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

Step 1: Note that your answer will be at most 2*n (if it exists).
Step 2: Create a new graph with vertexes that are a pairs of [vertex][cost]. (2*n^2 vertexes)
Step 3: Note that new graph will have all edges equal to one, and at most 2*n for each [vertex][cost] pair.
Step 4: Do a dfs over this graph, starting from [start][0]
Step 5: Find minimum k, such that [finish][k] is accesible.

Total complexity is at most O(n^2)*O(n) = O(n^3)

EDIT: Clarification on Step 1.
If there is a positive cycle, accesible from start, you can go all the way up to n. Now you can walk to any accesible vertex, over no more than n edges, each is either +1 or -1, leaving you with [0;2n] range. Otherwise you'll walk either through negative cycles, or no more than n +1, that aren't in negative cycle, leaving you with [0;n] range.