Search weighted graph, lowest cost, remember route

Question

Is there a rgaph searching algorithm that searches through a graph (from point a to point b, at the lowest cost possible - this is on a weighted graph) that remembers the path that it takes (e.g. not Dijkstra's as it does not remember the path but simply gives you the shortest distance)?

Answer 1

Have a look at this one: http://www.uweschmidt.org/projects/dijkstravis

You have to calculate the path step-wise