Is a c++ std::priority_queue the right structure for the dijkstra queue

Question

I don't think a c++ priority queue is the right structure for the dijkstra queue, because it contains no functionality for an easy lookup or deletion of elements.

The right structure would be a fibonacci heap, but there is none in the std library.

Does anyone have suggestions for a better, c++ implemented structure?

Answer 1

You can use std::set and store a pair<distance, vertex> in it. To lookup and delete elements, you can keep distance to each vertex in an array or in std::vector to obtain a pair<distance, vertex> for a given vertex quickly. The closest unvisited vertex is always in the first element of the set(and can obtained using set.begin() ).

Answer 2

For most practical purposes, the std::priority_queue based implementation is good enough for sparse graphs. Implementing Dijkstra this way has a runtime of O(E log V) . If you have a dense enough graph, you could simply use the basic O(V*V) version of Dijkstra's algorithm. As the graph gets denser, the asymptotics of the Fib-heap version move closer to the vanilla implementation.