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Why can no uninformed strategy avoid exponential time in the worst case?

  • A.The state space is always exponentially large by definition
  • B.Without guidance it cannot tell which branches are worth exploring
  • C.The frontier data structure imposes an exponential overhead
  • D.Goal testing every node necessarily takes exponential time

Answer: B

Lacking any information beyond the problem definition, the algorithm has no basis for preferring one branch over another and in the worst case must examine them all. A heuristic supplies exactly that basis, which is why informed search can do better. Data structures and goal testing contribute constant factors, and state spaces are not always exponential. Identifying the missing ingredient, rather than the inefficiency, is what points to the remedy. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

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