Priority Queue Based

Define the priority before choosing the heap

Ask what item is selected next, whether priority is minimum or maximum, how ties break, whether priorities change after insertion, and what constitutes completion. A heap is useful only when the algorithm repeatedly needs the current best frontier item; it does not solve an arbitrary problem merely because its title says priority queue.

Describe a baseline that scans all candidates per selection, then replace the repeated scan with heap push and pop. State what each heap entry contains and the invariant: the root is the best currently valid candidate under the confirmed comparator. If entries can become stale, validate them on pop or maintain indexed updates. With p pushes and pops, heap work is O(p log p) and storage is O(p) in the worst case. Test empty input, duplicate priorities, tie stability, stale records, and termination when no valid candidate remains. Choose a min-heap or max-heap based on the objective, not habit.