08-heaps

Min-Heap Pop (Sift Down)

Remove the minimum value, move the last item to the root, and sift downward.

Algorithm

Steps

  1. Store the heap in an array.
  2. Compare parent and child indexes instead of building explicit tree nodes.
  3. Swap only when the heap order is violated.
  4. Print the deterministic final heap state for replay comparison.

Complexity

  • Time: O(log n)
  • Space: O(1) extra
sift down After removing the root, the last value moves to the root and swaps with the smaller child until order is restored.

Visual walkthrough

JavaScript DSA Implementation

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

After popping the minimum, the last value moves to the root and sifts down by swapping with the smaller child.

Step 1 - Replace root

The saved minimum is 1; the last value 7 moves to the root before sifting down.

Replacement state [7, 4, 2, 9, 6] with removed value 1.1removed7root4left2smaller9i36i4

Step 2 - Swap with the smaller child

7 swaps with 2, producing the final heap [2, 4, 7, 9, 6].

Final heap after pop and one sift-down swap.2root4i17i29i36i4

Output

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

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 heapPop path; heapInsert is present in basic.js for the paired heap lesson but is not exercised by this replay.
  • heapPop(heap) saves const smallest = heap[0], then moves the last array slot to the root with heap[0] = heap.pop(). For the replay, that removes 1 and places 7 at index 0, leaving [7, 4, 2, 9, 6].
  • Sift-down starts at parent = 0. Child indexes are computed as left = parent * 2 + 1 and right = left + 1; the right child is selected only when right < heap.length && heap[right] < heap[left].
  • Min-heap comparisons use numeric Number ordering. The replay picks right child 2 over left child 4, swaps 7 with 2, and stops at [2, 4, 7, 9, 6] when the new parent has no children.
  • 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 swap.
  • console.log(\${popped} -> ${listString(heap)}`)prints1 -> [2, 4, 7, 9, 6]. Visible allocation is the heap array plus the strings created by join` and template formatting.