Implementation of decrease key function for a min heap priority queue

Question

I'm trying to run Dijkstra's algorithm and I need to implement a decreaseKey function. I'm having trouble doing it. I read one solution here but it uses a lot of memory by storing a hash map in the heap. Is there a way to implement decreaseKey without a hash map and still maintain O(log n) time?

So far my decreaseKey function takes two parameters: vertex and newDistance. When I call decreaseKey(vertex * v, int newDistance) , the algorithm has to find the index where vertex 'v' is stored and then change its distance. I can't figure out how to 'find' the vertex to get its index and keep it in O(log n) time.

Answer 1

You don't need a hash map to store the information; you only need a mapping from vertex to priority-queue position. If your vertices are identified by consecutive integers, then the mapping consists of an array of |V| integers (where |V| is the number of vertices).

While that is not a trivial amount of space, it is only one word per graph vertex, which is considerably less than the space occupied by edge lists.