The heap is stored as a plain array where parent(i) = (i - 1) / 2 and the children of i live at 2i + 1 and 2i + 2. push appends to the end and sifts up: bubble the new element toward the root while it is smaller than its parent. pop removes the root, moves the last element into its place, and sifts down: swap with the smaller child while invariant is broken. Both operations touch O(log n) levels. The comparator default (a, b) => a - b makes the structure a min-heap; pass (a, b) => b - a for a max-heap.

Pushing every element then popping every element gives a sorted result in O(n log n) total. This is heap sort, one of the canonical comparison-based sorts; it is in-place when the heap mutates the input array directly, but the version above is the simpler 'use the heap as a queue' variant. The advantage of heap sort over quicksort is its guaranteed O(n log n) worst case (no degenerate inputs), the disadvantage is its non-stable order. Use it as a baseline when you need predictable performance.

Finding the K largest elements in O(n log k) is one of the headline applications of a min-heap. Maintain a heap of size K, push every element, and pop the smallest whenever the heap grows beyond K. The heap always contains the running 'top K so far', and the smallest of those is the threshold. Reversing at the end gives the largest first. This pattern beats sorting (O(n log n)) when K is much smaller than n, which is common in stream processing and 'top trending' queries.