Kth Largest - Algorithm

Maintain a min-heap of size $k$:

$1.$ Insert the first $k$ elements into the heap.

$2.$ For each remaining element:

• If it's larger than the heap root, extract root and insert element.
• Otherwise, skip it.

$3.$ Return the heap root. The heap always contains the $k$ largest elements seen so far. Its root (minimum of these $k$) is the k-th largest overall. Time: $O(n \log k)$. Space: $O(k)$.