title: A Shortest path with fuel constraints
body: <p>I found this problem somewhere in a contest and haven't been able to come up with a solution yet. I am thinking on the lines of applying Dijkstra's or something but it is not very clear : </p>
  
  <p>''You are given a weighted connected graph of cities with all edges having positive weights. Some of the cities ( nodes ) have petrol pump whereas some don’t. You have a bike with the tank capacity of C. That is, with full tank, the car can travel for C units of distance. At any city with a petrol pump the car can fill its tank to full. Find out the shortest path between the a given source and a given destination. Assume that you start with a full tank.''</p>
  
  <p>I have a feeling O(mn logn) will be accepted by it. </p>