NPTEL Artificial Intelligence : Search Methods For Problem solving Week 5 Assignment Answers

1. The complete BnB search tree is shown below. What is the estimated cost of S0 as per the algorithm discussed in the lecture?

Enter the estimated cost (integer).

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2. Identify the first segment (S1) that will be used to refine S0. What is the estimated cost of ~S1 node? Enter the estimated cost (integer).

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3. Identify the second segment (S2) that will be used to refine S1. What is the estimated cost of S2 node? Enter the estimated cost (integer).

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4. What is the cost of the optimal tour? Enter the cost (integer).

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5. Start from city A, enter the path representation of the optimal tour.

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6. How many tours are represented by S1 node? Enter an integer.

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7. How many tours are represented by S2 node? Enter an integer.

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8. How many tours are represented by ~S3 node? Enter an integer.

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9. If we traverse a TSP BnB search tree from its root node to any leaf node, the estimated costs of nodes (along a path) _____________ .

monotonically increases as depth increases
monotonically decreases as depth increases
monotonically increases up to some depth and thereafter monotonically decreases as we go closer to a leaf node
monotonically decreases up to some depth and thereafter monotonically increases as we go closer to a leaf nod

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END GROUP – 1

BEGIN GROUP – 2

A tiny map on a grid (where each tile is 1×1 in size) is shown below. Use Manhattan distance as the heuristic value. The MoveGen function returns nodes in alphabetical order. Use alphabetical order of node labels to break ties.

10. Run A* algorithm to find a path from S to G. The path is ____________ .

Enter the path as a comma separated list.
Answer format: S,X,Y,Z,G

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11. The cost of the path found by A* algorithm is ____________ . Enter an integer

Answer :-

12. Run BnB-2 (a variation that avoids cyclic expansions like S,B,S,B,…) to find the path from S to G. The path is _______________ .

Enter the path as a comma separated list.
Answer format: S,X,Y,Z,G

Answer :-

13. The cost of the path found by BnB-2 is _____________ . Enter an integer.

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14. For the tiny map, ________________

A* found the shortest path
A* did not find the shortest path
BnB-2 found the shortest path
BnB-2 did not find the shortest path

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END GROUP – 2

BEGIN GROUP – 3

The figure (repeated from Week 3 but without edge HM) shows a map on a grid where each tile is 10×10 in size. In this map, S is the start node and G is the goal node, the locations are connected by two-way edges (roads) where each edge has a cost that is the same in both directions.

MoveGen returns nodes in alphabetical order.

Use Manhattan distance as the heuristic function.

Tie Breaker: when several nodes have the same cost, use alphabetical order to break ties.

IMPORTANT: In assignments and exams, when we say a node is inspected (or expanded or
refined) it means: the node is read from OPEN, then GoalTest is called, if it returns true then
the node is processed as a goal, otherwise MoveGen is called and the neighbours are
selectively placed in OPEN.

15. What is the path found by the Best First Search algorithm?

Enter the path as a comma separated list.
Answer format: S,X,Y,Z,G

Answer :-

16. What is the cost of the path found by the Best First algorithm? Enter an integer.

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17. In the map, let S be the first node refined by A* algorithm. Determine the next 5 nodes (from the 2nd node to the 6th node) refined by A* algorithm. Enter the 5 nodes, in the order they are refined, as a comma separated list.

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18. For the 5 nodes listed in the previous question, list the f-values of those nodes as a comma separated list. Use the same node order used in the previous question.