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. @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.

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)}`);

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