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6

1

A

D

F

1

3

h(S-G)=10

h(A-G)=7

h(D-G)=1

h(F-G)=1

h(B-G)=10

h(E-G)=8

h(C-G)=20

2

4

8

S

G

B

E

1

20

C

- The graph above shows the step-costs for different paths going from the start (S) to
- the goal (G). On the right you find the straight-line distances.
- Draw the search tree for this problem. Avoid repeated states.
- Give the order in which the tree is searched (e.g. S-C-B...-G) for the following search algorithms: a) Breadth-first search, Depth first search, uniform cost search,and A* search. For A* use the straight-line dist. as a heuristic function, i.e. h=SLD,and indicate for each node visited what the value for the evaluation function, f, is.
- For each algorithm indicate whether it is an informed or an uninformed search strategy.
- For each algorithm indicate separately whether its time complexity is polynomialor exponential in the number of nodes visited. Same for space complexity.
- For each algorithm indicate separately whether it is complete and/or optimal.

Answer these questions for generic search problems. Assume step-cost positive but not constant,

do not assume we can avoid repeated states, do not assume we have a very good heuristic

function h.

6

1

1

A

D

F

G

3

h(S-G)=10

h(A-G)=7

h(D-G)=1

h(F-G)=1

h(B-G)=10

h(E-G)=8

h(C-G)=20

2

8

4

S

B

E

G

1

20

C

G

- Solutions:
- (1pt) Search tree:
- (4pts) BF: e.g. S-A-B-C-D-E-G. | DF: e.g. S-C-G. | UC: S-C-B-A-E-D-F-G A*: S-A-D-F-G | f-values: 10,10,10,11,11.
- (1pt) BF,DF,UC are uninformed while A* is informed.
- (2pts) BF: Time&Space exp., DF: Time exp. Space pol. (linear), UC: Space&Time exp. A* Space&Time exponential.
- (2pts) BF: complete, not optimal, DF: not complete, not optimal, UC: complete, optimal, A*: complete, optimal.

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