## NPTEL An Introduction to Artificial Intelligence Week 3 Assignment Answers 2024

1. The heuristic path algorithm is a best-first search in which f(n) = (2-w) g(n) + w h(n).

Select the correct statement(s) –

- For w = 1, f(n) represents the A* algorithm.
- For w = 2, f(n) is complete.
- For w > 2, f(n) is optimal.
- For w = 0, f(n) represents UCS.

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2. Consider f(n) = g(n) + 5h(n). What is the order of nodes visited by best-first search algorithm? (Start-node is S, no duplicate detection)

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3. Start state is a, and goal state is z. Cost of transitioning from one node to another are mentioned over the corresponding edge. Numbers on the node are the heuristic values. Assume successors are returned in reverse lexicographic order. In case of ties, use lexicographic ordering for breaking ties.

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4. If h is an admissible heuristic (non-negative), which of the following can never be an admissible heuristic?

- h+1
- 2h
- √h
- They all can be admissible under some situation

Answer :-

5. If h1 and h2 are admissible heuristics, which of the following are guaranteed to be admissible?

- h
_{1}+ h_{2} - min(h
_{1}, h_{2}) - max(h
_{1}, h_{2}) - αh1 + (1 – α)h
_{2}for α є [0,1]

Answer :-

6. Which of the following statements are true?

- If a search graph has negative edge costs, Tree Search A* with Admissible Heuristics returns optimal solution.
- IDA* implementation does not need a priority queue, but A* does.
- If h
_{1}and h_{2}are two admissible heuristics, then max(h_{1 }, h_{2}) dominates h_{1 }and h_{2} - An inconsistent heuristic can never be admissible.
- Depth First Search can never terminate faster than A* search with an admissible heuristic

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7. Which of the following is/are true regarding Depth-First Search Branch and Bound (DFS B&B) ?

- It is optimal even if the search space is infinite
- It performs well in practice when it is easy to find suboptimal solutions to the goal
- It can prune certain subtrees in the search tree without the need for exploring them
- It performs well in practice when there is a single solution to the goal

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8. Which of the following is/are true for problem relaxation in the context of computing heuristics?

- For a problem involving finding the shortest path in a city from a source to a destination, removing certain edges from the graph will give a relaxed problem
- Given an original problem P, we remove certain constraints from P to get a relaxed problem P1 which we solve optimally to compute an heuristic function h1 for P. We then remove additional constraints from P1 to get another relaxed problem P2 which we solve optimally to compute another heuristic function h2 for P, then h2 dominates h1
- As we increase the number of constraints removed to get the relaxed problem the total time needed to solve the original problem (including computing the heuristic function) first decreases then increases
- Optimal solutions to relaxed problems give admissible heuristics to the original problem

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9. Which of the following is/are false regarding the A* search algorithm ?

- It always gives optimal solutions
- A* search algorithm has a better worst-case space time complexity than DFS if the heuristic used is admissible
- It is a systematic search algorithm
- It helps improve the worst-case time complexity of the search

Answer :-

10. Which of the following evaluation functions will result in identical behavior to greedy best-first search (assume all edge costs are positive)?

- f(n) = 100 * h(n)
- f(n) = g(n) * h(n)
- f(n) = h(n)^2
- f(n)=1/h(n)

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