Example on How to use A* algorithm.?

Let's walk through an example of the A* algorithm to find the shortest path between two points in a graph.

Suppose we have a map with the following nodes and connections:


A --5--> B --4--> C
|        ^       ^
2        3       6
v        |       |
D -----  E --2-- F

We want to find the shortest path from node A to node F using the A* algorithm. We will assume that the cost of moving from one node to an adjacent node is equal to the distance between them.

Initialize the open list with the start node A and the closed list as empty.
```
Open: A
Closed:
```
Select the node with the lowest f-score (estimated total cost) from the open list, which is A in this case. Add A to the closed list.
```
Open:
Closed: A
```
Expand the neighbors of A and calculate their f-scores. Add them to the open list if they are not already in the closed list. Assign A as their parent.
```
Open: B (f=7)
Closed: A
```
Select the node with the lowest f-score from the open list, which is B in this case. Add B to the closed list.
```
Open:
Closed: A, B
```
Expand the neighbors of B and calculate their f-scores. Add them to the open list if they are not already in the closed list. Assign B as their parent.
```
Open: D (f=8), C (f=11), E (f=10)
Closed: A, B
```
Select the node with the lowest f-score from the open list, which is D in this case. Add D to the closed list.
```
Open: C (f=11), E (f=10)
Closed: A, B, D
```
Expand the neighbors of D and calculate their f-scores. Add them to the open list if they are not already in the closed list. Assign D as their parent.
```
Open: E (f=10), B (f=11), C (f=11)
Closed: A, B, D
```
Select the node with the lowest f-score from the open list, which is E in this case. Add E to the closed list.
```
Open: B (f=11), C (f=11), F (f=12)
Closed: A, B, D, E
```
Expand the neighbors of E and calculate their f-scores. Add them to the open list if they are not already in the closed list. Assign E as their parent.
```
Open: F (f=12), B (f=11), C (f=11)
Closed: A, B, D, E
```
Select the node with the lowest f-score from the open list, which is B in this case. Add B to the closed list.


Open: C (f=11), F (f=12)
Closed: A, B, D, E, B

Expand the neighbors of B and calculate their f-scores. Add them to the open list if they are not already in the closed list. Assign B as their parent.


Open: C (f=11), F (f=12)
Closed: A, B, D, E, B

Select the node with the lowest f-score from the open list

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