具有障碍物和特定中途点的最短路径的寻路算法

Question

I have a 12x12 grid represented by a 2-d array.

0 c b 0 0 0 c 0 b 0 b 0
0 c c c 0 0 c 0 c c c 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
a 0 0 0 0 0 0 0 0 0 0 d
0 0 0 0 0 0 c 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
c c c c c c 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 c 0 c 0 0 0 0 0 0 0

a = Starting point

d = Ending point

c = Obstacle

b = Required point (still an obstacle)

I need to write an algorithm that will return all the b points in the optimal order, such that I'm starting at the a tile, then need to move next to all b tiles taking into consideration you can't pass through 'b' or 'c' tiles, then finally ending at d .

For the example given, I would want the return to be 3 points,

[Point(0,2), Point(0,8), Point(0,10)]

As I know I want to start at a already and end at d I want to return the order to visit b 's most optimally. Are there any libraries that can help with this? If not, what type of algorithm am I looking to build? If anyone could recommend some reading or something to help get me started that would be much appreciated.

Answer 1

Start by giving all open fields numbers. all adjacent fields to a get 1, all adjacent fields to 1 get 2, etc. Note that you do this only for free field You do this until you have reached all nodes. this becomes part of your path Graph.

you repeat this numbering for all nodes. so for B2 it will look like: The above gives the following Graph:

Now you can use eg Dijksta's algorithm, to solve shortest path.