeric Number comparison: heap[parent] <= heap[child] stops the sift-up when order is restored.
Swaps use destructuring assignment, [heap[parent], heap[child]] = [heap[child], heap[parent]], mutating array slots in place. JavaScript specifies the temporary right-hand values; engines may optimize the short-lived storage used for the destructuring swap.
The replay appends 1 to [2, 4, 7, 9, 6], swaps it with parent 7 to get [2, 4, 1, 9, 6, 7], then swaps it with parent 2 to get [1, 4, 2, 9, 6, 7]. listString(heap) joins values for the printed output [1, 4, 2, 9, 6, 7]; visible allocation is the heap array plus the strings created by join and the template literal in listString.