A binary heap is far weaker than a binary search tree: it only guarantees each parent beats its children, so it cannot search for an arbitrary value in better than O(n). Why is that weaker invariant an advantage rather than a defect?

A. Because finding the maximum only needs the root.

A priority queue is asked for the highest-priority item and nothing else, and the heap property puts it at the root by construction. Being weaker pays twice: restoring the invariant means sifting one node up a single path, and because left and right are unconstrained the tree stays complete and lives in a flat array. The best invariant is the weakest one that still works.