K-th Largest with Min-Heap

Why use a min-heap for k-th largest? It seems backwards. The trick: keep exactly $k$ elements in a min-heap.

The heap root is the smallest of these $k$ elements, which is the k-th largest overall. For each new element:

• If smaller than heap root, ignore it (not in top $k$)
• If larger, remove the root and insert the new element

After processing all elements, the root is the k-th largest.