Artificial Intelligence: Search Methods for Problem Solving Week 6 NPTEL Assignment Answers 2025
NPTEL Artificial Intelligence: Search Methods for Problem Solving Week 6 Assignment Answers 2025
1. In the map, on a grid with unit tiles, which of the following are true?
- The Manhattan distance heuristic function satisfies the monotone condition.
- The Manhattan distance heuristic function does not satisfy the monotone condition.
- The Euclidean distance heuristic function satisfies the monotone condition.
- The Euclidean distance heuristic function does not satisfy the monotone condition
Answer : See Answers
GROUP 2 :
The figure (repeated from Week 5) shows a map with several locations on a grid with 1unit x 1unit tiles. 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 which 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.
Where needed, use Manhattan distance as the heuristic function.
Simulate WA* with weight w=3, Breadth First Heuristic Search with U=27, Sparse-Memory Graph Search, and Beam Search with width w=2 on the above map and answer the following questions.
GROUP 2.1 :
2. Using w=3 in f = g + wh, simulate WA algorithm on the given map. Let S be the first node to be inspected, now list the 3rd, 4th and 5th nodes inspected by the algorithm.
Enter node labels as a comma separated list.
NO SPACES, TABS, DOTS, BRACKETS OR EXTRANEOUS CHARACTERS.
Answer :
3. What are the f-values of the 3rd, 4th and 5th nodes listed in the previous question?
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4. For WA* with w=3, what is the path found by the algorithm?
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5. What is the cost of the path found by WA* algorithm? (Compare 3A* with Best First Search and A* from Week 5 assignment.)
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GROUP 2.2 :
Simulate the Breadth First Heuristic Search (BFHS) with U=27 on the given map. Remember that MoveGen generates neighbours in alphabetic order and BFHS does not add to OPEN the neighbours that are already in OPEN or CLOSED.
BFHS = BFS + Pruning. BFHS follows BFS, in addition, it prunes new nodes with f-values (f=g+h) greater than or equal to U, and adds the remaining to OPEN.
6. List the 4th, 6th and 8th nodes inspected by BFHS.
Answer : See Answers
7. What are the f-values of the 4th, 6th and 8th nodes listed in the previous question?
Answer :
GROUP 2.3 :
For the following questions assume that the Sparse-Memory Graph Search (SMGS) has enough memory to only hold 4 nodes in Kernel. We will not count S to be part of the Kernel (because it is never deleted).
ALL answers in this group must be in ALPHABETIC order.
8. List the nodes in OPEN after SMGS has inspected the 3rd node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
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9. List the nodes in the BOUNDARY after SMGS has inspected the 3rd node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
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10. List the nodes in the KERNEL after SMGS has inspected the 3rd node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
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11. List the nodes in OPEN after SMGS has inspected the 5th node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
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12. List the nodes in the BOUNDARY after SMGS has inspected the 5th node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
Answer : See Answers
13. List the nodes in the KERNEL after SMGS has inspected the 5th node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
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14. List the nodes in OPEN after SMGS has inspected the 7th node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
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15. List the nodes in the BOUNDARY after SMGS has inspected the 7th node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
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16. List the nodes in the KERNEL after SMGS has inspected the 7th node, where S is the first node inspected.
Enter node labels in ALPHABETICAL ORDER as a comma separated list.
Enter NIL if there are no nodes.
Answer : See Answers
GROUP 2.4 :
Refer to the Beam Search algorithm given in Week 3 notes.
Simulate Beam Search (use h-values) with beam width w=2. In each layer, the best two nodes are retained irrespective of whether they are better than the previous layer or not. If nodes carry the same cost then use ALPHABETICAL ORDER to break ties.
17. What is the path found by Beam Search?
Enter the path as a comma separated list.
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18. What is the cost of the path found by Beam Search?
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19. What is the other node in the beam (apart from G) at the point when the algorithm terminates?
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20. Beam Search (of some width w) is used before DCBFS and BSS to find an upper bound U for the solution. Which variations of Beam will do the task of finding U for going from S to G in the given map?
- Using h(n) and the condition that only better nodes are selected at the next level.
- Using h(n) and moving forward irrespective of whether the next level nodes are better or not.
- Using f(n) and the condition that only better nodes are selected at the next level.
- Using f(n) and moving forward irrespective of whether the next level nodes are better or not.
Answer : See Answers
