How to implement O(logn) decrease-key operation for min-heap based Priority Queue?

Question

I am working on an application that demonstrates the Djikstra\'s algorithm, and to use it, I need to restore the heap property when my elements\' value is decreased

Answer 1

If you are using c++ stl make_heap()/pop_heap()/push_heap(), there is no way to keep an index from node id to index in the underline heap vector, I think you should implement your own heap functions to achieve O(logn) in Increase-Key/Decrease-key operation.