 Hello everyone, this is Alice Gao. In this video, I'm going to trace the A star search algorithm on a search graph. Recall that A star search chooses to remove the path with the lowest f value from the frontier. The f value is a sum of the cost and the heuristic values. I will use the same type-breaking rule as before. Order the path by their last nodes and choose the path that comes first in alphabetical order. During the process, I will keep track of the frontier, the f value for each path in the frontier, and the search tree. I will also label the nodes in the order of expansion. Let's get started. Let's add the initial state as to the frontier and to the search tree. Next, remove as from the frontier. As is not a goal, let's expand it. As has two successors, B and C. Let's add S, B and S, C to the frontier with f values 8 and 4. To give you a calculation example, for S, B, the cost is 1 and the heuristic value is 7, so the f value is 8. Next, S, C has the lowest f value of 4. Let's remove S, C from the frontier. C is not a goal, let's expand it. C has one successor, H. For S, C, H, the cost is 2 and the heuristic value is 100, so the f value is 102. Let's add S, C, H to the frontier. Next, S, B has the lowest f value of 8. Let's remove S, B from the frontier. B is not a goal, let's expand it. B has three successors, C, D and E. Let's add S, B, C, S, B, D and S, B, E to the frontier. The f values are 5, 11 and 6. Next, S, B, C has the lowest f value of 5. Let's remove S, B, C from the frontier. C is not a goal, let's expand it. C has one successor, H. Let's add S, B, C, H to the frontier. The f value is 103. Next, S, B, E has the lowest f value of 6. Let's remove S, B, E from the frontier. E is not a goal, let's expand it. E has one successor, F. Let's add S, B, E, F to the frontier with an f value of 9. Next, S, B, E, F has the lowest f value of 9. Let's remove S, B, F from the frontier. F is not a goal, let's expand it. F has no successor, let's keep going. Next, S, B, D has the lowest f value of 11. Let's remove S, B, D from the frontier. D is not a goal, let's expand it. D has two successors, F and H. Let's add S, B, D, F and S, B, D, G. D has two successors, F and G. Let's add S, B, D, F and S, B, D, G to the frontier. Their f values are 17 and 11. Finally, S, B, D, G has the lowest f value of 11. Let's remove S, B, D, G from the frontier. G is a goal, let's return the solution S, B, D, G. This completes the tracing process. As you can see, ASTAR Search explores all the paths in the increasing order of their f values. Thank you very much for watching. I will see you in the next video. Bye for now.