Efficiency of the STL priority_queue

Question

I have an application (C++) that I think would be well served by an STL priority_queue. The documentation says:

Priority_queue is a cont

Answer 1

If the underlying data structure is a heap, top() will be constant time, and push (EDIT: and pop) will be logarithmic (like you are saying). The vector is just used to store these things like this:

HEAP:
             1
        2         3
      8 12   11 9

VECTOR (used to store)

1 2 3 8 12 11 9

You can think of it as the element at position i's children is (2i) and (2i+1)

They use the vector because it stores the data sequentially (which is much more efficient and cache-friendly than discrete)

Regardless of how it is stored, a heap should always be implemented (especially by the gods who made the STD lib) so that pop is constant and push is logarithmic