Dijkstra's algorithm with 'must-pass' nodes

Question

I am trying to implement Dijkstra\'s algorithm which can find the shortest path between the start node and the end node. Before reach the end node there are some \'must-pass

Answer 1

Unfortunately this problem is reduced to TSP so dont expect a polynomial solution but if no of intermediate node are small then you can do this reasonably fast like following :-

1. try every sequence of nodes to visit possible.
2. say you have s->a->b->c->d
3. then evaluate min(s,d) + min(d,a) + min(c,d) using dijkstra
4. the sequence that has minimum distance is your answer.

Time complexity : O(k!*ElogV) where k is no of must pass nodes