Finding the shortest path in a graph without any negative prefixes

Question

Find the shortest path from source to destination in a directed graph with positive and negative edges, such that at no point in the path the sum of edges coming

Answer 1

I would like to clarify a few points :

1. yes there can be negative weight cycles.
2. n is the number of edges.
3. weights are arbitrary not just +1/-1.
4. Assume that a O(n) length path exists if the problem has a solution. (n is number of edges)