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## NPTEL An Introduction to Artificial Intelligence Assignment 2 Answers 2023:

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#### Q.1. Consider the “Vacuum World” discussed in the lecture. The state space of the problem is shown below.

We have two possible actions: moving the vacuum cleaner from one room to another (cost = 2 units) and clean the current room using the vacuum cleaner (cost = 1 unit). What is the minimum cost required to clean all the dirt, assuming we start in state 1?

- 8
- 6
**4**- 5

#### Q.2. Consider the following graph with start state A and goal state J. Assume that edges between nodes have cost equal to the absolute difference of the position of the corresponding letters in the alphabet. For example, cost of the edge between state F and J is 4 since F is the 6th and J is 10th letter of the alphabet. Also, assume that all edges are bidirectional and ties are broken lexicographically. What will be the total number of nodes visited by Uniform Cost Search (include the goal state in your calculation)?

**Answer:**10

#### Q.3. Consider the following graph. A is the initial state and we always pick the lexicographically smallest state in case of a tie. If the goal state is K, find the order of exploration of states in Breadth First Search with no duplicate checking. (Write the answer as a capitalized string with no spaces. For example, if the order of exploration is A followed by B followed by C followed by D then write ABCD. Include the goal state in the answer)

**Answer:***ABCDEFFGGHIIJIJJK*

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#### Q.4. Which of the following types of state representations assume a state to be indivisible without any internal structure?

#### Q.5.** **Which of the following data structures are most suited to be used in an implementation of Breadth First Search (BFS) and Depth First Search (DFS)?

- a. BFS: Queue, DFS: Queue
**b. BFS: Queue, DFS: Stack**- c. BFS: Stack, DFS: Queue
- d. BFS: Stack, DFS: Stack

#### Q.6. Which of the following search methods cannot be guaranteed to find a goal reaching plan to the 8-puzzle problem?

- a. Bidirectional Search
- b. Depth First Search
- c. Breadth First Search
**d. Beam Search**

#### Q.7. What is the best characterization of time and space complexity of Depth First Search with full duplicate detection (ensuring that the same state is never expanded again, b denotes maximum branching factor, m is maximum depth of search tree, d is the minimum depth of goal state and |S| is the total number of states, all of which are reachable from the start state)?

- a. Time: O(bd) Space: O(bd)
**b. Time: O(|S|) Space: O(|S|)**- c. Time: O(bd) Space: O(bd)
- d. Time: O(bm) Space: O(bm)

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#### Q.8. Consider a variant of Iterative Deepening Depth First Search (IDS) in whichwe increase the depth in steps of 2, i.e. the depth limits increase as 1,3,5,7…. Which of the following is true about this new variant?

**a. It is complete**- b. It is optimal
- c. It will always expand more nodes than standard IDS
**d. It can find the goal state faster than IDS in some cases**

#### Q.9. Which of the following algorithms are optimal, complete and systematic for a search problem with a single goal state and same cost for all edges?

**a. Breadth First Search****b. Bidirectional Breadth First Search**- c. Iterative Deepening Depth First Search
- d. Depth First Search

#### Q.10.** **Consider the following graph in which we are searching from start state A to goal state G. The number over each edge is the transition cost. Find the path to the goal found by Depth First Search with full duplicate detection. In case of ties, the unvisited child with the lowest cost edge connecting it to the current node is selected. Further ties are broken with the lexicographically smaller state chosen.

(Write answer as a capitalized string with no spaces. For example, if the order of exploration is A followed by B followed by C followed by D then write ABCD. Include the goal state in the answer)

**Answer:***ACDFG*

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#### About NPTEL An Introduction to Artificial Intelligence Course:

The course introduces the variety of concepts in the field of artificial intelligence. It discusses the philosophy of AI, and how to model a new problem as an AI problem. This describes a variety of models such as search, logic, Bayes nets, and MDPs, which can be used to model a new problem. It also teaches many first algorithms to solve each formulation. The course prepares a student to take a variety of focused, advanced courses in various subfields of AI.

##### Course Outcome:

**Week 1**:Introduction: Philosophy of AI, Definitions**Week 2**:Modeling a Problem as Search Problem, Uninformed Search**Week 3**:Heuristic Search, Domain Relaxations**Week 4**:Local Search, Genetic Algorithms**Week 5**:Adversarial Search**Week 6**:Constraint Satisfaction**Week 7**:Propositional Logic & Satisfiability**Week 8**:Uncertainty in AI, Bayesian Networks**Week 9**:Bayesian Networks Learning & Inference, Decision Theory**Week 10**:Markov Decision Processes**Week 11**:Reinforcement Learning**Week 12**:Introduction to Deep Learning & Deep RL

**CRITERIA TO GET A CERTIFICATE**:

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

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