decreaseKey in STL Priority Queue

[Senjuti]

I'm trying to implement Prim's Algorithm and for that I need to have a decreaseKey method for a priority queue (to update the key value in a priority queue). Can I implement this in the STL Priority Queue?

If it helps, this is the algorithm I'm following:

for each vertex u in graph G
set key of u to INFINITY
set parent of u to NIL
set key of source vertex to 0
en-queue to priority queue Q all vertices in graph
While Q is not empty
extract vertex u from Q // u is vertex with lowest key in Q
for each adjacent vertex v of u do if (v is still in Q) and (weight-function(u, v) < key of v) then
set u to be parent of v
update v's key to equal weight-function(u, v) //This part is giving me problems as I don't know how implement decreaseKey in priority queue

[JLBorges]

Instead of a std::priority_queue<>, use a std::set<> with an appropriate predicate.

To modify the value of a key:
a. erase the key
b. insert the key with the modified value.