Question

3. (a) Consider the state-space graph in the following figure. S is the start node and G is the goal node. For uniform cost search algorithm, draw the search tree and find out the solution paths and costs. [3] 1 2 S A B 1 2 2 2 G C 4 (b) "Iterative Deepening DFS is not optimal when all the step costs are not identical" - draw a state-space graph and corresponding search tree that supports this statement. [2] 4. a) Suppose that for some specific problem, heuristic function h is admissible. Is $h^2$ admissible? How about $\sqrt{h}$? If your answer is yes for any of these two functions, would you prefer them over h? Explain your answer. [3] b) Prove that if h is consistent, n and n' are two nodes on the path to goal and n' is the successor of n, then $f(n) \le f(n')$. [2]

          3. (a) Consider the state-space graph in the following figure. S is the start node and G is the
goal node. For uniform cost search algorithm, draw the search tree and find out the solution
paths and costs.
[3]
1
2
S
A
B
1
2
2
2
G
C
4
(b) "Iterative Deepening DFS is not optimal when all the step costs are not identical" - draw a
state-space graph and corresponding search tree that supports this statement.
[2]
4. a) Suppose that for some specific problem, heuristic function h is admissible. Is $h^2$
admissible? How about $\sqrt{h}$? If your answer is yes for any of these two functions, would you
prefer them over h? Explain your answer.
[3]
b) Prove that if h is consistent, n and n' are two nodes on the path to goal and n' is the
successor of n, then $f(n) \le f(n')$.
[2]

3. (a) Consider the state-space graph in the following figure. S is the start node and G is the
goal node. For uniform cost search algorithm, draw the search tree and find out the solution
paths and costs.
[3]
1
2
S
A
B
1
2
2
2
G
C
4
(b) "Iterative Deepening DFS is not optimal when all the step costs are not identical" - draw a
state-space graph and corresponding search tree that supports this statement.
[2]
4. a) Suppose that for some specific problem, heuristic function h is admissible. Is h^2
admissible? How about √(h)? If your answer is yes for any of these two functions, would you
prefer them over h? Explain your answer.
[3]
b) Prove that if h is consistent, n and n' are two nodes on the path to goal and n' is the
successor of n, then f(n) ≤ f(n').
[2]

Added by Benjamin C.

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