08-heaps

Min-Heap Insert (Sift Up)

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

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

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));

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