Since this is the comment thread talking about the algorithm I'm gonna add my 2 cents here:
Here's the problem statement as far as I see it:
Each tile has a number of move points to spend to go through it (1 for regular and 2 for water). Each tile also has a cost associated with it. Given a max number of move points find the lowest cost path between two tiles or return none if no such path exists.
I'm gonna say this is still modified dijkstra with a small twist. The fire has cost 1, the other tiles have cost 0. However instead of pathing on a 2d grid (x, y) we path on a 3d grid (x, y, moves). All "goal" tiles within (goal_x, goal_y, moves < total_move_points) have a 0 cost edge which brings them to the true goal node. The implementation difference is that the get neighbors function queries neighbors in later grid layers (x+..., y+..., moves + 1 or 2)
Here's the problem statement as far as I see it: Each tile has a number of move points to spend to go through it (1 for regular and 2 for water). Each tile also has a cost associated with it. Given a max number of move points find the lowest cost path between two tiles or return none if no such path exists.
I'm gonna say this is still modified dijkstra with a small twist. The fire has cost 1, the other tiles have cost 0. However instead of pathing on a 2d grid (x, y) we path on a 3d grid (x, y, moves). All "goal" tiles within (goal_x, goal_y, moves < total_move_points) have a 0 cost edge which brings them to the true goal node. The implementation difference is that the get neighbors function queries neighbors in later grid layers (x+..., y+..., moves + 1 or 2)