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Which of the following statement(s) is/are correct?S1: In A* Algorithm, f(n) = g(n) + h(n), if n=0, and cost of operators are equal, then A* becomes uniform cost searchS2: In A* Algorithm, if h = 0 for all nodes, A* becomes a breadth-first search.a)Neither S1 nor S2b)Both S1 and S2c)Only S1d)Only S2

Question

Which of the following statement(s) is/are correct?S1: In A* Algorithm, f(n) = g(n) + h(n), if n=0, and cost of operators are equal, then A* becomes uniform cost searchS2: In A* Algorithm, if h = 0 for all nodes, A* becomes a breadth-first search.a)Neither S1 nor S2b)Both S1 and S2c)Only S1d)Only S2

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Solution

The correct answer is b) Both S1 and S2.

Explanation:

S1: In the A* Algorithm, f(n) = g(n) + h(n). Here, g(n) is the cost from the start node to node n and h(n) is the heuristic estimate of the cost from node n to the goal. If n=0 and the cost of operators are equal, then A* becomes uniform cost search. This is because the heuristic function h(n) is not contributing to the cost function f(n), making it a cost-based search, which is the definition of a uniform cost search.

S2: In the A* Algorithm, if h = 0 for all nodes, A* becomes a breadth-first search. This is because when the heuristic function h(n) is zero for all nodes, the algorithm does not have any information about the goal, so it explores all nodes at a given depth before moving to the next depth level, which is the definition of a breadth-first search.

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