How to do an efficient priority update in STL priority_queue?

I can suggest 2 choices to solve the problem, although neither performs a real update.

1. Use the priority_queue and push element each time you would like to update it. Accept the fact that you will have useless entries in the queue. When popping the top value, check if it contains the up-to-date value. If not, ignore it and pop the next.

   This way you delay the removal of the updated element until it comes to the top. I noticed this approach being used by top programmers realizing Dijkstra algorithm.

2. Use set. It is also sorted so you are able to extract the greatest element in logarithmic time. You are also able to remove the outdated element before inserting it again. So still no update operation possible, but removal and reinsertion is doable.

Seems like the complexity of both approaches is the same.