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[Week 1-12] NPTEL An Introduction to Artificial Intelligence Assignment Answers 2022
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Q1. Consider the undirected graph below. Cost for each edge is written adjacent to
the edge. S is the start node and G is the goal node. The TREE-SEARCH version of A*
SEARCH is performed on this undirected graph. Assume that the heuristic function h
for a node is the least number of edges required to reach G from that node. For
example, h(A) =2 since we can reach G from A by the path ABG. However, h(S) is
defined as 0. Find the order of exploration of states. Ties are broken in the order
GSABC.
(Write the answer as a capitalized string with no spaces. For example, if the order of
exploration is A followed by B followed by A followed by D then write ABAD. Include
the goal state in the answer)
Answer:- (Type: String) SASBG
Q2. Which of the following evaluation functions will result in identical behaviour to
greedy best-first search (assume all edge costs are positive)?
f(n) = 100 * h(n)
f(n) = g(n) * h(n) 0
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f(n) = h(n)^2
f(n) = 1 / h(n)
Answer:- f(n) = 100 * h(n)f(n) = h(n)^2
Q3. Consider the following directed graph, having A as the starting node and G as the
goal node, with edge costs as mentioned, and the heuristic values for the nodes are
given as – {h(A)=8, h(B)=7, h(C)=6, h(D)=5, h(E)=4, h(F)=2, h(G)=0}:
Which of the following is correct regarding heuristic function h?
It is admissible
It is not admissible
It is consistent
It is not consistent
Answer:- It is admissibleIt is not consistent
Q4. Which of the following statements are true (assume all edge costs are positive)?
h(n) = 0 is always a consistent heuristic function
Manhattan distance is an admissible heuristic for the problem of moving a
rook from any square on a chessboard to another square in the smallest
number of moves
Depth First Search can never terminate faster than A* search with an
admissible heuristic
Straight line distance is an admissible heuristic for the problem
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from one city to another by covering the smallest distance
Answer:- h(n) = 0 is always a consistent heuristic functionStraight line
distance is an admissible heuristic for the problem of moving from one city
to another by covering the smallest distance
Q5. In the directed graph given below, with edge weights as cost of those edges, and
heuristic values of node written in red, TREE-SEARCH A* search is performed on the
graph with the starting node “0” and one goal node “4” (node numbers are written
inside the nodes). Consider the two sub cases: a) ties in selecting node for expansion
from the fringe are resolved by choosing the node with the LARGER index b) ties in
selecting node for expansion from the fringe are resolved by choosing the node with
the SMALLER index. Which of the following are correct statements?
In the first case, 5 node expansions are performed in the search.
In the second case, node with the index 7 is expanded twice.
The cost of path to the goal is different in the above two cases.
Number of nodes in the optimal path from the start node to the goal is same
for both the cases above.
Answer:- In the first case, 5 node expansions are performed in the search.In
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the second case, node with the index 7 is expanded twice.
Q6. Which of the following is(are) correct?
An inadmissible heuristic might be consistent.
An inconsistent heuristic might be admissible.
If the heuristic is consistent, A* using TREE-SEARCH is optimal.
If the heuristic is consistent, A* using GRAPH-SEARCH is optimal.
Answer:- An inconsistent heuristic might be admissible.If the heuristic is
consistent, A* using TREE-SEARCH is optimal.If the heuristic is consistent,
A* using GRAPH-SEARCH is optimal.
Q7. Consider the following directed graph.
The heuristic function for the nodes is defined as h(A) = 15, h(B) = 10, h(C) = 12, h(D)
= 7, h(E) = 10, h(F) = 6, h(G) = 4, h(H) = 0. The start node is A and the goal node is H.
Assume that ties in selecting node for expansion from the fringe are resolved by
choosing the alphabetically smaller node. Which of the following statements are
correct?
The optimal path has cost 10.
GRAPH-SEARCH A* results in a path with optimal cost.
TREE-SEARCH A* results in a path with optimal cost.
The heuristic is admissible.
Answer:- The optimal path has cost 10.TREE-SEARCH A* results in a path
with optimal cost.
Q8. Suppose there are two admissible heuristics h1 and h2 for some problem, which
of the following are correct?
max(h1,h2) is an admissible heuristic. 0
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max(h1,h2) dominates h1 and h2
min(h1,h2) is an admissible heuristic.
min(h1,h2) dominates h1 and h2
Answer:- max(h1,h2) is an admissible heuristic.max(h1,h2) dominates h1 and
h2min(h1,h2) is an admissible heuristic.
Q9. Which of the following algorithms are guaranteed to be complete and optimal?
(Assume positive edge costs greater than 1)
Depth-first search
GRAPH-SEARCH A* with zero heuristic
Uniform Cost Search
GRAPH-SEARCH A* with admissible heuristic
Answer:- GRAPH-SEARCH A* with zero heuristicUniform Cost Search
Q10. We want to sort an array of n distinct integers using A* search. The start state is
a random permutation of the integers. The expansion function applied on a given
state yields all permutations that can be achieved by swapping one pair of different
numbers in the original state with all edge costs as 1. There is one goal state: the
sorted array. Let S(p) be the number of elements of the array p that are not in the
position they are supposed to be in the sorted array. Which of the following are
admissible heuristics for this problem?
S(p)
S(p)/2
S(p)/3
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Answer:- S(p)/2S(p)/30
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