Dijkstra shortest path algorithm with edge cost

Question

I have a directed, positive weighted graph. Each edge have a cost of use. I have only A money, i want to calculate shortest paths with dijkstra algorithm, but sum of edges costs on route must be less or equal to A. I want to do this with most smallest Dijstra modification (if I can do it with small modification of Dijkstra). I must do this in `O(n*log(n))` if I can, but i think i can. Anyone can help me with this?

Accepted Answer

https://www.spoj.pl/problems/ROADS/

The problem was given at CEOI '98 and its official solution can be found here.

Dijkstra shortest path algorithm with edge cost

Solution

Problem