Lessons from Kth Largest

What did you learn?

$1.$ For k-th largest, use a min-heap of size $k$. For k-th smallest, use a max-heap of size $k$.

$2.$ The heap root is the "boundary" element. Anything smaller (for k-th largest) gets filtered out.

$3.$ Bounded heaps reduce time complexity from $O(n \log n)$ to $O(n \log k)$. This pattern extends to "top k elements," "k closest points," and similar problems.