Which among the following statement(s) is(are) FALSE?
A. Greedy best-first search is not optimal but is often efficient.
B. A* is complete and optimal provided h(n) is admissible or consistent.
C. Recursive best-first search is efficient in terms of time complexity but poor in terms of space complexity.
D. h(n) = 0 is an admissible heuristic for the 8-puzzle.

Correct option is C

Statement (C) is false because Recursive Best-First Search (RBFS) is efficient in terms of space complexity, not poor. The other statements are true based on the properties of Greedy Best-First Search, A* and heuristics.
Information Booster
1. Analysis of Statements:
(A): True. Greedy Best-First Search focuses on minimizing the heuristic h(n), which makes it fast but not guaranteed to find the optimal solution as it ignores the actual cost incurred.
(B): True. A* Search is both complete and optimal if h(n) is admissible (never overestimates the cost to reach the goal) or consistent (follows the triangle inequality).
(C): False. Recursive Best-First Search (RBFS) is designed to use limited memory by only keeping track of the current path and backtracking when necessary, making it space-efficient.
(D): True. h(n) = 0 is an admissible heuristic for the 8-puzzle as it does not overestimate the cost to reach the goal (though it is not efficient in practice because it provides no guidance).
2. Key Points:
· Admissible Heuristic: A heuristic is admissible if it never overestimates the true cost to the goal.
· Greedy Best-First Search: Optimizes heuristic evaluation but sacrifices optimality.
· A*: Combines actual cost (g(n)) and heuristic (h(n)) for optimal and complete solutions.
· RBFS: A variant of Best-First Search that uses less memory, suitable for large problem spaces.
Additional Knowledge
· Time Complexity:
· A*: Depends on the quality of the heuristic.
· RBFS: Similar to A* but more memory efficient.
· Space Complexity:
· A*: O(bd), where b is the branching factor and d is the depth.
· RBFS: O(d), where d is the maximum depth of the search tree.