https://en.wikipedia.org/wiki/Heap_(data_structure) A Binary tree which is complete and the children are smaller than the parents.

a specialized tree-based data structure that satisfies the heap property: If A is a parent node of B then the key (the value) of node A is ordered with respect to the key of node B with the same ordering applying across the heap. A heap can be classified further as either a "max heap" or a "min heap".

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Algorithms on heaps

• Get max O(1), it's at the root.
• Fixing the heap after Inserting into a heap, after deleting, after changing. All $O(\log{n})$.
• Finding indices when in level ordering
• Building a heap