Artificial Intelligence: Search Methods for Problem Solving Week 5 NPTEL Assignment Answers 2025
NPTEL Artificial Intelligence: Search Methods for Problem Solving Week 5 Assignment Answers 2025
1. A distance matrix for 5 cities is provided below. The Branch-and-Bound algorithm is about to start looking for a TSP tour. What will be the lower bound on the cost of the tour as per the algorithm discussed in class that it will begin with?
 Enter the lower bound in the text box.
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2. Estimate the (lower bound) cost of the tours that exclude the BC segment.
Enter the estimate in the text box.
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3. It is necessary to underestimate the cost of partial solutions for TSP because ___________ .
- when a fully refined candidate is picked it will be optimal because no candidate from OPEN can have a higher cost after full refinement
- when a fully refined candidate is picked it will be optimal because no candidate from OPEN can have a lower cost after full refinement
- it is easier to underestimate the cost than overestimate the cost
- it is easier to overestimate the cost than underestimate the cost
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4. A tiny map on a grid (each tile 1 unit by 1 unit) is shown below. Use Manhattan distance as the heuristic value and run A* algorithm to find a path from S to G. The path is _ .
Enter the path as a comma separated list.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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5. The cost of the path found by A* algorithm is ____________ .
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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6. What is the optimal path from S to G?
Enter the path as a comma separated list.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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7. The cost of the optimal path is _______________ .
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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The figure (repeated from Week 3) shows a map with several locations on a grid where each tile is 1 unit x 1 unit 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). Each edge has a cost that is the same in both directions.
For this map, MoveGen returns nodes in alphabetical order.
When several nodes have the same cost, use alphabetical order to break ties.
When the same node occurs multiple times with the same cost then use the open-sequence-number to break ties, i.e., refine the node occurrence that is oldest (was placed earliest in time) in the OPEN list.
Where needed, use Manhattan distance as the heuristic function.
BnB-1: is the simple Branch And Bound algorithm covered in the lecture, which allows cyclic refinements/paths like SCSCSC… in the search-tree.
BnB-2: is a variation on BnB-1, that prevents cyclic expansions, i.e., it does not refine nodes that are already present in the path from the root to the current node. And therefore, it keeps each path in the search tree free of duplicate nodes.
8. Run the Best First Search to completion. What is the path found by the Best First Search algorithm? List the path as a comma separated list of node labels.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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9. What is the cost of the path found by the Best First algorithm? The cost of the path is the sum of edge costs.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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10. Run BnB-1 on the given map. Let S be the first node to be refined. Determine the 5 nodes from the 2nd to the 6th node refined by BnB-1. List the node labels as a comma separated list and enter the nodes in the order it is refined.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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11. For the 5 nodes listed in the previous question, list the costs of those nodes as a comma separated list.
Use the same node order used in the previous question.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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12. Run BnB-2 on the given map. Let S be the first node to be refined. Determine the 5 nodes from the 2nd to the 6th node refined by BnB-2. List the node labels as a comma separated list and enter the nodes in the order it is refined.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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13. For the 5 nodes listed in the previous question, list the costs of those nodes as a comma separated list.
Use the same node order used in the previous question.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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14. In the map, let S be the first node to be refined. Determine the next 5 nodes from the 2nd node to the 6th node refined by A*. List the node labels as a comma separated list and enter the nodes in the order they are refined.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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15. For the 5 nodes listed in the previous question, list the costs (f-values) of those nodes as a comma separated list. Use the same node order used in the previous question.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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16. Determine the 10th node (NODE, PARENT, f-value, g-value, h-value) refined by A* algorithm.
- (J,S,17,6,11)
- (O,J,22,16,6)
- (L,F,24,22,2)
- (G,L,26,26,0)
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17. How many nodes does A* refine in total? Here, node refinement means that a node is picked up from OPEN and either GoalTest passes or MoveGen is called on that node.
- 5
- 10
- 20
- 40
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18. For the map, what is the path found by A* algorithm? List the path as a comma separated list of node labels.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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19. What is the cost of the path found by A* algorithm?
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
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20. In the map, if an agent uses A* algorithm to find a path from S to G, and for the return journey from G to S, if it recomputes the path by treating G as the start node and S as the goal node, then the agent will _______________ .
- take the same path back
- take a different path back
- get stuck on node E
- behave in arbitrary manner
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