Shortest path with a fixed number of edges

Question

Find the shortest path through a graph in efficient time, with the additional constraint that the path must contain exactly n nodes.

We have a directed, weighte

Answer 1

The alternative that comes to my mind is a depth first search (as opposed to Dijkstra's breadth first search), modified as follows:

• stop "depth"-ing if the required vertex count is exceeded

• record the shortest found (thus far) path having the correct number of nodes.

Run time may be abysmal, but it should come up with the correct result while using a very reasonable amount of memory.