1. Tutorial - 1 Course: CS60045 Pallab Dasgupta Professor,
Dept. of Computer Sc & Engg

2. Apply DFBB on the following graph1 A E 3
START 2 4 5 S -4 1 B D G
GOAL 6 2 8 3 C

3. Solution C* = ∞ -> 6-> 3 OPEN CLOSED (S,0) (A,3)(B,6)(C,8)
(E,4)(B,6)(C,8)
(S,0)(A,3)
(G,6)(D,9)(B,6)(C,8)
(S,0)(A,3)(E,4)
(D,9)(B,6)(C,8)
(S,0)(A,3)(E,4)(G,6)
(B,6)(C,8)
(S,0)(A,3)(E,4)(G,6)(D,9)
(D,2)(C,8)
(S,0)(A,3)(E,4)(G,6)(B,6)
(G,3)(C,8)
(S,0)(A,3)(E,4)(B,6)(D,2)
(C,8)
(S,0)(A,3)(E,4)(B,6)(D,2)(G,3)
(S,0)(A,3)(E,4)(B,6)(D,2)(G,3)(C,8)
Terminate
Note that the best cost is 6 here.
Considering a strict less than comparison with the path cost will prune all entries in OPEN including (D,9),(B,6), (C,8) without further expansion.

4. Apply DFBB on the following graph1 A E 3 -2
START 2 4 5 S -4 1 B D G
GOAL 6 2 8 3 C

5. Solution C*=∞->6->3->1->…… OPEN CLOSED (S,0)
(A,3)(B,6)(C,8)
(E,4)(B,6)(C,8)
(S,0)(A,3)
(G,6)(D,9)(B,6)(C,8)
(S,0)(A,3)(E,4)
(D,9)(B,6)(C,8)
(S,0)(A,3)(E,4)(G,6)
(B,6)(C,8)
(S,0)(A,3)(E,4)(G,6)(D,9)
(D,2)(C,8)
(S,0)(A,3)(E,4)(G,6)(B,6)
(A,0)(G,3)(C,8)
(S,0)(E,4)(B,6)(D,2)
(B,4)(E,1)(G,3)(C,8)
(S,0)(D,2)(A,0)
(D,0)(E,1)(G,3)(C,8)
(S,0)(A,0)(B,4)
(A,-2)(G,1)(E,1)(C,8)
(S,0)(B,4)(D,0)
…….
……..

6. Iterative Deepening SearchB D C E F G H I J K
GOAL
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7. Solution Depth(level) IDS A 1 A,B,C,D 2 A,B,E,C,F,G,D,H 3A 1
A,B,C,D 2
A,B,E,C,F,G,D,H 3
A,B,E,C,F,G,I,D,H,J,K
Advantages:-
Always finds goal node
Requires less memory
Disadvantages:-
1)Visits same nodes again and again
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8. Perform BFS & DFS 6 1 5 4 2 7 3 8 10 9
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9. Solution – BFS Spanning Tree1 4 2 3 5 7 8 10 9 6
1,4,2,3,5,8,7,10,9,6
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10. Solution – DFS Spanning Tree1 4 3 10 2 9 8 7
1,4,3,10,9,2,8,7,5,6 5 6
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11. Sample problem on A* search
Open =
{D,G}
{G}
{D,E}
{C,D}
{S}
{A,B}
{F,G}
{B,C}
Closed =
{S,A,B}
{S,A,B,C,E}
{S,A,B,C,E,D,F}
{S,A}
{S,A,B,C} {}
{S}
{S,A,B,C,E,D} S A C B D G E F
START
GOAL 2 3 1 6 4
3.5
Select : D
Select : E
Select : B
Select : S
Select : F
Select : A
Select : G GOAL TERMINATE
Select : C
Node
g()
f() S A B C D E F G 6 2 6 3 7 1 4 5 9 8 6 5
8.5
9.5 7 8 7 8 8 9 8 9

12. AO* : An Example AND NODE A OR NODE C B E F G H I L J K 18 16 14 10 7
START OR
NODE 2 1 3 16 8 C 7 6 4 B
SOLVED
NODE 1 2 5 7 14 2 E F G H 7 9 1 I L J K 3 10 4 3

13. Adversarial Search
1. Find the value returned to the root node (i) without alpha-beta pruning and (ii) alpha-beta pruning.
MAX
MIN 4 8 9 3 2 -2 -1
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14. V= 8
MAX
MIN 4 8 9 3 2 -2 -1
V= 8
V= 2
V= 8
V= 9
V= 2
V= 9
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15. 4 8 9 3 2 -2 -1 V= 8 α= 8 β= ∞ 8 8 V= 2 α= 8 β= 8 V= 8 α=- ∞ β= 8 8 8
MAX
MIN 4 8 9 3 2 -2 -1 8 8
V= 2
α= 8
β= 8
V= 8
α=- ∞
β= 8 8 8 8
V= 9
α=9
β=8
V= 2
α= 8
β= ∞
V= 8
α= 8
β= ∞
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16. 2. The following game trees are for a three player game
2. The following game trees are for a three player game. The vector <x, y, z > in each terminal node represents the payoffs for Player-1, Player-2, and Player-3 respectively. The square nodes represent moves for Player-1, the circular nodes represent moves of Player-2 and the oval nodes represent moves for Player-3. a) The three player game may assume that the opponents are rational, that is, each player’s sole motive is to maximize the payoff of that player. Under this assumption, show the preferred choice of successor at each node by marking the relevant edges.
P-1
P-2
P-3
<3,2,5>
<2,2,6>
<4,3,3>
<4,4,2>
<6,2,2>
<3,3,4>
<3,4,3>
<5,3,2>

17. b) A more conservative approach for Player-1 is to choose the move without making the assumption of rational opponents. This situation allows Player-2 and Player-3 to conspire to minimize the payoff of Player-1. If this is the case, then show the preferred choice of successor at each node by marking the relevant edges.
P-1
P-2
P-3
<3,2,5>
<2,2,6>
<4,3,3>
<4,4,2>
<6,2,2>
<3,3,4>
<3,4,3>
<5,3,2>
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18. c) Design a cut-off criterion similar to alpha-beta-pruning for the situation where Player-2 and Player-3 conspire against Player-1 to minimize the payoff for Player-1. Show the pruning on the following game tree. You don’t have to state the pruning criterion.
P-1
P-2
P-3
<6,2,2>
<3,3,4>
<3,4,3>
<5,3,2>
<2,2,6>
<3,2,5>
<4,3,3>
<4,4,2>
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19. 3. Perform alpha-beta pruning of the following tree.
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