Section Recap

You now have heap proficiency:

$1.$ Heap basics: $O(1)$ peek, $O(\log n)$ insert and extract. Stored as arrays.

$2.$ K-th element pattern: use a bounded heap of size $k$. For k-th largest, use a min-heap.

$3.$ K-way merge: heap tracks the frontier of $k$ candidates. $O(n \log k)$ to merge.

$4.$ Two heaps: partition data around median. $O(\log n)$ insertion, $O(1)$ median query.

$5.$ Combining structures: heaps often pair with hash maps (top k frequent) or other structures.

Heaps are your tool when you need efficient, repeated access to extrema. Learn these patterns and a whole class of problems becomes routine. Practice these patterns until they become automatic.