## NPTEL An Introduction to Artificial Intelligence Week 5 Assignment Answers 2024

1. Select the CORRECT statements –

- With perfect ordering, alpha-beta pruning reduces the time complexity from O(b^m) to O(b
^{m/2}) - With perfect ordering, alpha-beta pruning increases the depth that can be searched in same time T from d to d^2.
- Without alpha-beta pruning, the time complexity of search for depth m follows T(m) = b.T(m-1) + c
- With perfect ordering in alpha-beta pruning, the time complexity of search for depth m follows T(m) = T(m-1) + (b-2)T(m-2) + c

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2. Consider the following game tree. A is the maximizer node and D is the minimizer node. Chance node B chooses left action with probability p = 0.4 and right action with p = 0.6. Chance node C chooses left action with p = 0.7 and right action with p = 0.3. What will be the value at node A if we use expectiminimax to make decisions?

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3. Consider the same game tree. Now we have the prior information that all internal nodes have utility values in the range 1-10. Is it possible to perform any pruning? Answer the number of nodes of type D that can be pruned. (Answer 0 if you think no pruning can be done)

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4.

Consider the given adversarial search tree. Assume that the search always chooses children from left to right. The search tree uses alpha-beta pruning.

Which of the following nodes are pruned during the search?

- J
- K
- L
- M
- N
- O

Answer :-

5. What is the final value at node A?(from the above figure)

Answer :-

6. Define score of white as s(p, “white”) = 1 * n(white pawn) + 2 * n(white knight) + 3 * n(white bishop) + 4 * n(white rook) + 5 * n(white queen), where n(x) is number of pieces of type x on the board. Similarly, define the score of black. The utility of white f(p) is defined as score(p, “white”) – score(p, “black”). Calculate f(p) for white.

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7. Which of the following is/are true regarding the basic mini-max adversarial search algorithm?

- It is complete if the search tree is finite
- It is optimal for all kinds of adversaries
- The worst-case time complexity and space complexity is similar to that of Depth First Search
- By itself, it cannot play games like Chess and Go due to huge search depths.

Answer :-

8. Which of the following is/are false regarding the alpha-beta pruning for the mini-max search algorithm?

- It can potentially lead to suboptimal solutions compared to mini-max search without any pruning
- It is guaranteed to improve the running time in-comparison to the mini-max search without any pruning
- The order in which nodes are visited affects the amount of pruning
- If the successors of a node are chosen randomly, the time complexity (on average) is O(b3
^{m/4})

Answer :-

9. Which of the following techniques were used by Deep Blue for beating Garry Kasparov in the game of chess ?

- Opening and Endgame stage databases
- A version of mini-max search algorithm
- Neural Networks for computing Heuristic Functions
- Monte Carlo Tree Search algorithm

Answer :-

10. Which of the following is/are true for heuristic functions in the context of adversarial search ?

- They can be learnt from data/experience for eg. by playing games with another agent
- They help deal with the problem of extremely large search depths in practice
- They help reduce the worst-case time complexity of minimax search without comprising optimality against optimal adversaries
- They can be hand-engineered by humans/experts

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11. What will be the value of the node labelled ‘a’ after the run of the min-max search algorithm on the following search tree. Here upwards facing triangles are max nodes, downward facing triangles are min nodes and circles denote game-ends.

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