Min-Heap Insert (Sift Up) - TypeScript 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

TypeScript DSA Implementation

basic.ts

function listString(values: number[]): string { return `[${values.join(", ")}]`; }
function heapInsert(heap: number[], value: number): void {
  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: number[]): number {
  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: number[] = [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

In TypeScript, heapInsert(heap: number[], value: number): void mutates the caller's number[]; the sample heap is explicitly declared as const heap: number[] = [2, 4, 7, 9, 6].
heap.push(value) appends 1 in place, then child = heap.length - 1 tracks the inserted slot. Parent indexes use Math.floor((child - 1) / 2).
The sift-up loop stops at the root or when heap[parent] <= heap[child]. Swaps use destructuring assignment on two heap slots, then move child to the former parent index.
The trace shows [2, 4, 7, 9, 6], append to [2, 4, 7, 9, 6, 1], swap with parent 7 to [2, 4, 1, 9, 6, 7], then swap with parent 2 to [1, 4, 2, 9, 6, 7].
console.log(listString(heap)) prints [1, 4, 2, 9, 6, 7]. Visible allocation is the initial heap array and output string; mutation is the existing heap array growing and swapping numeric elements, with no second heap structure built.