Quiz Th. Oct. 20 Chapters 1,2,3,4

S B AD E C F G straight-line distances 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 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. 1.Draw the search tree for this problem. Avoid repeated states. 2.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. 3.For each algorithm indicate whether it is an informed or an uninformed search strategy. 4.For each algorithm indicate separately whether its time complexity is polynomial or exponential in the number of nodes visited. Same for space complexity. 5.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.

S B AD E C F G straight-line distances 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 Solutions: 1.(1pt) Search tree: 2.(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. 3.(1pt) BF,DF,UC are uninformed while A* is informed. 4.(2pts) BF: Time&Space exp., DF: Time exp. Space pol. (linear), UC: Space&Time exp. A* Space&Time exponential. 5.(2pts) BF: complete, not optimal, DF: not complete, not optimal, UC: complete, optimal, A*: complete, optimal. G G