## NPTEL Artificial Intelligence : Search Methods For Problem solving Week 7 Assignment Answers 2024

1. In the Alpha-Beta procedure presented in the lecture, ** __________** .

- α and β are global parameters
- α and β are local parameters in each call to Alpha-Beta procedure
- It is irrelevant whether α and β are local or global parameters

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2. In Alpha-Beta procedure, the eval n of a MIN node will lead to pruning when ** _______** .

- n <= α
- n <= β
- α < n < β
- α <= n
- β <= n

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3. Alpha-cut prunes ** ___________** .

- children of MIN node
- children of MAX node

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4. Select the correct statements.

- The total number of nodes pruned by Alpha-Beta algorithm changes when child ordering in the game tree changes.
- The total number of nodes pruned by Alpha-Beta is independent of child ordering in the game tree.
- The total number of nodes pruned by SSS* changes when child ordering in the game tree changes.
- The total number of nodes pruned by SSS* is independent of child ordering in the game tree.

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5. Select the correct statements.

- Alpha-Beta prunes at-least as many nodes as SSS
*. Alpha-Beta prunes the same nodes as SSS*, but Alpha-Beta does it efficiently. - SSS* prunes at-least as many nodes as Alpha-Beta.
- SSS* prunes the same nodes as Alpha-Beta, but SSS* does it efficiently.

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6. In the SSS* procedure, ** ________** .

- when any MIN node is solved its parent is solved
- only when the last MIN-child is solved its parent is solved
- when any MAX node is solved its parent is solved
- only when the last MAX-child is solved its parent is solved

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7. Two procedures for constructing game strategies are listed below

Which of these procedures construct a game strategy for MAX?

- Construct-Strategy-1
- Construct-Strategy-2
- None of the above

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8. Four game-trees are shown below with some edges highlighted in bold.

Which of these game trees depict a strategy for MAX? The root is MAX in all the game trees.

- Game Tree A
- Game Tree B
- Game Tree C
- Game Tree D

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END GROUP 1

BEGIN GROUP 2

The figure shows a game tree with evaluations W (win), L (loss) and D (draw) from Max’s perspective. In this game tree the labels P, Q, R, S, T indicate strategies/moves at the root.

9. What is the outcome (W, D or L) of the game when both players play perfectly?

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10. Which of the moves P, Q, R, S, T are the best moves for Max?

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11. Which of the moves P, Q, R, S, T are the best moves for MIN?

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The figure shows a 4-ply game tree with evaluation function values at the horizon. The nodes in the horizon are assigned reference numbers A,B,C,…,P. Use these reference numbers when you want to enter a list of horizon nodes in the short answer.

**Tie-breaker:** when several nodes have the same h-value then select the deepest node, if tie persists then select the left most of the deepest nodes.

12. What is the Minimax value of the game?

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13. List the horizon nodes (reference numbers) in the best strategy for MAX.

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14. Change the eval of exactly one horizon node to get a new Minimax value of 55. Which horizon node will you change? When multiple horizon nodes qualify then select one node of your choice.

Enter the reference number of the horizon node.

Enter NIL if no horizon node qualifies.

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15. Change the eval of one horizon node to get a new Minimax value of 64. Which horizon node will you change? When multiple horizon nodes qualify then select one node of your choice.

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16. List the horizon nodes pruned by alpha-cuts.

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17. List the horizon nodes pruned by beta-cuts.

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18. List the horizon nodes in the initial clusters formed by SSS*?

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19. What are the horizon nodes that are assigned SOLVED status by SSS*?

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20. What are the horizon nodes pruned (i.e., not assigned LIVE/SOLVED status) by SSS*?

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