This question already has an answer here:
Is it possible to modify Dijkstra´s algorithm in order to get the longest path from $s$ to $t$ ?.
My intuition says that I´ll need a different algorithm entirely. Finding the longest path is the same as finding the shortest path on a graph with negative weights. However, Dijkstra’s algorithm requires that the weights are positive, so it cannot be modified to calculate the longest path. A better algorithm to use could be: http://en.wikipedia.org/wiki/Longest_path_problem
Any idea of how to modify it?