Yes, they can. You can read about this in ‘Introduction to Algorithms’ (by Charles E. Leiserson, Clifford Stein, Thomas H. Cormen, and Ronald Rivest). According to the definition of binary heaps in Wikipedia: All nodes are either [greater than or equal to](max heaps) or [less than or equal to](min heaps) each of its children, according … Read more
The logical argument is as follows std::priority_queue is a container adaptor; basic memory considerations make the back the preferred place for modifications (with pop_back() and push_back()) for sequence containers such as std::vector. the priority_queue primitives are based on std::make_heap (constructor), std::pop_heap + container::pop_back (priority_queue::pop) and on container::push_back + std::push_heap (priority_queue::push) pop_heap will take the front … Read more
Typical Solution The usual solution is to mark an element as invalid and insert a new element, then eliminate the invalid entries as they are popped-off. Alternative Solution If that approach doesn’t suffice, it is possible restore the min-heap invariant in O(log n) steps as long as the location of the value being changed is … Read more