Fill a list to use the A* (a-star) algorithm with python

Question

I want to use the A* algorithm to find the fastest way in a map with non-weighted nodes.

My map is a nested list, and contains only 5 different values: 0 for the walls, 2, 3, and 4 for different types of blocks And 1 for empty spaces (you can only "walk" in an empty space)

Here is an example of a map:

[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, 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, 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, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, '*', 1, 1, 1, 1, 1, 1, 1, '$$$', 1, 1, 1, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0]
[0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 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, 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, 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, 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]

NOTE: The * item is the source, and the "$$$" item in the list is the destination. (I want to go from * to "$$$")

I read what this website explained about the A* algorithm, but I'm still not sure how to write my python function.

From the website, what I was able to understand is that I would have to progressively (and starting from the source point) convert my list of block into directions; left, right, up and down (if the block value is 1). Then, once I've reached the destination block, I should stop and follow the directions back to the source block; this will give me the best path.

Objective: I want to make a function with input the nested list that:

1. starting from the source point (*), fill the list with directions.
2. then, once the destination point is reached, go back from the destination point to the source point using the directions previously filled
3. return the list of point containing the path found

NOTE: I am new to path finding algorithm (but not to python), so please give me a readable answer.

Answer 1

Even though I think it might not be the best way to do whatever you have in mind, I can still try to answer your question: Given a nested list containing a map, you want to find the best path between two points using the A-star algorithm, knowing that you can only "walk" on blocks whose value is 1

You also want to use "directions", which I guess might be the four cardinal directions (up, down, left, right)

Knowing all that, here is how I think you want the function to be:

1. Starting from the source point, recursively replace every nearby item whose value is 1 with "directions" (up, down, left, right) so that you can follow the arrows from any point of the map, it will still lead back to the source point. Stop when you reach the destination point
2. Starting from the destination point, follow the arrows back to the source point, replacing each item with a certain symbol (maybe a star "*")

NOTE: Tell me if there is anything you would like me to change to the objective list

Before starting the program, here is the list you gave (you can change it)

mapList = [ # change this nested list to whatever your map is
    [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, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 2, 2, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 2, 2, 1, 1, 2, 2, 0, 0],
    [0, 0, 1, 1, 2, 2, 3, 3, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 2, 2, 3, 3, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 0, 0],
    [0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 3, 3, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 3, 3, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0],
    [0, 0, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0],
    [0, 0, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0],
    [0, 0, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 3, 3, 3, 3, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0],
    [0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 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, 0],
]

1. Replacing every item whose value is 1 with "directions":

sourceRow = 6 # value of the source row, change it according to your needs
sourceColumn = 2 # same thing
sourceSymbol = "Source" # You can change this to whatever you want
mapList[sourceRow][sourceColumn] = sourceSymbol

destRow = 2
destColumn = 15
destinationSymbol = "$$$" # same
mapList[destRow][destColumn] = destinationSymbol

up = "^" # the signs don't really matter
down = "v"
right = ">"
left = "<"


tempList = [(sourceRow, sourceColumn)]


def fillWithDirections(tempPoint: tuple):
    # tempPoint[0] is the row index, tempPoint[1] is the column index

    # List of all the positions to test
    positionToTestList = [
        (tempPoint[0]+1, tempPoint[1]), # this is the point directly below tempPoint
        (tempPoint[0]-1, tempPoint[1]), # this is the point directly above tempPoint
        (tempPoint[0], tempPoint[1]+1), # this is the point directly to the right of tempPoint
        (tempPoint[0], tempPoint[1]-1), # this is the point directly to the left of tempPoint
    ]

    for posTuple in positionToTestList:
        # looping through the 4 possible positions (up, down, left, right) and test if we can fill it with a "direction"
        
        if mapList[posTuple[0]][posTuple[1]] == destinationSymbol:
            # we reached the destination !!!, so end the program
            return 1

        if mapList[posTuple[0]][posTuple[1]] == 1:
            # This means that the current item is "fillable" with "directions"
            
            hasBeenFilled = True
            # fill with up, down, left, right
            if posTuple[0] == tempPoint[0] + 1:
                # means we are currently "below" the tempPoint, so fill with "direction up"
                mapList[posTuple[0]][posTuple[1]] = up
            elif posTuple[0] == tempPoint[0] - 1:
                # means we are currently "above" the tempPoint, so fill with "direction down"
                mapList[posTuple[0]][posTuple[1]] = down
            elif posTuple[1] == tempPoint[1] + 1:
                # means we are currently "to the right" the tempPoint, so fill with "direction left"
                mapList[posTuple[0]][posTuple[1]] = left
            elif posTuple[1] == tempPoint[1] - 1:
                # means we are currently "to the left" the tempPoint, so fill with "direction right"
                mapList[posTuple[0]][posTuple[1]] = right
            else:
                hasBeenFilled = False
            
            if hasBeenFilled:
                # once the we filled the point with the corresponding "direction", let's add it to tempList
                # so that we will eventually test the point
                tempList.append((posTuple[0], posTuple[1]))




while tempList: # run this while there are still points to test in tempList

    tempPoint = tempList.pop(0) # take out the first item of tempList

    # if the function returned anything, it means that it hit the destination point
    if fillWithDirections(tempPoint):
        # if so, break out of the while loop as it doesn't matter to continue
        break

NOTE: We have now filled the nested list with "directions" until we reach the destination point

2. Following the arrows from the destination back to the source point, and replacing every item on the path with a star "*"

# This is the list of all the positions surrounding the destination point
positionOfDestToTestList = [
    (destRow+1, destColumn),
    (destRow-1, destColumn),
    (destRow, destColumn+1),
    (destRow, destColumn-1),
]


tempPosTuple = None
# This is the list of all the "directions" possible (">", "<", ...)
listOfSigns = [up, down, right, left]

for posToTest in positionOfDestToTestList:
    # If one of the four surrounding items is a "direction"
    if mapList[posToTest[0]][posToTest[1]] in listOfSigns:
        # Then set tempPosTuple equal to the corresponding surrounding point
        tempPosTuple = posToTest

while tempPosTuple:
    currentItem = mapList[tempPosTuple[0]][tempPosTuple[1]]

    # If we reached the source point
    if currentItem == sourceSymbol:
        tempPosTuple = None
        break
    
    # Because the point is on the path, replace the "direction" by a star "*"
    mapList[tempPosTuple[0]][tempPosTuple[1]] = '*'
    # Because the point is on the path, replace the "direction" by a star "*"
    mapList[tempPosTuple[0]][tempPosTuple[1]] = '*'

    # change tempPosTuple according to the "direction" it is (ex: column + 1 if arrow is to the right)
    if currentItem == up:
        tempPosTuple = (tempPosTuple[0]-1, tempPosTuple[1])
    elif currentItem == down:
        tempPosTuple = (tempPosTuple[0]+1, tempPosTuple[1])
    elif currentItem == left:
        tempPosTuple = (tempPosTuple[0], tempPosTuple[1]-1)
    elif currentItem == right:
        tempPosTuple = (tempPosTuple[0], tempPosTuple[1]+1)

And it should be it!

You now have a map that contains stars "*" for the fastest path

I hope this helps