Hard Create Heaps & Priority Queues open_ended

Design an optimal solution for a real-world application of Heaps & Priority Queues.

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This question is from the Heaps & Priority Queues topic (Data Structures).

In a min-heap stored as an array, what is the parent index of the node at index i?

What is the time complexity of extracting the minimum from a min-heap?

What is the heap invariant for a min-heap?

What is the time complexity of peek() (see minimum without removing) in a min-heap?

Why use a min-heap of size k to find the kth LARGEST element?