Thought Process

Was stumped on this one for a long time, I was always wondering how to handle so many degrees of freedom using dynamic programming, but after taking a break I realised that I don't need to use dynamic programming, this problem perfectly suits the application of Dijkstra's algorithm. 

I then decided to try to code my own version of Dijkstra's algorithm and i'm very proud that it worked! A more general Dijkstra's algorithm is available in my essential functions