Show the search tree generated by Hill-Climbing search (text figure 4.2, page 122; or Local Search lecture, slide 6) for each of the two heuristics (a) and (b) applied to the following 8- puzzle problem. Search tree should show all states generated along with their heuristic value.

If two neighbor states have the same value, then consider them in order of the actions (movement of blank): up, down, left, right. Also indicate the final state returned by the Hill- Climbing function.

Initial State:

1 0 2

8 4 3

7 6 5

Goal State:

1 2 3

8 0 4

7 6 5

a. Value = 1 / (number of tiles out of place, including the blank tile). For example, the value of the initial state = 1/4.

b. Value = 1 / (number of tiles out of place, not including the blank tile). For example, the value of the initial state = 1/3.